Papers Abstracts

TurboCodes and Interleaving for TurboCodes
HyperCodes & SkewCodes
Convolutional & LDPC Codes
SISO Decoding
Multiuser Detection & MIMO
Modulation and/or Coding
Synchronization

TurboCodes and Interleaving for TurboCodes

[LOD92] J.Lodge, P. Hoeher, and J. Hagenauer, "The Decoding of Multidimensional Codes Using Separable MAP 'Filters' ", Proceedings of the 16th Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 343-346, May 27-29, 1992.

Very efficient signalling in radio channels requires designing very powerful codes that have special structure so that practical decoding schemes can be used with excellent results. In this paper, powerful codes are obtained by using simple block codes to construct multidimensional product codes. The decoding of multidimensional product codes, using separable symbol-by-symbol maximum a-posteriori (MAP) "filters", is described. Simulation results are presented for four-dimensional single parity bit codes, as well as for three-dimensional product codes constructed with the (16,11) extended Hamming code. Potential applications and extension of the concept to convolutional codes are discussed.
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[LOD93] J. Lodge, R. Young, P. Hoeher, and J. Hagenauer, "Separable MAP 'Filters' for the Decoding of Product and Concatenated Codes", Proceedings of the International Conference on Communications (ICC'93), Geneva, Switzerland, pp. 1740-1745, May 23-26, 1993.

Very efficient signalling in radio channels requires the design of very powerful codes having special structure suitable for practical decoding schemes. In this paper, powerful codes are obtained by using simple block codes to construct multidimensional product codes. The decoding of multidimensional product codes, using separable symbol-by-symbol maximum a-posteriori (MAP) "filters", is described. Simulation results are presented for three-dimensional product codes constructed with the (16,11) extended Hamming code. The extension of the concept to concatenated convolutional codes is given and some simulation results are presented. Potential applications are briefly discussed.
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[GUI94] P. Guinand and J. Lodge, "Trellis Termination for Turbo Encoders", Proceedings of the 17th Biennial Symposium on Communications, Queen's University, Kingston, ON, Canada, pp. 389-392, May 30-June 1, 1994.

In this paper, we consider the problem of the termination of the trellises for Turbo codes. Trellis termination is required to fully implement the decoding procedure associated with such codes. We describe a procedure for doing the termination and give results pertaining to the positive effects of the termination on performance.
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[YOU96] R. Young and J. Lodge, "New Results for Separable Concatenated Convolutional Codes", Proceedings of the 1996 IEEE International Symposium on Information Theory and its Applications (SITA '96), Victoria, British Columbia, Canada, pp. 575-578, September 17-20, 1996.

New results for separable concatenated convolutional codes, using a log-MAP processor, have been generated. These results display improved performance at low Eb/No values and require fewer iterations to achieve asymptotic performance. These iterative decoding techniques were also applied to separable concatenated convolutional codes with tail-biting blocks. For block sizes of 384 and 768 bits, we have been able to achieve frame error rates of 10-3 at Eb/No values of 2.25 and 1.9 dB respectively.
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[CRO98a] S. Crozier, A. Hunt, K. Gracie and J. Lodge, "Performance and Complexity Comparison of Block Turbo-Codes, Hyper-Codes and Tail-biting Convolutional Codes", Proceedings of the 19th Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 84-88, May 31-June 3, 1998.

This paper compares the bit and packet error-rate performance, and complexity, of block turbo-codes, hyper-codes, and flushed and tail-biting convolutional codes. Emphasis is given to block sizes in the range of 64 to 1024 information bits. Each codec has been implemented on an Analog Devices 16-bit fixed-point ADSP-2181 processor. The complexity comparison is primarily based on these real-time implementations.
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[GRA98] K. Gracie, S. Crozier, A. Hunt and J. Lodge, "Performance of a Low-Complexity Turbo Decoder and its Implementation on a Low-Cost, 16-Bit Fixed-Point DSP", Proceedings of the 10th International Conference on Wireless Communications (Wireless '98), Calgary, Alberta, Canada, pp. 229-238, July 6-8, 1998.

This paper presents the bit error rate, packet error rate, and throughput performance of a turbo decoder implemented on the Analog Devices ADSP-2181, a 16-bit fixed-point digital signal processing (DSP) chip. A simplified decoding algorithm is described, and example performance is given for block sizes between 64 and 512 information bits with a number of different code rates. Some implementation issues are also discussed.
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[CRO98b] S. Crozier, P. Guinand, J. Lodge and A. Hunt, "Construction and Performance of New Tail-Biting Turbo Codes", Proceedings of the 6th International Workshop on Digital Signal Processing Techniques for Space Applications (DSP '98), Estec, Noordwijk, The Netherlands, Paper 1.3, September 23-25, 1998.

A problem that was recognized early in the design of turbo-codes is the termination of the trellises. Tail-biting turbo encoders and decoders have been mentioned previously in the literature but none are as general and/or flexible as the approaches presented here. Included is a review of the dual termination method described in [7], which is extended to the dual tail-biting case here, and a review of the frame-oriented turbo-code described in [8], which is extended to full tail-biting here. Other tail-biting approaches are also presented. It is shown that the increase in complexity with tail-biting is typically only about 5%. Simulation results show that the improvement in performance with full tail-biting is typically between 0.1 and 0.2 dB for small blocks (on the order of 100 bits). The improvement at high SNRs is even greater.
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[CRO99a] S. Crozier, "Turbo-Code Design Issues: Trellis Termination Methods, Interleaving Strategies, and Implementation Complexity", Invited presentation for Panel Session on "Application of Turbo Codes" at International Conference on Communications (ICC'99), Vancouver, British Columbia, Canada, June 6-10, 1999.

What are Turbo-Codes?
Turbo-Code Design Issues
Trellis Termination Methods
Interleaving Strategies
Example Performance Results
DSP Implementations and Complexity
Other Turbo-Like Codes:
Turbo Product Codes (TPC's)
Hyper-Codes (HC's)
Conclusions
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[CRO99b] S. Crozier, J. Lodge, P. Guinand and A. Hunt, "Performance of Turbo Codes with Relative Prime and Golden Interleaving Strategies", Proceedings of the 6th International Mobile Satellite Conference (IMSC '99), Ottawa, Ontario, Canada, pp. 268-275, June 16-18, 1999.

This paper describes a number of new interleaving strategies based on the golden section. The new interleavers are called golden relative prime interleavers, golden interleavers, and dithered golden interleavers. The latter two approaches involve sorting a real-valued vector derived from the golden section. Random and so-called "spread" interleavers are also considered. Turbo-code performance results are presented and compared for the various interleaving strategies. Of the interleavers considered, the dithered golden interleaver typically provides the best performance, especially for low code rates and large block sizes. The golden relative prime interleaver is shown to work surprisingly well for high puncture rates. These interleavers have excellent spreading properties in general and are thus useful for many applications other than Turbo-codes.
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[HUN99] A. Hunt, S. Crozier, M. Richards and K. Gracie, "Performance Degradation as a Function of Overlap Depth when using Sub-Block Processing in the Decoding of Turbo Codes", Proceedings of the 6th International Mobile Satellite Conference (IMSC '99), Ottawa, Ontario, Canada, pp. 276-280, June 16-18, 1999.

This paper presents results related to the decoding of Turbo codes. In particular, the results relate to the decoding of Turbo codes using sub-blocks, and show the degradation in error-rate performance as a function of the overlap depth used. These results are relevant to the design of high-speed hardware or software Turbo code decoders. Sub-block processing is desirable in such implementations because the technique can provide significant reductions in the memory requirements of the decoder, as well as allowing increased parallelism. There is a computational overhead, however, associated with using sub-block processing, and so it is desirable to keep the overlap depth as short as possible while still achieving the required error-rate performance specifications. Results are presented for a range of overlap depths showing the bit error rate (BER) and packet error rate (PER) performance over an additive white Gaussian noise (AWGN) channel. Results for code rates r=1/3, r=1/2, and r=4/5 are presented, showing the need for longer overlap depths as the code rate is increased.
Full Paper [PDF 191kb] | Back to Papers

[GRA99] K. Gracie, S. Crozier and A. Hunt, "Performance of a Low-Complexity Turbo Decoder with a Simple Early Stopping Criterion Implemented on a SHARC Processor", Proceedings of the 6th International Mobile Satellite Conference (IMSC '99), Ottawa, Ontario, Canada, pp. 281-286, June 16-18, 1999.

A modified turbo decoder structure using the max-log-a posteriori-probability (APP) algorithm with correction is described, followed by a simple method of halting the decoding process when a packet has converged early. Use of the early stopping feature is shown to substantially increase average throughput as the signal-to-noise ratio (SNR) rises while incurring virtually no loss in either bit error rate (BER) or packet error rate (PER) performance.
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[CRO99c] S. Crozier, K. Gracie and A. Hunt, "Efficient Turbo Decoding Techniques", Proceedings of the 11th International Conference on Wireless Communications (Wireless '99), Calgary, Alberta, Canada, pp.187-195, July 12-14, 1999.

A modified turbo decoder structure using the max-log-a-posteriori-probability (APP) algorithm with correction is described. Several methods of metric combining that can be used with this structure are then discussed. These methods are all equivalent in terms of error rate performance but they have different implementation complexities and processing requirements. Several of the techniques have been implemented on different processors, and measured throughput values are given in each case. Additional optimizations are also discussed, including a simple yet highly effective early stopping technique.
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[CRO00] S. Crozier, "New High-Spread High-Distance Interleavers for Turbo-Codes", Proceedings of the 20th Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 3-7, May 28-31, 2000.

This paper presents two new methods for designing high-spread, high-distance interleavers for Turbo-codes. The first approach is called high-spread random interleaving, and is based on a new and more effective definition of interleaver spread. The second approach is called dithered-diagonal interleaving. Both methods can be used to design interleavers of arbitrary length. The second approach can actually achieve the theoretical maximum spread for many specific block sizes, and at the same time include significant dither for the elimination of low-weight codewords. Both design methods are easy to implement and require very little processing (seconds in Matlab). It is shown that, for a block size of only 512 data bits and an unpunctured code rate of 1/3, the flares in the packet error rate (PER) and bit error rate (BER) curves can be kept below 10-8 and 10-10, respectively.
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[CRO01] S. Crozier and P. Guinand, "High-Performance Low-Memory Interleaver Banks for Turbo-Codes", Proceedings of the 54th IEEE Vehicular Technology Conference (VTC 2001 Fall), Atlantic City, New Jersey, USA, pp. 2394-2398, October 7-11, 2001.

A new method of designing high-performance, low-memory, interleaver banks for Turbo-codes is presented. The new interleavers are called dithered relative prime (DRP) interleavers. Only a small number of parameters are required to both store and implement each interleaver in the bank. The error rate performance is similar to that achieved by other good interleaver designs that typically require the storage of all K indexes for each interleaver of length K.
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[CRO02] S. Crozier and P. Guinand, "Distance Bounds and the Design of High-Distance Interleavers for Turbo-Codes", Proceedings of the 21st Biennial Symposium on Communications, Kingston, Ontario, Canada, pp.10-14, June 2-5, 2002.

This paper presents a number of distance lower bounds for Turbo-codes. These bounds, and their associated interleaver gain powers, help determine which input data patterns to test when designing high-distance interleavers. Distances of 36, 58 and 110 have been achieved for rate 1/3 Turbo-codes with 4, 8 and 16-state constituent codes, respectively.
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[CRO03] S. Crozier and P. Guinand, "Distance Upper Bounds and True Minimum Distance Results for Turbo-Codes Designed with DRP Interleavers", Proceedings of the 3rd International Symposium on Turbo Codes & Related Topics, Ecole Nationale Supérieure des Télécommunications de Bretagne, Brest, France, September 1-5, 2003.

This paper presents a number of distance upper bounds for Turbo-codes designed with dithered relative prime (DRP) interleavers. These bounds help determine how much dither should be applied and which input data patterns to test when designing high-distance interleavers with different lengths. Using a block length of only 640 data bits, true minimum distances of 30, 42 and 53 have been achieved for rate 1/3 Turbo-codes with 4, 8 and 16-state constituent codes, respectively. Simulated error rate results for a block length of 1504 data bits (188 bytes, MPEG packet) show excellent flare performance.
Full Paper [PDF 71.4kb] | Back to Papers

[MOU03] Y. Ould-Cheikh-Mouhamedou, P. Kabal, P. Guinand, "Enhanced Max-Log-APP and Enhanced Log-APP Decoding for DVB-RCS", Proceedings of the 3rd International Symposium on Turbo Codes & Related Topics (Poster), Ecole Nationale Supérieure des Télécommunications de Bretagne, Brest, France, September 1-5, 2003.

We present a new decoding technique for double-binary turbo codes, such as in the Digital Video Broadcasting for Return Channel via Satellite (DVB-RCS) standard. The proposed techniques are referred to as the Enhanced Max-Log A Posteriori Probability (APP) Decoding and Enhanced Log-APP Decoding. Results for ATM packets show a degradation of 0.05 dB in BER/FER for enhanced max-log-APP compared to conventional log-APP. For MPEG packets the enhanced max-log-APP outperforms the log-APP at high SNRs. For both packet lengths, enhanced log-APP outperforms log-APP at high SNRs. Simulation results for an effective early stopping criterion are also presented.
Full Paper [PDF 537kb] | Back to Papers

[CRO04a] S. Crozier, P. Guinand and Andrew Hunt, "Computing the Minimum Distance of Turbo-Codes Using Iterative Decoding Techniques", Proceedings of the 22nd Biennial Symposium on Communications, Kingston, Ontario, Canada, pp.306-308, May 31-June 3, 2004.

High Hamming distance is important for lowering the error rate flares of Turbo-codes at high signal-to-noise ratios (SNRs). A long-standing problem for Turbo-codes has been the efficient and accurate determination of the distance spectrum, or even just the minimum distance, for specific interleavers. This problem is especially difficult for long blocks, where Turbo-codes offer the greatest potential for achieving high coding gain. This paper compares a number of distance estimation techniques and introduces two new approaches based on iterative processing. The new approaches are more reliable and are particularly significant for longer block sizes, which can have higher minimum distances. Distance measurement results are presented for random, high-spread random (HSR), and highly structured dithered relative prime (DRP) interleavers.
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[GRA04] K. Gracie, S. Crozier and P. Guinand, "Performance of an MLSE-based Early Stopping Technique for Turbo Codes", Proceedings of the 60th IEEE Vehicular Technology Conference 2004 - Fall (VTC 2004 - Fall), Los Angeles, California, USA, September 26-29, 2004.

A crucial issue in the practical application of Turbo codes is decoding complexity. A common approach to reducing decoding complexity is to stop the iterative decoding process early. It is demonstrated that an early stopping technique based on maximum-likelihood sequence estimation (MLSE) can significantly reduce average decoder processing. Specifically, it is shown that an 8-state Turbo code with 512 data bits and a nominal code rate of 1/3 can be decoded in less than 2 iterations on average when E_b/N₀ 2 dB (packet error rate 10^-7). This reduction is achieved with virtually no loss in error rate performance relative to performing a large fixed number of iterations.
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[MOU04] Y. Ould-Cheikh-Mouhamedou, S. Crozier and P. Kabal, "Distance Measurement Method for Double Binary Turbo Codes and a New Interleaver Design for DVB-RCS", Proceedings of the 47th annual IEEE Global Telecommunications Conference (Globecom 2004), Dallas, Texas, USA, November 29-December 3, 2004.

This paper presents a computationally efficient distance measurement method for double binary turbo codes, such as these used in the Digital Video Broadcast with Return Channel via Satellite (DVB-RCS) standard, based on Garello’s method. Distance spectra for all standardized DVB-RCS packet sizes and all standardized code rates are presented. A new interleaver design for DVB-RCS based on the dithered relative prime (DRP) interleaving approach is also presented. A minimum distance (d_min) of 36 has been achieved for an unpunctured ATM packet of 424 information bits with a DRP interleaver, whereas the d_min of the standardized DVB-RCS interleaver is 31. A d_min of 38 has been achieved for an unpunctured MPEG packet of size 1504 information bits with a DRP interleaver, whereas the d_min of the standardized DVB-RCS interleaver is 33. Simulation results for code rate 1/3 show an improvement at high signal to noise ratios of at least 0.15 dB and 0.25 dB for ATM and MPEG packets, respectively.
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[CRO05a] S. Crozier and P. Guinand, "Distance Upper Bounds and True Minimum Distance Results for Turbo-Codes Designed with DRP Interleavers", Annals of Telecommunications, Special Issue on Turbo Codes, Vol.60, No.1-2, pp.10-28, January/February, 2005.

[CRO05b] S. Crozier, P. Guinand, and A. Hunt, "On Designing Turbo-Codes with Data Puncturing", Proceedings of the 2005 Canadian Workshop on Information Theory (CWIT 2005), Montréal, Quebec, Canada, June 5-8, 2005.

A traditional turbo-code is a systematic block code whose code rate is typically adjusted by puncturing parity bits. It is shown that a small amount of data puncturing can significantly improve the minimum distance and error rate flare performance. However, certain puncture patterns can lead to semi-catastrophic or catastrophic puncturing. It is shown how to avoid such patterns. Structured interleavers, such as dithered relative prime (DRP) interleavers, that can have their structure matched to the data and parity puncture patterns, provide excellent performance.
Full Paper [PDF 144kb] | Back to Papers

[GRA05a] K. Gracie, A. Hunt, S. Crozier, and P. Guinand, "MLSE-Based Early Stopping for Turbo Codes - Finite Quantization Effects", Proceedings of the 2005 Canadian Workshop on Information Theory (CWIT 2005), Montréal, Quebec, Canada, June 5-8, 2005.

A central concern in the use of Turbo codes is computational complexity. Early stopping techniques that can effectively halt the decoding process before it performs a fixed maximum number of decoding iterations are therefore of substantial value. This paper investigates the effects of quantizing the decoder inputs as it relates to a stopping method based on maximum likelihood sequence estimation (MLSE). It is shown that coarse quantization of the decoder inputs can lead to degraded error rate performance if this stopping method is not applied correctly, particularly in the so-called "flare" region. It is also shown that adding a very simple "path ambiguity check" to the decoder can effectively address this problem.
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[MOUO5]Y. Ould-Cheikh-Mouhamedou, S. Crozier and P. Kabal, "Comparison of Distance Measurement Methods for Turbo Codes", Proceedings of the 2005 Canadian Workshop on Information Theory (CWIT 2005), Montréal, Quebec, Canada, June 5-8, 2005.

Reliable distance measurement methods for turbo codes are a key element in the design of interleavers with high minimum distances, which are essential for lowering the flare effect at low error rates. The usefulness of such methods depends strongly on their computational complexity, especially for long interleavers with high minimum distances. This paper improves the reliability of the double-impulse iterative decoding method and compares it with Garello’s true minimum distance method, the error-impulse method and the all-zero iterative decoding method. The comparison is based on the interleavers specified in the Digital Video Broadcasting with Return Channel via Satellite (DVB-RCS) standard, random interleavers and dithered relative prime (DRP) interleavers. A new interleaver for an MPEG packet of size 1504 information bits is designed for the DVB-RCS standard. The new interleaver provides an improvement of at least 0.4 dB at low error rates.
Full Paper [PDF 66.7kb] | Back to Papers

[CRO05c] S. Crozier, P. Guinand and A. Hunt, "Estimating the Minimum Distance of Turbo-Codes Using Double and Triple Impulse Methods", IEEE Communications Letters, Vol. 9, No.7, pp.631-633, July 2005.

A long-standing problem for Turbo-codes has been the efficient and accurate determination of the distance spectrum, or even just the minimum distance, for specific interleavers. This letter compares a number of distance estimation techniques and introduces two new approaches based on iterative processing. The new approaches are more reliable and are particularly useful for long blocks with high minimum distances. Distance measurement results are presented for random, high-spread random (HSR), and dithered relative prime (DRP) interleavers.
Full Paper [PDF 144kb] | Back to Papers

[CRO06a] S. Crozier, P. Guinand and A. Hunt, "Estimating the Minimum Distance of Large-Block Turbo Codes Using Iterative Multiple Impulse Methods", 4th International Symposium on Turbo Codes & Related Topics, Munich, Germany, April 3-7, 2006.

A difficult problem for turbo codes is the efficient and accurate determination of the distance spectrum, or even just the minimum distance, for specific interleavers. This is especially true for large blocks, with many thousands of data bits, if the distance is high. This paper compares a number of recent distance estimation techniques and introduces a new approach, based on using specific event impulse patterns and iterative processing, that is specifically tailored to handle long interleavers with high spread. The new method is as reliable as two previous iterative multiple-impulse methods, but with much lower complexity. A minimum distance of 60 has been estimated for a rate 1/3, 8-state, turbo code with a dithered relative prime (DRP) interleaver of length K=65,536.
Full Paper [PDF 251kb] | Back to Papers

[HUN06a] A. Hunt, S. Crozier, K. Gracie and J. Lodge, "A completely safe early-stopping criterion for max-log Turbo code decoding", 4th International Symposium on Turbo Codes & Related Topics, Munich, Germany, April 3-7, 2006.

Techniques for early stopping of the iterative decoding of Turbo codes are of interest for a variety of reasons, such as increasing average decoder throughput or reducing average decoder power consumption. Various forms of early stopping have been proposed to date. Something that seems lacking, however, is an early-stopping technique for Turbo codes that can mathematically be proven to have no effect on the decoder error-rate performance, whatsoever. This paper presents such an early-stopping criterion, and for the case of Turbo code decoding using max-log-APP type SISO processing, provides a proof showing that the new criterion is completely safe: early stopping according to the new criterion will not have any effect on the output decisions of the Turbo code decoder. The new early-stopping criterion can be used to significantly reduce processing compared to decoding to the maximum number of allowed iterations, and adds little implementation complexity.
Full Paper [PDF 76kb] | Back to Papers

[GRA06a] K. Gracie, A. Hunt and S. Crozier, "Performance of Turbo Codes using MLSE-Based Early Stopping and Path Ambiguity Checking for Inputs Quantized to 4 Bits", 4th International Symposium on Turbo Codes & Related Topics, Munich, Germany, April 3-7, 2006.

The large performance gains of Turbo codes are achieved with computationally intensive iterative decoding. Early stopping rules reduce this computational burden but require some overhead and can even introduce degradations in error rate performance, particularly in the so-called "flare" region. This paper investigates the performance of a fixed-point Turbo decoder using an early stopping rule based on maximum likelihood sequence estimation (MLSE) when the decoder inputs are quantized to only 4 bits. The MLSE-based early stopping rule is shown to deliver performance that is virtually equivalent to that for a fixed maximum number of iterations provided that the decoder produces valid MLSE bit sequences. Quantization effects are also investigated.
Full Paper [PDF 119kb] | Back to Papers

[MOU06a] K. Gracie, A. Hunt and S. Crozier, "Performance of Turbo Codes using MLSE-Based Early Stopping and Path Ambiguity Checking for Inputs Quantized to 4 Bits", 4th International Symposium on Turbo Codes & Related Topics, Munich, Germany, April 3-7, 2006.

Turbo codes exhibit an “error floor” or “flare” making it difficult to further improve the error performance without a significant increase in the signal-to-noise ratio (SNR). The error flare is mainly characterized by the distance properties of the code. The conventional way to lower the error flare is to increase the minimum distance, which is mainly determined by the interleaver. Unfortunately, the design of interleavers that yield high minimum distances is not a simple task. In fact, the design of such interleavers for applications requiring very low frame error rates (FERs) can be a real challenge. This paper introduces a new method that significantly lowers the error flare while leaving the interleaver unchanged. It also improves the error performance in the waterfall region. The key element of this method is the insertion of correction impulses in the received codeword and the use of repeated decoding. The effectiveness of this method is demonstrated by its ability to reduce the error rate by one order of magnitude in the waterfall region and more than three orders of magnitude in the flare region for 8-state single- and double-binary turbo codes of code rate 1/3 and 1/2 that use high-spread random (HSR) interleavers and packets of 1504 bits.

Full Paper [PDF 119kb] | Back to Papers

[GRA06b] K. Gracie and S. Crozier, "Improving the Performance of 4-State Turbo Codes with the Correction Impulse Method and Data Puncturing", Proceedings of the 23rd Biennial Symposium on Communications, Queen's University, Kingston, Canada, May 29-June1, 2006.

Turbo codes offer excellent error-rate performance and have been included in a wide variety of systems and standards. However, these gains are limited as the signal-to-noise ratio (SNR) increases by “flares” in their error-rate curves. These flares may disqualify Turbo codes from applications that require very low error rates. Recently, an effective method for reducing these error flares that is applicable to any Turbo or Turbo-like code has been proposed. This paper shows that this technique is of tremendous value even when applied to relatively weak 4-state, single-binary Turbo codes, particularly when used in conjunction with data puncturing and well-designed interleavers.

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[KER06b] R. Kerr, K. Gracie, and S. Crozier, "Performance of a 4-State Turbo Code with Data Puncturing and a BCH Outer Code", Proceedings of the 23rd Biennial Symposium on Communications, Queen's University, Kingston, Canada, May 29-June 1, 2006.

The performance of a concatenated Turbo code with an outer BCH code is examined. The Turbo code was based on simple 4-state constituent codes with a constrained high spread random (HSR) interleaver. Data puncturing, as opposed to puncturing only the parity bits, was used with the Turbo code to improve the convergence performance in the waterfall region. It is shown that this simple approach achieves performance better than the rate 1/2 DVB-S2 concatenated LDPC-BCH code.

Full Paper [PDF 119kb] | Back to Papers

[MOU06b] Y. Ould-Cheikh-Mouhamedou, S. Crozier, and P. Kabal, "Efficient Distance Measurement Method for Turbo Codes that use Structured Interleavers", IEEE Communications Letters, Vol. 10, No. 6, pp.477-479, June 2006.

This letter presents an efficient and accurate distance measurement method for tail-biting turbo codes that use structured interleavers. This method takes advantage of the structure in the interleaver as well as the circular property of tail-biting. As such, it significantly reduces the computational complexity, which allows the accurate determination of high minimum distance (dmin) in reasonable time. The efficiency of this method is demonstrated by its ability to determine the true dmin of 51 and the corresponding true multiplicities for a rate-1/3 turbo code that uses the UMTS 8-state polynomial generators and an MPEG-sized interleaver (1504 information bits) in reasonable time.

Full Paper [PDF 119kb] | Back to Papers

[GRA07] K. Gracie and M.-H. Hamon, "Turbo and Turbo-Like Codes: Principles and Applications in Telecommunications", Proceedings of the IEEE, Vol. 95, No. 6, pp.1228-1254, June 2007.

For decades, the de facto standard for forward error correction was a convolutional code decoded with the Viterbi algorithm, often concatenated with another code (e.g., a Reed–Solomon code). But since the introduction of turbo codes in 1993, much more powerful codes referred to collectively as turbo and turbo-like codes have eclipsed classical methods. These powerful error-correcting techniques achieve
excellent error-rate performance that can closely approach Shannon’s channel capacity limit. The lure of these large coding gains has resulted in their incorporation into a widening array of telecommunications
standards and systems. This paper will briefly characterize turbo and turbo-like codes, examine their implications for physical layer system design, and discuss standards and systems where they are being used. The emphasis will be on telecommunications applications, particularly wireless, though others are mentioned. Some thoughts on the use of turbo and turbo-like codes in the future will also be given.

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[MOU07] Y. Ould-Cheikh-Mouhamedou and S. Crozier, "Improving the Error Rate Performance of Turbo Codes using the Forced Symbol Method", IEEE Communications Letters, Vol. 11, No. 7, pp.616-618, July 2007.

This letter presents a method that significantly improves the error rate performance of turbo codes, especially in the error flare region, without changing the basic encoder structure. This method applies repeated decoding, with one or more symbols being forced to certain values, when an error is detected. This forces the decoder to output alternate sets of decisions that can then be checked for errors. The effectiveness of this method is demonstrated by its ability to lower the error flare by several orders of magnitude as soon as the error flare region is encountered. For the DVB-RCS 8-state, rate 1/2, double-binary turbo code and packets of 1504 information bits (MPEG-size), this method yields performance about 0.4 dB from the sphere-packing bound down to a packet error rate of 1e−7.

Full Paper [PDF 85.5kb] | Back to Papers

[CRO08] S. Crozier and K. Gracie, "Improving the Flare Performance of Turbo Codes using Error Detection and Event Flipping", 5th International Symposium on Turbo Codes & Related Topics, Lausanne, Switzerland, September 1-5, 2008.

The error rate performance of turbo codes tends to flare at high SNRs due to poor distance properties. It is shown that the flare performance can be significantly improved by using an outer error detection code and a low-complexity event flipping cleanup approach. Using a rate 1/2, single-binary, 4-state turbo code with a 2048-bit data block, the packet error rate at 1.8 dB is lowered from 1e-4 to about 1e-7, with only a small increase in peak decoder complexity. The approach also requires significantly fewer overhead bits than algebraic cleanup codes with hard decoding.

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[GRA08] K. Gracie and S. Crozier, "Convergence Performance and EXIT Analysis of 4-State Partially-Systematic Turbo Codes", 5th International Symposium on Turbo Codes & Related Topics, Lausanne, Switzerland, September 1-5, 2008.

The error-rate performance of punctured Turbo codes may be significantly improved by puncturing data symbols as well as parity symbols, yielding partially-systematic Turbo codes (PSTCs). In this paper, it is shown that relatively simple 4-state PSTCs are able to achieve convergence (i.e., waterfall) performance that is 0.26 dB from the binary channel capacity limit at rate 1/2 and 0.18 dB from the limit at rate 8/9. It is also demonstrated that extrinsic information transfer (EXIT) charts do not accurately predict convergence performance for 4-state PSTCs.

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[CRO10] S. Crozier, K. Gracie, and R. Kerr, "Estimating the Minimum Distance of Large-Block Turbo Codes using the Event Impulse Method", 6th International Symposium on Turbo Codes & Related Topics, Brest, France, September 6-10, 2010.

This paper describes the application of an iterative technique referred to as the event impulse method (EVIM) to estimating the minimum distances of large-block turbo codes with 4-, 8- and 16-state binary constituent codes. The EVIM is specifically tailored to handle long interleavers with high spread. It is shown that the reliability of the EVIM is similar to that of a previous iterative triple impulse method (TIM), but the complexity is much lower. Minimum distances of 38, 60 and 92 have been obtained (estimated) for rate 1/3 turbo codes with 4-, 8- and 16-state constituent codes, respectively, using dithered relative prime (DRP) interleavers of length K=16384.

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[CRO11a] S. Crozier, K. Gracie, P. Guinand, A. Hunt, R. Kerr, and J. Lodge, "Universal Turbo Code Design for Wireless Communications," CRC White Paper, February 2011.

Using a common structure, turbo code design techniques are described that result in turbo codes that are as good as or better than any other known turbo codes for a wide range of block sizes, code rates, and performance operating points. This suggests that there is no need to design a distinct set of turbo codes for each new wireless application or system, but rather the same turbo codecs can be reused with the parameters selected appropriately. The key to this universally-good turbo code approach is a class of interleavers referred to as dithered relative prime (DRP) interleavers. They are simple to implement and memory-efficient, especially when the storage of large banks of long interleavers is required. The repetitive structure of these interleavers facilitates finding interleaver parameters that guarantee excellent performance at both high and low error rates. Data and parity puncture patterns can be matched to the interleaver, thereby maintaining excellent performance even for very high code rates. Also, DRP interleavers are well-suited to contention-free parallel-window processing that is typically required for implementing high-speed low-latency turbo code decoders.

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HyperCodes & SkewCodes

[HUN98a] A. Hunt, "Hyper-codes: High-performance low-complexity error-correcting codes", Master's Thesis, Carleton University, Ottawa, Ontario, Canada, May 1998.

The existence of a very low complexity soft-in / soft-out decoder for simple parity equations makes code structures composed of such equations attractive because they can be efficiently decoded using an iterative approach. A basic way of creating code structures from simple parity equations is to arrange the equations in N-dimensional "box" configurations. Codes created in this manner offer good, but not exceptional, error-rate performance, for a given block size and code rate. This thesis presents methods of augmenting such basic structures to produce codes with significantly enhanced distance properties. Also, novel enhancements to the decoding process have been developed that both improve performance and reduce implementation complexity. This new family of coding schemes has been given the name "hyper-codes". These codes can provide very good error-correcting performance for a wide range of communications applications, and are especially attractive for applications requiring short block lengths or high code rates.
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[HUN98b] A. Hunt, S. Crozier and D. Falconer, "Hyper-codes: High-performance low-complexity error-correcting codes", Proceedings of the 19th Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 263-267, May 31-June3, 1998.

The existence of a very low complexity soft-in, soft-out decoder for simple parity equations makes code structures composed of such equations attractive because they can be efficiently decoded using an iterative approach. A basic way of creating code structures from simple parity equations is to arrange the equations in N-dimensional "box" configurations. Codes created in this manner offer good, but not exceptional, error-rate performance, for a given block size and code rate. This paper presents methods of augmenting such basic structures to produce codes with significantly enhanced distance properties. Also, novel enhancements to the decoding process have been developed that both improve performance and reduce implementation complexity. The new family of codes that has been created using these developments has been given the name "hyper-codes". These codes can provide good error-correcting performance for a wide range of communications applications, but are especially attractive for applications requiring high code rates. As an example, in AWGN and using QPSK modulation, a 4096 information bit hyper-code with rate 0.79 can achieve a BER of 10_5 at an Eb=N0 of 3 dB, which is only 1 dB above the capacity limit for QPSK modulation.
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[KER99a] R. Kerr and M. Moher, "Hyper-codes for TCP/IP over Mobile Satellites", Proceedings of the 6th International Mobile Satellite Conference (IMSC '99), Ottawa, Ontario, Canada, pp. 292-296, June 16-18, 1999.

In this paper, we compare and contrast the design considerations when using Turbo-like codes versus raditional coding techniques for transmitting Internet traffic using TCP/IP over a mobile satellite link. This paper presents the throughput efficiency for various file sizes over a geostationary link using a commonly available TCP/IP protocol stack. We briefly discuss some proposed changes to TCP/IP and their effect on throughput for our application.
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[LOD00a] J. Lodge, A. Hunt, and P. Guinand, "High Code Rate Iteratively-Decodable FEC Codes with Low Complexity and High Minimum Distance", Proceedings of the 20th Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 8-12, May 28-31, 2000.

The existence of a very low complexity soft-in, soft-out decoder for single-bit-parity equations makes code structures composed of such equations attractive because they can be efficiently decoded using an iterative approach. A basic way of creating a code from single-bit-parity equations is to arrange the bits in a square array and then form a product code by applying one set of parity equations along the rows and a second along the columns. These simple codes have a minimum distance of only 4, and all error patterns are linear combinations of simple rectangular (i.e., weight 4) error patterns. If one were to stack these parity squares to form a 3-dimensional cubic array, a third set of parity equations could be applied straight through the third dimension to form 3-dimensional product code. However, such a code has a minimum distance of only 8. Here we propose an alternate technique for adding additional sets of single-bit-parity equations across the third dimension, that achieves superior distance properties by explicitly avoiding the situation where a rectangular pattern in one square array can match up with a rectangular pattern in another. Example codes are described and their performance, as determined using computer simulation, is given.
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[LOD00b] J. Lodge, A. Hunt, and P. Guinand, "High Code Rate Iteratively-Decodable FEC Codes for Applications Requiring Low Packet Error Rates", Proceedings of the 2nd International Symposium on Turbo Codes & Related Topics, Ecole Nationale Supérieure des Télécommunications de Bretagne, Brest, France, pp. 117-120, September 4-7, 2000.

A product code can be created from single-bit-parity equations by arranging the bits (both information and parity) in a square array and then applying one set of parity equations along the rows and a second set along the columns. These simple codes have a minimum distance of only 4, and all error patterns are linear combinations of simple rectangular (i.e., distance 4) error patterns. If one were to stack these parity squares to form a 3-dimensional cubic array, a third set of parity equations could be applied straight through the third dimension to form a 3-dimensional product code. However, such a code has a minimum distance of only 8. Here we propose an alternate technique for adding additional sets of single-bit-parity equations across the third dimension, that achieves superior distance properties by avoiding the situation where a rectangular pattern in one square can match up with a rectangular pattern in another.
Full Paper [PDF 48kb] | Back to Papers

[SAU00] P-P. Sauvé, A. Hunt, S. Crozier, and P. Guinand "Hyper-Codes: High-Performance, Low-Complexity Codes", Proceedings of the 2nd International Symposium on Turbo Codes &Related Topics, pp. 121-124, Ecole Nationale Supérieure des Télécommunications de Bretagne, Brest, France, September 4-7, 2000.

This paper describes the construction and performance of Hyper-codes, which are high-performance, iteratively decoded FEC codes for which encoding and decoding is of low complexity [7], [6], [8]. In its most basic embodiment, a Hyper-code is formed from a very structured set of single parity check (SPC) equations which are decoded via max-log-APP decoding. These codes are of interest primarily when high code rates and low complexity are issues. Error rate performance is comparable to, and are performance is typically better than, that of classical RSC Turbo-codes at code rates above 2/3.
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[GRA01] K. Gracie, P-P. Sauvé and P. Guinand, "Selective Processing in the Iterative Decoding of Hyper-Codes", Proceedings of the 13th International Conference on Wireless Communications (Wireless 2001), Calgary, Alberta, Canada, pp.489-496, July 9-11, 2001.

This paper introduces a method of selective processing for use in the iterative decoding of systems of single parity check equations (SPCs). The method is examined in the context of Hyper-codes and enhanced max-log-APP decoding. A criterion for detecting convergence on a per-equation basis, useful where processing is limited, is described and investigated. Performance results for a decoder employing this technique are presented for BPSK and rectangular 16-QAM modulation in both additive white Gaussian noise (AWGN) and Rayleigh fading channels. It is shown that for 16-QAM, an (810,512) Hyper-code and processing equivalent to 4 full decoding iterations in AWGN, this selective processing method delivers a performance improvement of between 0.1 and 0.2 dB at a packet error rate (PER) of 10-3.
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Convolutional & LDPC Codes

[GUI96] P. Guinand and J. Lodge, "Design of Generalized Product Codes Suitable for Iterative Decoding", Proceedings of the 1996 IEEE International Symposium on Information Theory and its Applications (SITA '96), Victoria, British Columbia, Canada, pp. 579-582, September 17-20, 1996.

In this paper we consider generalizations of product codes in which the constituent codes are Hamming codes. First we formulate the problem of error patterns within the data bits in terms of hypergraphs. Then in three dimensions we construct a couple of examples of permutations of interleavers that eliminate some of these error patterns. Combining these codes with an inner single parity check product code we obtain codes with enhanced distance spectra. Some simulation results are presented.
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[GUI97a] P. Guinand and J. Lodge, "Tanner Type Codes Arising from Large Girth Graphs", Proceedings of the 1997 Canadian Workshop on Information Theory (CWIT '97), Toronto, Ontario, Canada, pp. 5-7, June 3-6, 1997.

In this paper we use the bipartite graphs of high girth recently developed by Ustimenko, Lazebnik et. al. as the basis for Tanner type error correcting codes.
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[GUI97b] P. Guinand and J. Lodge, "Graph Theoretic Construction of Generalized Product Codes", Proceedings of the 1997 IEEE International Symposium on Information Theory (ISIT '97), Ulm, Germany, p. 111, June 29-July 4, 1997.

In this note we describe a construction, based on bipartite graphs of high girth, of codes which lend themselves to an iterative MAP decoding strategy.
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[GUI99a] P. Guinand, D. Boudreau, and R. Kerr, "Construction of UEP Codes Suitable for Iterative Decoding", Proceedings of the 1999 Canadian Workshop on Information Theory (CWIT '99), Kingston, Ontario, Canada, pp. 17-20, June 15-18, 1999.

Tanner [1] showed how a graph can be associated with a set of parity equations or component codes. More recently Cheng and McEliece [2] have considered the use of biregular graphs to specify single parity check formulas. In this paper we consider two constructions of similar codes which provide unequal error protection (UEP). In the first construction the codes arise from graphs that are not biregular. This results in systematic UEP codes in which the tradeoffs in levels of protection can be fairly easily adjusted. An example of such a code designed for a G.729 vocoder is presented. The second construction uses two different rate codes and relies on the ability of the decoder to determine which of the codes has been employed.
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[SAU99] P-P. Sauvé, S. Crozier and A. Hunt, "High-Speed DSP Implementations of Viterbi Decoders", Proceedings of the 6th International Mobile Satellite Conference (IMSC '99), Ottawa, Ontario, Canada, pp. 297-302, June 16-18, 1999.

This paper describes a number of techniques useful in implementing very efficient Viterbi decoders on general-purpose digital signal processors (DSPs). Also described is the application of these techniques to the design of a fast decoder for the ADSP-2106x (SHARC) DSP with an efficiency approaching 2 processor cycles per state for constraint lengths above K=7. Options include rates 1/2 and 1/3, as well as both flushed and tail-biting blocks.
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[GUI01] P. Guinand and J. Lodge, "Combinatorial Constructions of LDPC Codes", Proceedings of the 2001 Canadian Workshop on Information Theory (CWIT '01), Vancouver, British Columbia, Canada, pp. 16-19, June 3-6, 2001.

In this paper we study low density parity check (LDPC) codes where the structure of the equations arises from high girth graphs. We also discuss two modifications, recoding and optimization of scale factors, to the standard decoding methods for LDPC codes.
Full Paper [PDF 126kb] | Back to Papers

[GUI02] P. Guinand and J. Lodge, "Iterative Decoding of Truncated Simplex Codes", in Proceedings of the 21st Biennial Symposium on Communications, Queen's University, Kingston, Canada, pp. 82-85, June 2-5, 2002.

In this paper we describe an iterative decoding approach for simplex codes. This decoding approach is based on using low weight codewords of the Hamming code, which is dual to the simplex code, as parity checks. This construction permits the use of large numbers of low weight, redundant parity checks, a property that is desirable for iterative decoding. Typically the simplex codes will be truncated (but still low rate).
Full Paper [PDF 4346kb] | Back to Papers

SISO Decoding

[LOD04] J. Lodge and R. Kerr, "Vector Soft-in-soft-out Decoding of Linear Block Codes", Proceedings of the 22nd Biennial Symposium on Communications, Kingston, Ontario, Canada, pp.373-375, May 31-June 3, 2004.

This paper presents a vector soft-in-soft-out (SISO) algorithm applicable to decoding linear block codes. A description of the basic algorithm is given and simulation results are provided that show its effectiveness when used as a SISO decoder for the constituent codes of a Turbo Product Code (TPC). Results for low complexity decoding of low rate block codes, such as quadratic residue codes, are also presented.
Full Paper [PDF 257kb] | Back to Papers

[KER04] R. Kerr and J. Lodge, "Vector Soft-in-soft-out Decoding Applied to Non-binary Linear Block Codes", Proceedings of the 22nd Biennial Symposium on Communications, Kingston, Ontario, Canada, pp.376-378, May 31-June 3, 2004.

The vector soft-in-soft-out (SISO) decoding algorithm provides a low complexity method of decoding linear block codes. In this paper, we examine its use as an iterative decoder for decoding non-binary linear block codes. For codes over GF(2^m) we can convert the non-binary code to a binary code and apply the binary version of the vector SISO. We present performance results for this method compared with both hard decision decoding and soft-decision decoding of a Reed-Solomon code over GF(16). A non-binary version of the vector SISO was developed to provide SISO decoding for codes over GF(p^m) where p is any prime. The latter version is more general and deals with the cases which can not be converted to a binary code. We show the effectiveness of the algorithm with example codes over GF(3), GF(4), and GF(8).
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[KER06a] R. Kerr and J. Lodge, "Near ML Performance for Linear Block Codes Using an Iterative Vector SISO Decoder", 4th International Symposium on Turbo Codes & Related Topics, Munich, Germany, April 3-7, 2006.

In this paper, we present an iterative soft-decision decoding algorithm applicable to binary linear block codes. The algorithm uses a modified Vector SISO algorithm that utilizes soft input information to form candidate codewords. A threshold test is used to determine whether the codeword is likely to be the ML codeword. If the codeword is not accepted, the decoder biases the input vector "away" from the candidate codeword and the decoding repeats this process up to a maximum number of decodings. Occasionally, this process does not find an acceptable codeword. When this happens the algorithm perturbs the input vector by modification of the sign of the input values and repeats the decoding process. The average complexity of the algorithm at reasonable Eb/No is low and the performance is near ML. A detailed description of the algorithm and simulations results are presented for low rate linear block codes. We present results for (80,40,16), (104,52,20) and (168,84,24) quadratic residue codes and (256,191,18) and (128,29,44) extended BCH codes.
Full Paper [PDF 102kb] | Back to Papers

[ASH08] A.-R. Abdul-Shakoor, R. Kerr, J. Lodge, and V. Szwarc, "An FPGA Implementation of a Soft-in Soft-out Decoder for Block Codes," in Proceedings of the 24th Biennial Symposium on Communications, Queen's University, Kingston, Canada, pp. 226-230, June 24-26, 2008.

This paper presents an FPGA implementation of the Vector SISO algorithm for the (64, 57) extended Hamming code (EH) and (64, 51) extended Bose, Chaudhri, and Hocquenghem code (EBCH). The decoder architecture is defined in VHDL and the circuit is implemented on a Xilinx XC2VP100-1704ff-5 FPGA device. To achieve the required throughput, a pipelined data path architecture operating off a master clock was selected. To reduce gate count, the dynamic range of intermediate results was limited through use of saturation arithmetic. The decoder functionality was verified by means of a test bench that compared the decoded bit stream with error free transmitted signals. SISO decoder design choices that impact the bit error rate (BER) are also presented.
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[KER08] R. Kerr, A. Hunt, S. Crozier, and J. Lodge, "Forward Error Correction for an Enhanced SARSAT Distress Message," in Proceedings of the 10^th International Workshop on Signal Processing for Space Communication, Rhodes Island, Greece, Oct 6-8, 2008.

This paper presents a proposed enhancement to the current SARSAT distress message that is backward-compatible with the existing Local User Terminals (LUT) (i.e., ground stations) receivers. Additional coding is appended to the current message to allow for better performance for the new LUTs. Soft-decision decoding is used in the evaluation of the current and enhanced format. Performance results on the AWGN channel are presented. It is shown that near maximum-likelihood performance is achieved for the new code format.
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Multiuser Detection & MIMO

[MOH93] M. Moher, "Decoding via Cross-Entropy Minimization", Proceedings of the 1993 Global Telecommunications Conference (GLOBECOM '93), pp. 809-813, Houston, Texas, USA, November 29-December 2, 1993.

An intuitive algorithm by Lodge et al [1] for iterative decoding of block codes is shown to follow from entropy optimization principles. This approach provides a novel and effective algorithm for the soft decoding of block codes which have a product structure.
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[MOH97] M. Moher, "Turbo-based Multiuser Detection", Proceedings of the 1997 International Symposium on Information Theory (ISIT '97), Ulm, Germany, p. 195, June 29-July 4, 1997.

This paper describes the application of cross-entropy minimization techniques to coded multiuser detection.
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[LOD97] J. Lodge and M. Gertsman, "Joint Detection and Decoding by Turbo Processing for Fading Channel Communications", Proceedings of the 1st International Symposium on Turbo Codes &Related Topics, pp. 88-95, Ecole Nationale Sup!rieure des T!l!communications de Bretagne, Brest, France, September 3-5, 1997.

The concept of joint detection and decoding by turbo processing is described, and then a generic structure for a suitable bit-by-bit maximum a posteriori (MAP) receiver is developed. Examples for particular channels and modulations are discussed, with the most detailed treatment being for the case of CPM and PSK over flat-fading Rayleigh channels. Computer simulation results are presented for QPSK modulation and rate-1/2 constraint length 7 convolutional coding. For a 1:16 pilot symbol rate, close to 5 dB of improvement was obtained by iterating. In fact, for good bit error rates the resulting performance is within a small fraction of a decibel of that of a receiver utilizing ideal channel state information!
Full Paper [PDF 368kb] | Back to Papers

[GUI98] P. Guinand and M. Moher, "Classical Approaches to Multi-User Detection for Highly Correlated Asynchronous Users", Proceedings of the 19th Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 106-109, May 31-June 3, 1998.

In this note we describe a number of techniques designed for multiple user detection and intended for use with asynchronous users employing highly correlated waveforms for modulation. The approaches include decorrelation and iterative interference cancellation.
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[MOH98a] M. Moher and P. Guinand, "An Iterative Multiuser Decoder for Asynchronous BPSK Users", Proceedings of the 19th Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 115-119, May 31-June 3, 1998.

A multiuser decoding algorithm is presented for asynchronous users that use BPSK modulation. The algorithm assumes each user has forward error correction coding with pseudo-random interleaving. The algorithm is derived from iterative techniques for cross-entropy minimization and has similarities with Turbo decoding. Simulations support the theoretical results showing that the detector asymptotically achieves single user performance at high SNR. The complexity per bit of the resulting decoder is approximately m(O(23K)+O(2k)) where m is the number of iterations, K is the number of users, and k is the constraint length of the code.
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[MOH98b] M. Moher, "An Iterative Multiuser Decoder for Near-Capacity Communications", IEEE Transactions on Communications, Vol. 46, No. 7, pp. 870-880, July 1998.

The combination of forward error correction (FEC) coding and random interleaving is shown to overcome the limitations of multiuser detectors/decoders when the user cross correlations are high. In particular, one can asymptotically achieve single-user performance in a highly correlated multiuser system. In addition, an optimal iterative multiuser detector is derived from iterative techniques for cross-entropy minimization. A practical suboptimal implementation of this algorithm is presented, and simulations demonstrate that, even with highly correlated users, it achieves optimal asymptotic efficiency. The effects of the theoretical limits on channel capacity are evident in many of the simulation results. The complexity of the suboptimal algorithm is approximately (O(2K)+O(2k)) per bit per iteration where K is the number of users and k is the code constraint length.
Full Paper [PDF 375kb] | Back to Papers

[MOH98c] M. Moher, "An Iterative Multiuser Decoder for Asynchronous BPSK Users", Proceedings of the International Symposium on Information Theory (ISIT '98), Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, p. 423, August 16-21, 1998.

A multiuser decoding algorithm is presented for asynchronous BPSK users. The algorithm is derived from iterative techniques for cross-entropy minimization and has similarities with Turbo decoding. Simulations show the algorithm asymptotically achieves single user performance. The complexity per bit of the decoder is (O(23K)+O(2k)) per bit per iteration where K is the number of users and k is the constraint length of the code.
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[MOH98d] M. Moher and P. Guinand, "An Iterative Algorithm for Asynchronous Coded Multiuser Detection", IEEE Communications Letters, Vol. 2, No. 8, pp. 229-231, August 1998.

A multiuser detection algorithm, applicable to asynchronous users having the same signaling waveform and power levels, is presented. Users are assumed to employ forward error correction coding but with different pseudo-random interleaving. The algorithm is derived from iterative techniques for cross-entropy minimization, similar to turbo decoding. Simulations show that the detector is limited by theoretical channel capacity at low signal-to-noise ratio (SNR) and asymptotically achieves single user performance at high SNR.
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[MOH98e] M. Moher and T. Gulliver, "Cross-Entropy and Iterative Decoding", IEEE Transactions on Information Theory, Vol. 44, No. 7, pp. 3097-3104, November 1998.

In this correspondence, the relationship between iterative decoding and techniques for minimizing cross-entropy is explained. It is shown that minimum cross-entropy (MCE) decoding is an optimal lossless decoding algorithm but its complexity limits its practical implementation. Use of a maximum a posteriori (MAP) symbol estimation algorithm instead of the true MCE algorithm provides practical algorithms that are identical to those proposed in the literature. In particular, turbo decoding is shown to be equivalent to an optimal algorithm for iteratively minimizing cross-entropy under an implicit independence assumption.
Full Paper [PDF 299kb] | Back to Papers

[KER99b] R. Kerr, P. Guinand, and M. Moher, "An Iterative Multiuser Decoder with Soft Interference Cancellation", Proceedings of the International Conference on Communications (ICC'99), Vancouver, British Columbia, Canada, June 6-10, 1999.

Two multi-user soft-interference cancellation algorithms are presented for synchronous narrow-band BPSK users. The two techniques are designed for multiple user detection where the users use highly correlated waveforms for modulation. The techniques perform close to the optimal cross-entropy multiuser decoder on the K-symmetric channel for cross-correlations up to 0.5. For higher cross-correlations on this channel, we introduce an initial decorrelation step prior to the first iteration, which greatly improves performance for the high values of cross correlation. The complexity per bit per iteration increases linearly for the two interference cancellation algorithms rather than exponentially as the cross-entropy decoder.
Full Paper [PDF 55kb] | Back to Papers

[GUI99b] P. Guinand, R. Kerr, M. Moher, "Serial Interference Cancellation for Highly Correlated Users", Proceedings of the 1999 IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing (PACRIM '99), Victoria, British Columbia, Canada, pp. 133-136, August 23-25, 1999.

In this note we describe some serial interference cancellation techniques designed for multiple user detection where the users are employing highly correlated waveforms for modulation. Simulation results are presented which indicate that performance is in some circumstances close to that produced by a cross entropy multi-user detector.
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[MOH00] M. Moher, "Multiuser Decoding for Multibeam Systems", IEEE Transactions on Vehicular Technology, Vol. 49, No. 4, pp. 1226-1234, July 2000.

An iterative multiuser decoding algorithm for co-channel BPSK/QPSK users in a multibeam system is presented. The approach can be applied to the return link of multibeam satellites and to terrestrial systems with sectored base-station antennas. It allows the reuse of the same spectrum in each beam. The algorithm is based on the extension of turbo-decoding techniques to the iterative decoding of parallel users. Simulation results show one can asymptotically achieve single user performance in a high multiuser interference environment; often this includes some diversity gain. The complexity of the algorithm is approximately O(2K+2k) operations per bit per iteration where K is the number of co-channel users and k is the constraint length of the forward error correction code.
Full Paper [PDF 159kb] | Back to Papers

[SEL02a] M. Sellathurai, P. Guinand, and J. Lodge, "Performance of Polarization Multiplexing Schemes in Satellite Communications", Proceedings of the 21st Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 302-306, June 2-5, 2002.

We consider the design of channel codes for improving the data rate and the link reliability of communications over satellite-land mobile channels using dual polarized transmit and receive antennas. In this system, data is encoded by a channel code and the encoded data is mapped into two streams of data and simultaneously transmitted using dual orthogonal polarizations. At the receiving end, we use a corresponding dual polarized receive antenna to receive the simultaneously transmitted differently polarized signals. In this paper, we present an appropriate polarization multiplexing channel model for satellite-earth communications, and techniques to mitigate the cross-coupling due to cross-polarization discrimination.
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[SEL02b] M. Sellathurai and S. Haykin, "TURBO_BLAST for Wireless Communications: Theory and Experiments", IEEE Transactions on Signal Processing, Vol. 50, No. 10, pp. 2538-2546, October 2002.

TURBO-BLAST is a novel multi-transmit multi-receive (MTMR) antenna scheme for high-throughput wireless communications. It exploits the following ideas: (1) The Bell-Labs Layered Space Time (BLAST) architecture (2) Random layered space-time (RLST) coding scheme by using independent block codes and random space-time interleaving, and (3) Sub-optimal turbo-like receiver that performs iterative decoding of the RLST codes and estimation of the channel matrix in an iterative and, most important, simple fashion. The net result is a new transceiver that is not only computationally efficient compared to the optimal maximum likelihood decoder but it also yields a probability of error performance that is orders of magnitude smaller than traditional BLAST schemes for the same operating conditions. This paper also presents experimental results using real-life indoor channel measurements demonstrating the high-spectral efficiency of TURBO-BLAST.
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[SEL03a] M. Sellathurai, P. Guinand, and J. Lodge, "Approaching Near-Capacity on a Multi-Antenna Channel using Multirate Encoding and Successive Decoding Receivers", to appear in the Proceedings of the 2003 IEEE Information Theory Workshop, La Sorbonne, Paris, France, March 31-April 4, 2003.

[SEL03b] M. Sellathurai, P. Guinand, and J. Lodge, "Multirate Coded MIMO Systems with Successive Decoding and Interference Cancellation Receivers", Proceedings of the 8th Canadian Workshop on Information Theory, pp. 215-218, Waterloo, Ontario, Canada, May 18-21, 2003.

We design multirate coded multiple-input and multiple-output (MIMO) systems by using punctured turbo codes and by restricting the receiver to be a successive decoding and interference cancellation type when each of the antennas is encoded independently. We assume that the receiver fading channel states, which are changing sufficiently rapidly that the channel can be viewed as ergodic. Further, it is assumed that transmitter knows only the statistical characteristics of the channel. Simulation results show performances within two dBs of MIMO channel capacity.
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[SEL03c] M. Sellathurai, P. Guinand, and J. Lodge, "Approaching Near-Capacity on a Multi-Antenna Channel using Successive Decoding and Interference Cancellation Receivers ", Journal on Communication Networks, Vol. 5, No. 2, pp. 116-123, June 2003.

In this paper, we address the problem of designing multirate codes for a multiple-input and multiple-output (MIMO) system by restricting the receiver to be a successive decoding and interference cancellation type, when each of the antennas is encoded independently. Furthermore, it is assumed that the receiver knows the instantaneous fading channel states but the transmitter does not have access to them. It is well known that, in theory, minimum-mean-square error (MMSE) based successive decoding of multiple access (in multi-user communications) and MIMO channels achieves the total channel capacity. However, for this scheme to perform optimally, the optimal rates of each antenna (per-antenna rates) must be known at the transmitter. We show that the optimal per-antenna rates at the transmitter can be estimated using only the statistical characteristics of the MIMO channel in time-varying Rayleigh MIMO channel environments. Based on the results, multirate codes are designed using punctured turbo codes for a horizontal coded MIMO system. Simulation results show performances within about one to two dBs of MIMO channel capacity.
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[SEL03d] S. Haykin and M. Sellathurai, "Turbo-BLAST with Multi-loop Feedback Receiver", Invited Paper, Proceedings of the 3rd International Symposium on Turbo Codes é Related Topics, Ecole Nationale Supérieure des Télécommunications de Bretagne, Brest, France, September 1-5, 2003.

In a series of papers going back to 1999, we described a new MIMO wireless communication system integrating two novel concepts:

The BLAST architecture for improved spectral efficiency
The Turbo learning principle for iterative detection and decoding

For the purpose of this paper, the MIMO wireless system described therein is referred to as the standard Turbo-BLAST system, using a convolutional encoder for channel encoding. In this paper, we will describe an improved version of the system, referred to as the improved Turbo-BLAST system, using a Turbo encoder for channel encoding. (The two terminologies "Standard Turbo-BLAST" and "Improved Turbo-BLAST" are used herein to distinguish the old from the new.) For a number of receive antennas equal to or greater than the number of transmit antennas, experimental results (obtained using real-life as well as simulated data) show that the performance of improved Turbo-BLAST is superior to the performance of standard Turbo-BLAST. Moreover, the experimental results demonstrate the attainment of a performance within one or two dBs of MIMO channel capacity for i.i.d. Gaussian channels and about two to four dBs for real-life channels.
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Modulation and/or Coding

[MOH89] M. Moher and J. Lodge, "TCMP - a Modulation and Coding Strategy for Rician Fading Channels", IEEE Journal on Selected Areas in Communications, Vol. 7, No. 9, pp. 1347-1355, December 1989.

Conventional digital modulation schemes provide poor performance over moderately and severely fading channels without the use of coding. The drawback of applying recently developed trellis coded modulation schemes to such channels is that they require coherent detection to achieve their full potential. This paper describes TCMP, a novel modulation strategy for Rician fading channels, which multiplexes a time domain pilot sequence with trellis coded data to permit coherent detection. This technique to shown to provide remarkably robust performance in the presence of fading. It is also shown that when choosing trellis codes for fading channels, time diversity is of greater importance than asymptotic coding gain. The motivation for studying this strategy is to find efficient signalling schemes for transmitting data at a 4.8 kbit/s rate over a mobile satellite channel, with 5 kHz channel spacing.
Full Paper [PDF 731kb] | Back to Papers

[YOU90] R. Young and J. Lodge, "Linear-Prediction-Aided Differential Detection of CPM Signals Transmitted over Rayleigh Flat Fading Channels", Proceedings of the 40th IEEE Vehicular Technology Conference (VTC '90), Orlando, Florida, USA, pp. 437-442, May 6-9, 1990.

A receiver structure, called Linear-Prediction-Aided Differential Detection (LPADD), for detection of continuous phase modulation (CPM) signals with Nyquist III pulse shaping in fast Rayleigh flat-fading channels is presented. The receiver utilizes linear prediction to estimate the fading induced phase error and subsequently removes the estimated phase error from the received signal prior to differential detection. Simulations showed that, with practical predictor lengths, the error floor of conventional differential detection can be reduced by more than a factor of 30.
Full Paper [PDF 340kb] | Back to Papers

[LOD90] J. Lodge and M. Moher, "Maximum Likelihood Sequence Estimation of CPM Signals Transmitted Over Rayleigh Flat-Fading Channels", IEEE Transactions on Communications, Vol. 38, No. 6, pp. 787-794, June 1990.

A method for the sequential updating of log-likelihood functions for maximum likelihood sequence estimation is presented. It is shown that, in a general case, this method can be implemented using Kalman filtering techniques. Then, for the special case of Rayleigh flat-fading and CPM signaling, this approach is shown to lead to an attractive receiver structure. This type of receiver, called the linear predictive receiver, can be implemented in the form of the Viterbi algorithm with the trellis updates being computed using a bank of FIR and square operations. Simulation results are presented that demonstrate the superiority of the linear predictive receiver over receivers employing differential detection, in the presence of fast fading. Also, it is shown that the optimal linear predictive receiver does not possess an irreducible error rate for a class of Rayleigh fading channels frequently used to model terrestrial mobile channels.
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[CRO94b] S. Crozier and R. Datta, "Direct Modulation of Filtered QPSK and p /4-QPSK using Frequency and Amplitude Modulation Techniques", Proceedings of the 17th Biennial Symposium on Communications, pp. 182-185, Queen's University, Kingston, Ontario, Canada, May 30-June 1, 1994.

Direct modulation to L-band radio frequencies (RF) using frequency and amplitude modulation (FM/AM) techniques is described. Results are presented for 60% roll-off root-raised-cosine (RRC) filtered QPSK and p /4-QPSK.
Full Paper [PDF 881kb] | Back to Papers

[YOU95] R. Young and J. Lodge, "Detection of CPM signals in Fast Rayleigh Flat-Fading Using Adaptive Channel Estimation", IEEE Transactions on Vehicular Technology, Vol. 44, No. 2, pp. 338-347, May 1995.

Differential detection techniques, which are commonly used in fast fading environments, are characterized by an irreducible error rate that increases with fading rate. The main source of this error floor is the phase error introduced by the multiplicative fading process. This paper describes a detection technique for continuous phase modulation (CPM) that employs decision feedback carrier recovery and adaptive channel estimation. This receiver was evaluated by software simulation and the results show a substantial reduction of the error floor relative to that of differential detection. Furthermore, in additive white Gaussian noise (AWGN) channels, the adaptive nature of the receiver allows it to perform close to ideal coherent detection of differentially encoded phase shift keying (DE-PSK).
Full Paper [PDF 798kb] | Back to Papers

[CRO96a] S. Crozier, "Precompensated Frequency Modulation (PFM) designed for pi/4-QPSK Receivers", Proceedings of the 18th Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 343-346, June 2-5, 1996.

Precompensated frequency modulation (PFM) refers to a family of constant envelope modulation schemes which can be detected in standard I-Q type receivers. This paper presents results for PFM4, which is specifically designed for detection in a conventional p/4-shifted-QPSK (p/4-QPSK) receiver. Performance results are presented in terms of power spectrums, adjacent channel interference (ACI), and bit error rates (BER), with and without ACI. It is shown that PFM4 can offer both good BER performance and spectral efficiency with simple, power-efficient, transmit and receive structures.
Full Paper [PDF 44kb] | Back to Papers

[CRO96b] S. Crozier, "Precompensated Frequency Modulation (PFM) Designed for pi/2-BPSK and Offset-QPSK Receivers", Proceedings of the 8th International Conference on Wireless Communications (Wireless'96), Calgary, Alberta, Canada, pp. 155-170, July 8-10, 1996.

Precompensated frequency modulation (PFM) refers to a family of constant envelope modulation schemes which can be detected in standard I-Q type receivers. This paper presents results for PFMO, which is specifically designed for detection in a conventional Offset-QPSK (OQPSK) receiver. Performance results are presented in terms of power spectrums, adjacent channel interference (ACI), and bit error rates (BER), with and without ACI. It is shown that PFMO can offer both good BER performance and spectral efficiency with simple, power-efficient, transmit and receive structures.
Full Paper [PDF 77kb] | Back to Papers

[CRO97a] S. Crozier, P. Guinand, and B. Mazur, "Design and Performance of Precompensated Frequency Modulation (PFM) for use with a Quasi-Synchronous CDMA Return Link", Proceedings of the 5th International Mobile Satellite Conference (IMSC'97), Pasadena, California, USA, pp.467-472, June 16-18, 1997.

This paper presents the design and performance of a constant envelope modulation scheme, known as precompensated frequency modulation (PFM), appropriate for use with a quasi-synchronous code division multiple access (QS-CDMA) return link for future satellite based mobile and personal communications systems. The design is based on the results of a recent study performed for the European Space Agency (ESA), on the performance of candidate options for a third generation mobile satellite system [1]. This study involved detailed simulation and numerical analysis of a number of candidate forward and return link technologies. Only the design and performance of PFM, as it applies to a QS-CDMA return link, is presented in this paper. The QS-CDMA/TDMA frame structure and return link synchronization approach are described in more detail in a companion paper [2].
Full Paper [PDF 156kb] | Back to Papers

[GER97] M. Gertsman and J. Lodge, "Symbol-by-Symbol MAP Demodulation of CPM and PSK Signals on Rayleigh Flat-Fading Channels", IEEE Transactions on Communications, Vol. 45, No. 7, pp. 788-799, July 1997.

Demodulation using the symbol-by-symbol maximum a posteriori probability (MAP) algorithm is presented. The algorithm is derived for the case of continuous phase modulation (CPM) signals transmitted over Rayleigh flat-fading channels, and a corresponding receiver structure is specified. It is shown that the MAP algorithm requires computing, for each trellis branch, the sum of the products of the weights of all paths through the trellis which pass through that branch, and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis. Simulation results are presented which show both the hard and soft decision performance of the MAP receiver to be robust, even in the presence of fade rates of up to 30% of the symbol rate. The application of the receiver concept to phase shift keying (PSK) signals is also discussed, and then evaluated via simulation. The concept of joint demodulation and decoding using iterative processing techniques is introduced. It is shown that the MAP receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions. Simulation results for the reception of quaternary PSK (QPSK) show that the bit error rate (BER) performance of the iterative MAP receiver can approach that of a receiver operating with perfect knowledge of the fading process.
Full Paper [PDF 331kb] | Back to Papers

[KER02] R. Kerr, "Iterative Techniques for Coded GMSK", Proceedings of the 21st Biennial Symposium on Communications, Queen's University, Kingston, Ontario, Canada, pp. 91-94, June 2-5, 2002.

We consider using soft-decision demodulation and decoding techniques for Gaussian minimum shift keying (GMSK) modulation. GMSK is under consideration for several terrestrial and satellite systems. We present reduced complexity GMSK demodulators based on Viterbi and max-log-Maximum a posteriori (MAP) algorithms. We present the coded performance with 8 and 16 state Turbo codes, HyperCodes, and convolutional codes and discuss the potential of iterative demodulation with the max-log-MAP GMSK demodulator and a soft-output decoder for the outer code.
Full Paper [PDF 53kb] | Back to Papers

[KER03]] R. Kerr and S. Crozier, "Performance of Coded GMSK", Proceedings of the 2003 Military Communications Conference (MILCOM 2003), Boston, Massachusetts, USA, October 13-16, 2003.

In this paper, we present bit error performance for coded Gaussian minimum shift keying (GMSK). We consider the case where the communication channel consists of one or more partialprocessing satellite links. The satellite on-board processor can demodulate, repacketize and remodulate the incoming data prior to transmission. We model the system by a cascade of binary symmetric channels followed by an additive white Gaussian noise channel. We investigate the performance of a Turbo-code with two 16-state component codes and convolutional codes for this application through simulation. The interleaver design for Turbo-codes is essential and we consider dithered relative prime interleavers, which have excellent flare performance.
Full Paper [PDF 53kb] | Back to Papers

Synchronization

[CRO92] S. N. Crozier and K. W. Moreland, "Performance of a Simple Delay - Multiply - Average Technique for Frequency Estimation", Proceedings of the Canadian Conference on Electrical and Computer Engineering, Toronto, Ontario, Canada, paper WM10.3, Sept. 13-16, 1992.

A simple open-loop, discrete-time, delay-multiply-average (DMA) technique for estimating the frequency offset for digitally modulated MPSK signals is investigated. An M-power nonlinearity is used to remove the modulation and generate the carrier component to be extracted. Theoretical performance results are presented and compared to the Cramer-Rao lower bound (CRLB) for the variance of the frequency estimation error. It is shown that, when optimum delays are employed, performance can be within 0.5 dB of the CRLB for good SNRs.
Full Paper [PDF 81kb] | Back to Papers

[YOU92] "Implementation of a simple delay-multiply-average technique for frequency estimation on a fixed point DSP", R. Young and S. Crozier, Proceedings of the 3rd IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC ''92), pp. 59 - 63, Boston, USA, October 19-21, 1992.

This paper describes the implementation of an efficient algorithm for frequency estimation. The algorithm uses a bank of simple delay-multiply-average operations with an increasing delay in each branch. The branch outputs are combined to obtain the frequency estimate. This approach is capable of performance that is close to the Cramer-Rao lower bound. The implementation on a fixed point DSP is described for use in a burst acquisition application. A comparison is made to FFT based techniques.
Full Paper [PDF 392kb] | Back to Papers

[CRO93] S. N. Crozier, "Theoretical and Simulated Performance of a Novel Frequency Estimation Technique", Proceedings of the 1993 International Mobile Satellite Conference (IMSC’93), Pasadena, California, pp. 423-428, June 16-18, 1993.

A low complexity, open-loop, discrete-time, delay-multiply-average (DMA) technique for estimating the frequency offset for digitally modulated MPSK signals is investigated. A nonlinearity is used to remove the MPSK modulation and generate the carrier component to be extracted. Theoretical and simulated performance results are presented and compared to the Cramer-Rao lower bound (CRLB) for the variance of the frequency estimation error. For all signal-to-noise ratios (SNRs) above threshold, it is shown that the CRLB can essentially be achieved with linear complexity.
Full Paper [PDF 81kb] | Back to Papers

[CRO93b] "Low complexity frequency estimator with close-to-optimum performance", S. Crozier, Proceedings of the 2nd IEEE International Conference on Universal Personal Communications (ICUPC '93), Volume 1, pp. 426 - 430, Ottawa, Canada, October 12-15, 1993.

A low complexity, open-loop, discrete-time, delay-multiply-average (DMA) technique for estimating the frequency offset for digitally modulated MPSK signals is investigated. A nonlinearity is used to remove the MPSK modulation and generate the carrier component to be extracted. Theoretical and simulated performance results are presented and compared to the Cramer-Rao lower bound (CRLB) for the variance of the frequency estimation error. For all signal-to-noise ratios (SNRs) above threshold, it is shown that performance very close to the CRLB can be achieved with linear complexity.
Full Paper [PDF 504kb] | Back to Papers

[CRO94a] S. Crozier, "Performance and Complexity Comparison of Discrete-Time Frequency Estimation Algorithms", Proceedings of the 17th Biennial Symposium on Communications, pp. 271-275, Queen's University, Kingston, Ontario, Canada, May 30-June 1, 1994.

This paper compares the performance and complexity of two open-loop, discrete-time, frequency estimation approaches. The first approach is based on the simple delay-multiply-accumulate (DMA) technique. The second approach uses the fast Fourier transform (FFT). Simulated performance results are presented and compared to the Cramer-Rao lower bound (CRLB). It is shown that both methods can achieve the CRLB, for all signal-to-noise ratios (SNRs) above threshold. The DMA approach offers the lowest complexity, while the FFT approach can provide slightly lower SNR thresholds.
Full Paper [PDF 1.1Mb] | Back to Papers

[MAN96] R. Mantha and S. Crozier, Implementation of a Delay-Multiply-Average Frequency Estimator with Rotate Add Decimate Processing , Proceedings of the 18th Biennial Symposium on Communications, Queen’s University, Kingston, Ontario, Canada, pp. 147-150, June 2-5, 1996.

This paper describes the implementation of an efficient frequency estimator based on a delay-multiply-average (DMA) technique. Performed on a block of carrier signal, the algorithm measures the phase difference between delayed samples in order to compute a frequency estimate. Multiple branches with different delays are combined in the calculation of the final frequency estimate. Performance is improved through the use of a rotate-add-decimate (RAD) operation on the signal prior to each new branch computation. The RAD extension gives the algorithm linear complexity. For all signal to noise ratios above threshold, this algorithm can achieve performance within 0.5 dB of the Cramer Rao Lower Bound (CRLB) for the variance of the frequency estimator. The resolution and complexity of this frequency estimation approach is compared to FFT based techniques. A real-time implementation of the algorithm on a fixed-point digital signal processor (DSP) is described.
Full Paper [PDF 81kb] | Back to Papers

[CRO97b] S. Crozier and K. Gracie, "Low Complexity Frequency Estimation with Close-to-Optimum Performance for QPSK and Offset-QPSK Modulated Signals", Proceedings of the 9th International Conference on Wireless Communications (Wireless '97), pp. 294-306, Calgary, Alberta, Canada, July 9-11, 1997.

A low complexity frequency estimation algorithm is described and performance results are presented for QPSK and Offset-QPSK (OQPSK) modulated signals. A carrier component is extracted by removing the phase portion of the modulation. This can be done by either using the known data symbols, in the case of a known unique word, or by using estimates of the data symbols, when in decision directed mode. A simple preprocessing step is useful in the case of OQPSK to improve performance. Simulated performance results are presented and compared to the Cramer-Rao lower bound (CRLB) for the variance of the frequency estimation error. For all signal-to-noise ratios (SNRs) above threshold, it is shown that the CRLB can essentially be achieved with QPSK modulation, and a degradation of only 0.5 dB is typical with OQPSK modulation. The frequency estimator achieves this performance with linear complexity in both cases.
Full Paper [PDF 84kb] | Back to Papers

[GRA03] K. Gracie and J. Lodge, "Carrier Estimation for SSB Modulated Speech", Proceedings of the 15th International Conference on Wireless Communications (Wireless 2003), pp.278-286, Calgary, Alberta, Canada, July 7-9, 2003.

A novel technique for automatically estimating the carrier frequency of single sideband (SSB) modulated speech signals is described. A brief review of the relevant properties of both SSB modulation and speech is followed by a description of the algorithm and subjective performance results. The method is shown to deliver high voice quality when significant pitch variation is present and fair voice quality even with relatively little pitch variation.
Full Paper [PDF 81kb] | Back to Papers

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