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Irregular repeat accumulate codes

Hao Jin

Published Jan 1, 2000• 580 citations
OpenAlex

Abstract

In this paper we will introduce an ensemble of codes called irregular repeat-accumulate (IRA) codes. IRA codes are a generalization of the repeat-accumulate codes introduced in [1], and as such have a natural linear time encoding algorithm. We shall prove that on the binary erasure channel, IRA codes can be decoded reliably in linear time, using iterater] sum-product decoding,a# ra#SJ a#SJ8T a#SJ8 close tocha#T36 ca pa#J464 Asimila# resulta#u ea#S to be true on the AWGN channel, although we have no proof of this. We illustrate our results with numerical and experimenta# examples.

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This paper is concerned with the construction of a class of nonbinary irregular repeat accumulate (IRA) codes. Since they are defined on the finite field GF(q) (q>2), we will refer to the constructed codes as q-ary IRA (QIRA) codes. While preserving the excellent error correcting capability of q-ary LDPC codes, QIRA codes can be efficiently encoded like conventional binary IRA codes. By adopting the progressive edge growth (PEG) algorithm to construct the parity check matrices, we can achieve the increased girth of their factor graphs and improved decoding performance. Simulation results show that, using the sum-product algorithm on GF(q), QIRA codes outperform binary LDPC codes and turbo codes in terms of bit error ratio and frame error ratio on AWGN channels. Especially, they could achieve excellent error performance when combined with high order modulations. Feasibility study indicates, with the use of the extended min-sum (EMS) decoding algorithm, QIRA codes are competitive candidates for practical applications.

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Gaussian approximation models the message density in message passing decoders as Gaussian distribution.In this paper,irregular repeat accumulate(IRA) codes over the mixed white Gaussian noise/erasure channels are designed using Gaussian approximation.Recursive equations of density evolution and analytic expressions of bit error rate are derived.The analytic results not only provide a way to predict asymptotic performance of IRA codes but also help us design good IRA codes over the mixed channel.Comparison between simulation results and thresholds computed from analytic results shows that predication from the theoretical results is accurate enough.The optimized IRA codes designed for the mixed channels have better performance than that of IRA codes designed for AWGN channels when the designed erasure probability is close to the actual probability.

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Repeat-accumulate (RA) codes have a natural linear-time encoding algorithm. Under BP decoding algorithm, RA codes can be decoded reliably in linear time at rates arbitrarily closed to channel capacity.However,BP algorithm has high complexities.Minimum sum decoding algorithm is a sub-optimum algorithm and is easy for hardware implementation,but the decoding performance is degraded. Normalized algorithm and offset algorithm are proposed as a good tradeoff between decoding performance and complexities. Simulation results show that with little complexity increased, normalized algorithm and offset algorithm have better performance than that of minimum sum algorithm.

Journal of Sichuan University•Jan 1, 2004•4 citations
In this paper we will introduce an ensemble of codes called irregular repeat-accumulate (IRA) codes. IRA codes are a generalization of the repeat-accumulate codes introduced in [1], and as such have a natural linear time encoding algorithm. We shall prove that on the binary erasure channel, IRA codes can be decoded reliably in linear time, using iterater] sum-product decoding,a# ra#SJ a#SJ8T a#SJ8 close tocha#T36 ca pa#J464 Asimila# resulta#u ea#S to be true on the AWGN channel, although we have no proof of this. We illustrate our results with numerical and experimenta# examples.
This paper is concerned with the construction of a class of nonbinary irregular repeat accumulate (IRA) codes. Since they are defined on the finite field GF(q) (q>2), we will refer to the constructed codes as q-ary IRA (QIRA) codes. While preserving the excellent error correcting capability of q-ary LDPC codes, QIRA codes can be efficiently encoded like conventional binary IRA codes. By adopting the progressive edge growth (PEG) algorithm to construct the parity check matrices, we can achieve the increased girth of their factor graphs and improved decoding performance. Simulation results show that, using the sum-product algorithm on GF(q), QIRA codes outperform binary LDPC codes and turbo codes in terms of bit error ratio and frame error ratio on AWGN channels. Especially, they could achieve excellent error performance when combined with high order modulations. Feasibility study indicates, with the use of the extended min-sum (EMS) decoding algorithm, QIRA codes are competitive candidates for practical applications.
Gaussian approximation models the message density in message passing decoders as Gaussian distribution.In this paper,irregular repeat accumulate(IRA) codes over the mixed white Gaussian noise/erasure channels are designed using Gaussian approximation.Recursive equations of density evolution and analytic expressions of bit error rate are derived.The analytic results not only provide a way to predict asymptotic performance of IRA codes but also help us design good IRA codes over the mixed channel.Comparison between simulation results and thresholds computed from analytic results shows that predication from the theoretical results is accurate enough.The optimized IRA codes designed for the mixed channels have better performance than that of IRA codes designed for AWGN channels when the designed erasure probability is close to the actual probability.
The field of error correcting codes was revolutionized by the introduction of turbo codes [7] in 1993. These codes demonstrated dramatic performance improvements over any previously known codes, with significantly lower complexity. Since then, much progress has been made towards understanding the performance of these codes, as well as in using this understanding to design even better codes. This thesis takes a few more steps in both these directions. We develop a new technique, called the typical set bound, for analyzing the asymptotic performance of code ensembles based on their weight enumerators. This technique yields very tight bounds on the maximum-likelihood decoding threshold of code ensembles, and is powerful enough to reproduce Shannon's noisy coding theorem for the class of binary-input symmetric channels. We also introduce a new class of codes called irregular repeat-accumulate~(IRA) codes, which are adapted from the previously known class of repeat-accumulate~(RA) codes. These codes are competitive in terms of decoding performance with the class of irregular low-density parity-check~(LDPC) codes, which are arguably the best class of codes known today, at least for long block lengths. In addition, IRA codes have a significant advantage over irregular LDPC codes in terms of encoding complexity. We also derive an analytical bound regarding iterative decoding thresholds of code ensembles on general binary-input symmetric channels, an area in which theoretical results are currently lacking
A simplified decoding algorithm for Irregular Repeat Accumulate(IRA) code is studied.BP decoding algorithm is difficult for hardware implementation of IRA code because of its high complexity.To reduce the decoding complexity,minimum-sum algorithm is applied to the IRA decoder.However,the decoding performance is degraded.To have a good tradeoff between decoding performance and complexities,improved algorithms,i.e.normalized algorithm and offset algorithm,are proposed.Simulation results showed that the improved algorithms have better performance than that of minimum-sum algorithm with little complexity increased.
Repeat-accumulate (RA) codes have a natural linear-time encoding algorithm. Under BP decoding algorithm, RA codes can be decoded reliably in linear time at rates arbitrarily closed to channel capacity.However,BP algorithm has high complexities.Minimum sum decoding algorithm is a sub-optimum algorithm and is easy for hardware implementation,but the decoding performance is degraded. Normalized algorithm and offset algorithm are proposed as a good tradeoff between decoding performance and complexities. Simulation results show that with little complexity increased, normalized algorithm and offset algorithm have better performance than that of minimum sum algorithm.