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IEEE International Symposium on Information Theory (ISIT)

Design methods for irregular repeat accumulate codes

Aline Roumy, Souad Guemghar, Giuseppe Caire, S. Verdu

Published Jan 1, 2003• 11 citations
Publisher

Abstract

We optimize the low-complexity random-like ensemble of irregular repeat accumulate (IRA) codes for binary-input symmetric channels in the large blocklength limit. IRA codes Jin, H et al. (2000) are special subclasses of both irregular LDPCs and irregular turbo codes. We present numerical results for the BIAWGNC and formulate the density evolution (DE) Richardson, TJ et al. (2001) for IRA codes. We study the stability condition of the fixed-point corresponding to zero BER.

DOI
10.1109/isit.2003.1228016

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China Communications•Aug 1, 2016•3 citations
We optimize the low-complexity random-like ensemble of irregular repeat accumulate (IRA) codes for binary-input symmetric channels in the large blocklength limit. IRA codes Jin, H et al. (2000) are special subclasses of both irregular LDPCs and irregular turbo codes. We present numerical results for the BIAWGNC and formulate the density evolution (DE) Richardson, TJ et al. (2001) for IRA codes. We study the stability condition of the fixed-point corresponding to zero BER.
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
In this paper, we consider the finite-length performance of a capacity-achieving sequence of irregular repeat-accumulate (IRA) code ensembles. We focus on a sequence of bit-regular ensembles with degree 3 which was shown to achieve capacity with bounded complexity [Pfister, 2005]. To characterize how fast the block length of the code must grow with respect to the truncation point of the degree distribution (i.e., maximum check degree), we compute an upper bound on the average weight enumerator. Based on this analysis, we present a particular truncation sequence that could achieve a minimum distance which grows like n/sup 1/3/ even as the gap to capacity goes to zero. We also consider the performance of these codes in the waterfall region by extending the finite-length scaling law [Amraoui] from low-density parity-check codes to IRA codes. This shows that the performance near the iterative decoding threshold is well characterized by a suitably scaled Q-function for large enough block length. Numerical results are given for the scaling parameters of this ensemble sequence and for a few other IRA codes. Unfortunately, the simulation results for the capacity-achieving sequence start to match the scaling law only for very large block lengths.
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 non-binary (NB) Irregular Repeat Accumulate (IRA) codes, as a subclass of NB LDPC codes, potentially have an excellent error-correcting performance. They are also known to provide linear complexity of encoding, but the basic encoding method with the serial rate-1 accumulator significantly limits the encoder throughput. Then the objective of the research presented in this paper is to develop an encoding method providing significantly increased throughput of an NB-IRA encoder altogether with a flexible code construction methods for the structured (S-NB-IRA) codes eligible for the proposed encoding method. For this purpose, we reformulate the classic encoding algorithm to fit into the partial parallel encoder architecture. We propose the S-NB-IRA encoder block diagram and show that its estimated throughput is proportional to the submatrix size of the parity check matrix, which guarantees a wide complexity-throughput tradeoff. Then, in order to facilitate the S-NB-IRA coding systems design, we present a computer search algorithm for the construction of good S-NB-IRA codes. The algorithm aims at optimizing the code graph topology along with selecting an appropriate non-binary elements in the parity check matrix. Numerical results show that the constructed S-NB-IRA codes significantly outperform the binary IRA and S-IRA codes, while their performance is similar to the best unstructured NB-LDPC codes.