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Journal of Sichuan University

Reduced Complexity Decoding Algorithms for Repeat Accumulate Codes

XU Zong-ze

Published Jan 1, 2004• 4 citations
OpenAlex

Abstract

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.

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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.
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.
To mitigate the problems of high computation complexity and deteriorated error correction performance in decoding Repeat-Accumulate(RA) codes with Belief Propagation(BP) and Min-Sum algorithms,the idea of Weighted Bit-Flipping(WBF) is applied to improve the BP algorithm.The improved BP decoding algorithm based on the WBF scheme is proposed for systematic RA codes.If decoding is failure in each iteration,bit flipping measure is to be taken according to specific rules in order to obtain legitimate code words.Simulation results demonstrate that the proposed algorithm can decrease the computation complexity effectively for such RA codes while maintaining the excellent error-correction performance.
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.
BP decoding algorithm is usually used to realize decoding of IRA codes,but the hardware circuit of BP decoding algorithm is complicated. A modified IRA decoding algorithm is proposed in order to have a good tradeoff between complexity and decoding performance. The proposed algorithm is approximate to BP decoding algorithm by the method of offset approximation ,which can simplify the complexity of BP decoding algorithm. The simulation results show that,compared with BP decoding algorithm,the modified IRA decoding algorithm can decrease algorithm complexity and keep good decoding performance. Compared with minimum-sum decoding algorithm,the complexity of modified IRA decoding algorithm is almost unchanged,but the decoding performance improves significantly.
Iterative decoding techniques have been receiving more and more attentions with the invention of turbo codes and the rediscovery of low-density parity-check (LDPC) codes. An important aspect in the study of iterative decoding is the tradeoff between decoding performance and complexities. For both LDPC codes and turbo codes, optimum decoding algorithms can provide very good performance. However, complicated operations are involved in the optimum decoding, and prohibit the wide applications of LDPC codes and turbo codes in the next generation digital communication and storage systems. Although there exist sub-optimum decoding algorithms for both LDPC codes and turbo codes, the decoding performance is degraded with the sub-optimum algorithms, and under some circumstances, the gap is very large. This research investigates the reduced complexity decoding algorithms of LDPC codes and turbo codes. For decoding LDPC codes, new algorithms, namely the normalized BP-based algorithm and the offset BP-based algorithm, are proposed. For these two reduced complexity algorithms, density evolution algorithms are derived, and are used to determine the best decoder parameters associated with each of the algorithms. Numerical results show that the new algorithms can achieve near optimum decoding performances for infinite code lengths, and simulation results reveal the same conclusion for short to medium code lengths. In addition to the advantage of low computational complexities, the two new algorithms are less subject to quantization errors and correlation effects than the optimum BP algorithm, and consequently are more suitable for hardware implementation. For a special kind of LDPC codes - the geometric LDPC codes, we propose the normalized APP-based algorithm, which is even more simplified yet still can achieve the near optimum performance. For decoding turbo codes, two new sub-optimum decoding algorithms are proposed. The first is the bi-directional soft-output Viterbi algorithm (bi-SOVA), which is based on utilizing a backward SOYA decoding in addition to the conventional forward one, and can achieve better performance than the uni-directional SOYA. The second is the normalized Max-Log-MAP algorithm, which improves the performance of the Max-Log-MAP decoding by scaling the soft outputs with some predetermined factors.
LLR BP decoding algorithm and its improved version Minimum-Sum decoding algorithm are usually used to realize the decoding of LDPC codes.But the calculation of LLR BP decoding algorithm is too complicated,and the performance of Minimum-Sum decoding algorithm is not good enough because of the approximation.A modified BP decoding algorithm is proposed by using some parameters in order to have a good tradeoff between complexity and decoding performance.The simulation results demonstrate that the modified algorithm keeps good decoding performance,and supplies a significant reduction of the complexity compared to LLR BP decoding algorithm and minimum-sum decoding algorithm.