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Electronics Optics & Control

Improved algorithm of minimum-sum decoding algorithm for irregular repeat accumulate codes

XU Zong-ze

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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.

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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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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.
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.
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.
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.
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.
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.