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International Conference on ITS Telecommunications

Iterative Decoding for the Concatenation of LDPC Codes and BCH Codes Based on Chase Algorithm

Zhiping Shi, Liang Zhou, Hong Wen, Shaoqian Li

Published Jun 1, 2006• 2 citations
Publisher

Abstract

In this paper, an iterative joint decoding algorithm for low density parity check codes with BCH codes based on Chase algorithm is proposed. After a certain number of iterations, the soft output values delivered by belief propagation algorithm of LDPC codes are used as reliability values to perform Chase decoding of BCH codes. And BCH decoder also will return soft information to LDPC decoder as input. This approach presents an option scheme for LDPC with medium length because of the relevant presence of short loops. It allows to bridge the gap between error performance and maximum likelihood decoding. Simulation result for the scheme is given.

DOI
10.1109/itst.2006.288749

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In this paper, an iterative joint decoding algorithm for low density parity check codes with BCH codes based on Chase algorithm is proposed. After a certain number of iterations, the soft output values delivered by belief propagation algorithm of LDPC codes are used as reliability values to perform Chase decoding of BCH codes. And BCH decoder also will return soft information to LDPC decoder as input. This approach presents an option scheme for LDPC with medium length because of the relevant presence of short loops. It allows to bridge the gap between error performance and maximum likelihood decoding. Simulation result for the scheme is given.
In this work, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between BP decoding which remains suboptimum, and maximum likelihood decoding (MLD) which is too complex to be implemented for the codes considered. A stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is also proposed for this combined decoding approach. Simulations results for several Gallager LDPC codes and different set cyclic (DSC) codes of hundreds of information bits are given and elaborated.
In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated.
This paper presents a lowered complexity version of a reliability-based iterative decoding algorithm for Generalized Low Density Parity Check (GLDPC) codes with BCH constituent codes using Soft-Input Soft-Output (SISO) Chase-II algorithm. Applied to Gallager-based global LDPC code, it shows that the proposed algorithm, when employed on GLDPC with the multi-error correction BCH subcodes, reduces the complexity of the conventional Soft-Decision Decoding (SDD) with Chase algorithm at a cost of slight degradation in the error performance. The approach is built on eliminating the employment of the Chase SISO decoder at the Generalized Check Nodes (GCNs) where the expected number of errors is within the correction capability of the Hard-Decision Decoder (HDD). As a case study, the decoder is considered under AWGN channel and Simulation results are presented showing the complexity and performance of the conventional and proposed algorithms.
A novel coding scheme is presented for encoding and iterative soft-decision decoding of binary BCH codes of prime lengths. The encoding of such a BCH code is performed on a collection of codewords which are mapped through Galois Fourier transform into a codeword of a nonbinary low-density parity-check (LDPC) code which has a binary parity-check matrix for transmission. Using this matrix, a binary iterative soft-decision decoding algorithm based on belief-propagation is applied to jointly decode a collection of codewords of the BCH code. The joint-decoding allows information sharing among the received vectors corresponding to the codewords in the collection during the iterative decoding process. For decoding a BCH code of prime length, the proposed decoding scheme not only requires low decoding complexity, but also yields superior performance. The proposed decoding scheme can achieve a joint-decoding gain over the maximum likelihood decoding of individual codewords.
This paper presents a new evaluation and performance comparison of a reliability-based iterative decoder for Generalized LDPC codes with BCH subcodes, using Soft-Input Soft-Output (SISO) Chase algorithm, compared with the same algorithm employing Hamming subcodes. While the single-error correction code with length n is accorded a preference over the double error correction one with length 2n (in terms of error performance over AWGN channels), this article shows that the GLDPC code with BCH subcodes surpasses the Hamming-based one under nearly the same overall code rate. It also converges in less than half the number of iterations compared to different corresponding Hamming-based soft-decision decoding (SDD) systems. As a case study, Gallager-based global LDPC code is applied and the decoder is considered over AWGN channel. The simulation results are showing the performance against the code block length, number of iterations and Chase algorithm parameters.
In conventional satellite broadcasting systems,e.g.DVB-S2,the error-correction schemes are often based on the concatenation of BCH and low-density parity-check(LDPC) codes,so as to obtain excellent bit error rate(BER) performance.As the inner codes,LDPC codes are traditionally decoded by iterative algorithms with many iteration cycles.In virtue of the concatenated structure of BCH and LDPC codes,a novel iterative decoding structure involving the embedment of BCH error-check function into each iterative cycle of LDPC is proposed.Computer simulations show that the iteration number of LDPC decoding with the proposed algorithm is obviously smaller than with traditional algorithm,thus greatly lowering the additional complexity of BCH error-check codes.Therefore,the total complexity and latency of the iterative decoding could be sufficiently reduced,while the similar system BER performance is maintained.