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International Conference on Computer Engineering & Systems (ICCES)

Lowered-complexity soft decoding of generalized LDPC codes over AWGN channels

Sherif Elsanadily, Ashraf M. Mahran, Osama M. Elghandour

Published Dec 1, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1109/icces.2017.8275325

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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.
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.
A class of pseudo-random compound error-correcting codes, called generalized low density (GLD) parity-check codes, has been proposed recently. As a generalization of Gallager's low-density parity check (LPDC) codes, GLD codes are also asymptotically good in the sense of minimum distance criterion and can be effectively decoded based on iterative soft-input soft-output (SISO) decoding of individual constituent codes. The code performance and decoding complexity of GLD codes are heavily dependent on the employed SISO decoding algorithm. In this paper, we present an efficient SISO decoding algorithm for GLD codes. The proposed algorithm utilizes Kaneko's decoding algorithm for soft-input hard-output decoding. These hard outputs are converted to soft-decision using reliability calculations. The algorithm proposed here presents a major advantage over existing decoding algorithms for GLD codes by being applicable even when long and powerful component codes are used. The complexity of the proposed algorithm is less than that of trellis-based decoding algorithms with a performance degradation of only 0.3 dB.
A class of pseudo-random compound error-correcting codes, called generalized low-density (GLD) parity-check codes, has been proposed recently. As a generalization of Gallager's low-density parity-check (LDPC) codes, GLD codes are also asymptotically good in the sense of minimum distance criterion and can be effectively decoded based on iterative soft-input soft-output (SISO) decoding of individual constituent codes. The code performance and decoding complexity of GLD codes are heavily dependent on the employed SISO decoding algorithm. In this paper, we show that Max-Log-MAP is an attractive SISO decoding algorithm for GLD coding scheme, considering the trade-off between performance and complexity in the practical implementations. A normalized Max-Log-MAP is presented to improve the GLD code performance significantly compared with using conventional Max-Log-MAP. Moreover, we propose two techniques, decoding task scheduling and reduced search Max-Log-MAP, to effectively reduce the decoding complexity without any performance degradation.
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.
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.