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International Conference on Computer Engineering & Systems (ICCES)

Improving the Decoding Performance of High-Rate GLDPC Codes in Low Error-Rate Applications

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

Published Dec 1, 2018• 2 citations
Publisher

Abstract

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.

DOI
10.1109/icces.2018.8639318

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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.
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.
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.
Scientists have competed to find codes that can be decoded with optimal decoding algorithms. Generalized LDPC codes were found to compare well with such codes. LDPC codes are well treated with both types of decoding; HDD and SDD. On the other hand GLDPC codes iterative decoding, on both AWGN and BSC channels, was not sufficiently investigated in the literature. This chapter first describes its construction then discusses its iterative decoding algorithms on both channels so far. The SISO decoders, of GLDPC component codes, show excellent error performance with moderate and high code rate. However, the complexities of such decoding algorithms are very high. When the HDD BF algorithm presented to LDPC for its simplicity and speed, it was far from the BSC capacity. Therefore involving LDPC codes in optical systems using such algorithms is a wrong choice. GLDPC codes can be introduced as a good alternative of LDPC codes as their performance under BF algorithm can be improved and they would then be a competitive choice for optical communications. This chapter will discuss the iterative HDD algorithms that improve decoding error performance of GLDPC codes. SDD algorithms that maintain the performance but lowering decoding simplicity are also described.
We consider the iterative decoding of generalized low-density (GLD) parity-check codes where, rather than employ an optimal subcode decoder, a Chase (1972) algorithm decoder more commonly associated with "turbo product codes" is used. GLD codes are low-density graph codes in which the constraint nodes are other than single parity-checks. For extended Hamming-based GLD codes, we use bit error rates derived by simulation to demonstrate this new strategy to be successful at higher code rates. For long block lengths, good performance close to capacity is possible with decoding costs reduced further since the Chase decoder employed is an efficient implementation.
A generalised low-density parity-check code (GLDPC) is a low-density parity-check code in which the constraint nodes of the code's graph are replaced with component or subcodes other than single parity checks. Gallager's bit-flipping algorithm for LDPCs is generalised to the class of GLDPCs with Hamming subcodes. The proposed weighted bit-flip voting (WBFV) method is iterative and uses only the hard decision decoder of the Hamming subcodes. Decoding of Hamming-based GLDPCs using WBFV has been simulated on the binary symmetric channel. Simulation results are presented showing the variation in performance with voting rule, graph construction and block length. In terms of the dependence of coding gains and complexity on the GLDPC block length, the proposed method is found to display a good performance to decoding complexity trade-off. Performance is found to compete well with other more conventional hard decision decoding schemes.
A generalized low-density parity check code (GLDPC) is a low-density parity check code in which the constraint nodes of the code graph are block codes, rather than single parity checks. In this paper, we study GLDPC codes which have BCH or Reed-Solomon codes as subcodes under bounded distance decoding (BDD). The performance of the proposed scheme is investigated in the limit case of an infinite length (cycle free) code used over a binary erasure channel (BEC) and the corresponding thresholds for iterative decoding are derived. The performance of the proposed scheme for finite code lengths over a BEC is investigated as well. Structures responsible for decoding failures are defined and a theoretical analysis over the ensemble of GLDPC codes which yields exact bit and block error rates of the ensemble average is derived. Unfortunately this study shows that GLDPC codes do not compare favorably with their LDPC counterpart over the BEC. Fortunately, it is also shown that under certain conditions, objects identified in the analysis of GLDPC codes over a BEC and the corresponding theoretical results remain useful to derive tight lower bounds on the performance of GLDPC codes over a binary symmetric channel (BSC). Simulation results show that the proposed method yields competitive performance with a good decoding complexity trade-off for the BSC.