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Normalized Switch SchemesforLowDensity Parity CheckCodes

Chen Gong

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Thispaperaddresses switch schemes forswitch typehybridharddecision iterative algorithms decoding finite length lowdensity parity check(LDPC)codes. After piecewise analysis forextrinsic transfer information (EXIT) chartfamily andexploration offixed points, onegeneral switch schemenamednormalized switch scheme, forwhich majority based(MB)algorithms andGallager's decoding algorithm B (GB)areextremecases, isproposed. Several specific normalized switchscheme,named expanded optimal switch schemeandtail-cut (TC)optimal switch scheme, aregivenandtheir convergence properties are analyzed. Simulation showsthatcompared withGB that holdsoptimality forinfinity length codes, proposed switch schemesshowperformance improvements whileenjoying lesssensitivity tochannel parameter underestimations for finite length codes.

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IEEE International Symposium on Information Theory (ISIT)•Jan 1, 2005•4 citations
Thispaperaddresses switch schemes forswitch typehybridharddecision iterative algorithms decoding finite length lowdensity parity check(LDPC)codes. After piecewise analysis forextrinsic transfer information (EXIT) chartfamily andexploration offixed points, onegeneral switch schemenamednormalized switch scheme, forwhich majority based(MB)algorithms andGallager's decoding algorithm B (GB)areextremecases, isproposed. Several specific normalized switchscheme,named expanded optimal switch schemeandtail-cut (TC)optimal switch scheme, aregivenandtheir convergence properties are analyzed. Simulation showsthatcompared withGB that holdsoptimality forinfinity length codes, proposed switch schemesshowperformance improvements whileenjoying lesssensitivity tochannel parameter underestimations for finite length codes.
This paper addresses switch schemes for switch type hybrid hard decision iterative algorithms decoding finite length low density parity check (LDPC) codes. After piecewise analysis for extrinsic transfer information (EXIT) chart family and exploration of fixed points, one general switch scheme named normalized switch scheme, for which majority based (MB) algorithms and Gallager's decoding algorithm B (GB) are extreme cases, is proposed. Several specific normalized switch scheme, named expanded optimal switch scheme and tail-cut (TC) optimal switch scheme, are given and their convergence properties are analyzed. Simulation shows that compared with GB that holds optimality for infinity length codes, proposed switch schemes show performance improvements while enjoying less sensitivity to channel parameter underestimations for finite length codes
This correspondence presents the switch strategies for switch-type hybrid hard decision decoding algorithms for regular low-density parity-check (LDPC) codes. After the piecewise analysis of extrinsic information transfer functions for Gallager decoding algorithm B (GB), the normalized switch scheme (NSS), for which the majority-based algorithms and GB are two examples, is proposed. Then, several other examples of NSSs are presented and their convergence properties are analyzed based on the extrinsic information transfer (EXIT) functions. In simulations, the proposed NSSs show meaningful performance improvements and less sensitivity to channel parameter underestimations compared with GB for small and moderate block length codes.
In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over additive white Gaussian noise (AWGN) channels. We present the iterative decoding algorithm of LDPC codes, and we also discuss the encoding methods and the bipartite graph representation of LDPC codes ensemble. Finite-length LDPC code performances are investigated, and the influence of cycle is pointed out. Simulation results show that irregular LDPC codes with variable and check node degree distribution optimized for infinite-length codes are not optimal for finite-length LDPC codes, and the error patterns of both regular and irregular codes are investigated as an effort to improve the performance and design methodology of finite-length LDPC codes.
Time-invariant hybrid (HscrTI) decoding of irregular low-density parity-check (LDPC) codes is studied. Focusing on HscrTIalgorithms with majority-based (MB) binary message-passing constituents, we use density evolution (DE) and finite-length simulation to analyze the performance and the convergence properties of these algorithms over (memoryless) binary symmetric channels. To apply DE, we generalize degree distributions to have the irregularity of both the code and the decoding algorithm embedded in them. A tight upper bound on the threshold of MB HscrTIalgorithms is derived, and it is proven that the asymptotic error probability for these algorithms tends to zero, at least exponentially, with the number of iterations. We devise optimal MB HscrTIalgorithms for irregular LDPC codes, and show that these algorithms outperform Gallager's algorithm A applied to optimized irregular LDPC codes. We also show that compared to switch-type algorithms, such as Gallager's algorithm B, where a comparable improvement is obtained by switching between different MB algorithms, MB HscrTIalgorithms are more robust and can better cope with unknown channel conditions, and thus can be practically more attractive.
Effectofchannelmismatchon decoding performance oflowdensity parity check(LDPC)codes over binarysymmetric channel(BSC)undersum-product algorithm (SPA)isanalyzed inthis paper. Density evolution isemployedintheoretical analysis togetoptimal initial valueforSPA.Basedon theresults, a modified SPA algorithm isproposed. Whendecoding using this modified SPAalgorithm, nochannel information isneededatthe decoderside.Thiswillbe of significant valuefor time-varying channels. Theoretical claimsfromdensity evolution areconfirmed by extensive simulations. Our simulations showthatbyfixing theinitial valueforall channel conditions, decoding performance canbeimproved. Onechannel state estimation algorithm isproposed inthis paperbasedontheerrordetection ability ofLDPC codes. Maximumnumberofiterations takenwhendecoding a LDPC codecanbedynamically adjusted according tothe estimatedchannel state.Further performance improvements canbe achieved by usingthedynamic iteration numberadjusting schemetogether withthe modified sum-product algorithm.
Time-invariant hybrid (HTI) decoding of irregular low-density parity-check (LDPC) codes is studied. Focusing on HTIalgorithms with majority-based (MB) binary message-passing constituents, we use density evolution and finite-length simulation to analyze the performance and the convergence properties of these algorithms. Tight upper bounds on the threshold of MB HTIalgorithms are derived, and it is proven that the asymptotic error probability for these algorithms tends to zero at least exponentially with the number of iterations. We devise optimal MB HTIalgorithms for irregular LDPC codes, and show that these algorithms outperform Gallager's algorithm A applied to optimized irregular LDPC codes. We also show that compared to switch-type algorithms, such as Gallager's algorithm B, where a comparable improvement is obtained by switching between different MB algorithms, MB HTIalgorithms are more robust, and can better cope with unknown channel conditions, and thus can be practically more attractive