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The Multiconference on Computational Engineering in Systems Applications

Normalized Switch Schemes for Low Density Parity Check Codes

Gong Chen, Liu Qi, Cui Huiluan, Tang Kun

Published Oct 1, 2006• 0 citations
Publisher

Abstract

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

DOI
10.1109/cesa.2006.4281890

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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.
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.
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.
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
Hybrid decoding means to combine different iterative decoding algorithms with the aim of improving error performance or decoding complexity. In this work, we introduce "time-invariant" hybrid (H/sub TI/) algorithms, and using density evolution show that for regular low-density parity-check (LDPC) codes and binary message-passing algorithms, H/sub TI/ algorithms perform remarkably better than their constituent algorithms. We also show that compared to "switch-type" hybrid (H/sub ST/) algorithms, such as Gallager's algorithm B, where a comparable improvement is obtained by switching between different iterative decoding algorithms, H/sub TI/ algorithms are far less sensitive to channel conditions and thus can be practically more attractive.
Hybrid decoding is to combine different iterative decoding algorithms with the aim of improving error performance or decoding complexity. In this work, we introduce "time-invariant" hybrid (HTI) algorithms, and show that for regular low-density parity-check codes and binary message-passing algorithms, HTIalgorithms perform remarkably better than their constituent algorithms. We also show that compared to "switch-type" hybrid algorithms, such as Gallager's algorithm B, where a comparable improvement is obtained by switching between different iterative decoding algorithms, HTIalgorithms are far less sensitive to channel conditions and thus can be practically more attractive.