NDLI: Threshold values and convergence properties of majority-based algorithms for decoding regular low-density parity-check codes

Content Provider	IEEE Xplore Digital Library
Author	Zarrinkhat, P. Banihashemi, A.H.
Copyright Year	1972
Abstract	This work presents a detailed study of a family of binary message-passing decoding algorithms for low-density parity-check (LDPC) codes, referred to as "majority-based algorithms." Both Gallager's algorithm A (G/sub A/) and the standard majority decoding algorithm belong to this family. These algorithms, which are, in fact, the building blocks of Gallager's algorithm B (G/sub B/), work based on a generalized majority-decision rule and are particularly attractive for their remarkably simple implementation. We investigate the dynamics of these algorithms using density evolution and compute their (noise) threshold values for regular LDPC codes over the binary symmetric channel. For certain ensembles of codes and certain orders of majority-based algorithms, we show that the threshold value can be characterized as the smallest positive root of a polynomial, and thus can be determined analytically. We also study the convergence properties of majority-based algorithms, including their (convergence) speed. Our analysis shows that the stand-alone version of some of these algorithms provides significantly better performance and/or convergence speed compared with G/sub A/. In particular, it is shown that for channel parameters below threshold, while for G/sub A/ the error probability converges to zero exponentially with iteration number, this convergence for other majority-based algorithms is super-exponential.
Starting Page	2087
Ending Page	2097
Page Count	11
File Size	563673
File Format	PDF
ISSN	00906778
Volume Number	52
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Convergence Parity check codes Iterative algorithms Iterative decoding Algorithm design and analysis Turbo codes Scholarships Code standards Heuristic algorithms Performance analysis message-passing decoders Density evolution hard-decision iterative decoding algorithms low-density parity-check (LDPC) codes majority-based iterative decoding algorithms
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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