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

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 famil...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:IEEE transactions on communications Ročník 52; číslo 12; s. 2087 - 2097
Hlavní autoři: Zarrinkhat, P., Banihashemi, A.H.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.12.2004
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithm design and analysis
Algorithms
Applied sciences
Code standards
Codes
Coding, codes
Convergence
Density evolution
Exact sciences and technology
hard-decision iterative decoding algorithms
Heuristic algorithms
Information, signal and communications theory
Iterative algorithms
Iterative decoding
low-density parity-check (LDPC) codes
majority-based iterative decoding algorithms
message-passing decoders
Parity check codes
Performance analysis
Scholarships
Signal and communications theory
Studies
Telecommunications and information theory
Turbo codes
message-passing decoders
Majority logic
Iterative method
Decoding
Density evolution
hard-decision iterative decoding algorithms
majority-based iterative decoding algorithms
Algorithm
Binary code
Simulation
low-density parity-check (LDPC) codes
Signal processing
Parity check codes
ISSN:0090-6778, 1558-0857
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ObjectType-Article-2
ObjectType-Feature-1
content type line 23
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2004.838738