Decoding Algorithms for Nonbinary LDPC Codes Over GF (q)

In this letter, we address the problem of decoding nonbinary low-density parity-check (LDPC) codes over finite fields GF(q), with reasonable complexity and good performance. In the first part of the letter, we recall the original belief propagation (BP) decoding algorithm and its Fourier domain impl...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 55; no. 4; pp. 633 - 643
Main Authors: Declercq, D., Fossorier, M.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Back propagation
Belief propagation
Codes
Coding, codes
Complexity reduction
Computational complexity
Computer simulation
Decoders
Decoding
EMS
Exact sciences and technology
Fourier transforms
Galois fields
Information, signal and communications theory
Iterative algorithms
iterative decoder
Iterative decoding
Low density parity check codes
Mathematical analysis
Medical services
nonbinary low-density parity-check (LDPC) codes
Offsets
Parity check codes
Signal and communications theory
Studies
Table lookup
Telecommunications and information theory
Tensile stress
Performance evaluation
Finite field
Error rate
Correction factor
iterative decoder
Algorithm
Binary code
Iterative decoding
Implementation
nonbinary low-density parity-check (LDPC) codes
Simulation
Parity check codes
Error correcting code
Complexity reduction
ISSN:0090-6778, 1558-0857
Online Access:Get full text
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Summary:In this letter, we address the problem of decoding nonbinary low-density parity-check (LDPC) codes over finite fields GF(q), with reasonable complexity and good performance. In the first part of the letter, we recall the original belief propagation (BP) decoding algorithm and its Fourier domain implementation. We show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding. In the second part of the letter, we introduce a simplified decoder which is inspired by the min-sum decoder for binary LDPC codes. We called this decoder extended min-sum (EMS). We show that it is possible to greatly reduce the computational complexity of the check-node processing by computing approximate reliability measures with a limited number of values in a message. By choosing appropriate correction factors or offsets, we show that the EMS decoder performance is quite good, and in some cases better than the regular BP decoder. The optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution. Our simulations on ultra-sparse codes over very-high-order fields show that nonbinary LDPC codes are promising for applications which require low frame-error rates for small or moderate codeword lengths. The EMS decoder is a good candidate for practical hardware implementations of such codes
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2007.894088