Low-Complexity LP Decoding of Nonbinary Linear Codes

Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most important problem with LP decoding for both binary and nonbina...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 61; no. 8; pp. 3073 - 3085
Main Authors: Punekar, M., Vontobel, P. O., Flanagan, M. F.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Binary system
Blocking
Channels
Codes
Coding, codes
Complexity
Complexity theory
coordinate-ascent algorithm
Decoding
Exact sciences and technology
Information, signal and communications theory
Iterative decoding
Keying
LDPC codes
Linear code
Linear programming
Linear programming decoding
Mathematical analysis
Modulation, demodulation
nonbinary codes
Signal and communications theory
Solvers
subgradient algorithm
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Transmission and modulation (techniques and equipments)
Vectors
coordinate-ascent algorithm
Error estimation
Iterative method
Linear programming
subgradient algorithm
Decoding
Algorithm
Binary code
Computational complexity
LDPC codes
Quadrature phase shift keying
Linear programming decoding
AWGN channels
nonbinary codes
Linear code
Phase shift keying
Simulation
Simplex method
Error correcting code
Parity check codes
Error correction
ISSN:0090-6778, 1558-0857
Online Access:Get full text
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Summary:Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most important problem with LP decoding for both binary and nonbinary linear codes is that the complexity of standard LP solvers such as the simplex algorithm remains prohibitively large for codes of moderate to large block length. To address this problem, two low-complexity LP (LCLP) decoding algorithms for binary linear codes have been proposed by Vontobel and Koetter, henceforth called the basic LCLP decoding algorithm and the subgradient LCLP decoding algorithm. In this paper, we generalize these LCLP decoding algorithms to nonbinary linear codes. The computational complexity per iteration of the proposed nonbinary LCLP decoding algorithms scales linearly with the block length of the code. A modified BCJR algorithm for efficient check-node calculations in the nonbinary basic LCLP decoding algorithm is also proposed, which has complexity linear in the check node degree. Several simulation results are presented for nonbinary LDPC codes defined over Z 4 , GF(4), and GF(8) using quaternary phase-shift keying and 8-phase-shift keying, respectively, over the AWGN channel. It is shown that for some group-structured LDPC codes, the error-correcting performance of the nonbinary LCLP decoding algorithms is similar to or better than that of the min-sum decoding algorithm.
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2013.070213.120801