DocumentCode :
43748
Title :
Low-Complexity LP Decoding of Nonbinary Linear Codes
Author :
Punekar, M. ; Vontobel, P.O. ; Flanagan, Mark F.
Author_Institution :
Dept. of Electr. & Comput. Eng., Texas A&M Univ., Doha, Qatar
Volume :
61
Issue :
8
fYear :
2013
fDate :
Aug-13
Firstpage :
3073
Lastpage :
3085
Abstract :
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 Z4, 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.
Keywords :
AWGN channels; computational complexity; decoding; linear codes; linear programming; parity check codes; phase shift keying; AWGN channel; basic LCLP decoding algorithm; check node calculation; computational complexity; linear programming decoding; low complexity LP decoding; low density parity check code; modified BCJR algorithm; nonbinary linear codes; quaternary phase shift keying; subgradient LCLP decoding algorithm; Algorithm design and analysis; Complexity theory; Decoding; Iterative decoding; Linear code; Vectors; LDPC codes; Linear programming decoding; coordinate-ascent algorithm; nonbinary codes; subgradient algorithm;
fLanguage :
English
Journal_Title :
Communications, IEEE Transactions on
Publisher :
ieee
ISSN :
0090-6778
Type :
jour
DOI :
10.1109/TCOMM.2013.070213.120801
Filename :
6559989
Link To Document :
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