DocumentCode :
1404732
Title :
Iterative Algorithms for Decoding a Class of Two-Step Majority-Logic Decodable Cyclic Codes
Author :
Zhang, Li ; Huang, Qin ; Lin, Shu
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of California, Davis, CA, USA
Volume :
59
Issue :
2
fYear :
2011
fDate :
2/1/2011 12:00:00 AM
Firstpage :
416
Lastpage :
427
Abstract :
Codes constructed based on finite geometries form a large class of cyclic codes with large minimum distances which can be decoded with simple majority-logic decoding in one or multiple steps. In 2001, Kou, Lin and Fossorier showed that the one-step majority-logic decodable finite geometry codes form a class of cyclic LDPC codes whose Tanner graphs are free of cycles of length 4. These cyclic finite geometry LDPC codes perform very well over the AWGN channel using iterative decoding based on belief propagation (IDBP) and have very low error-floors. However, the standard IDBP is not effective for decoding other cyclic finite geometry codes because their Tanner graphs contain too many short cycles of length 4 which severely degrade the decoding performance. This paper investigates iterative decoding of two-step majority-logic decodable finite geometry codes. Three effective algorithms for decoding these codes are proposed. These algorithms are devised based on the orthogonal structure of the parity-check matrices of the codes to avoid or reduce the degrading effect of the short cycles of length 4. These decoding algorithms provide significant coding gains over the standard IDBP using either the sum-product or the min-sum algorithms.
Keywords :
AWGN channels; cyclic codes; geometry; iterative decoding; parity check codes; AWGN channel; LDPC code; iterative decoding based on belief propagation; parity-check matrix; tanner graph; two-step majority-logic decodable cyclic finite geometry codes; Finite geometry code; cyclic code; iterative decoding; two-fold EG-code;
fLanguage :
English
Journal_Title :
Communications, IEEE Transactions on
Publisher :
ieee
ISSN :
0090-6778
Type :
jour
DOI :
10.1109/TCOMM.2010.120710.090624
Filename :
5668918
Link To Document :
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