A Soft-Decision Recursive Decoding Algorithm Using Iterative Bounded-Distance Decoding for u|u+v Codes

Hitoshi TOKUSHIGE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.4   pp.996-1000
Publication Date: 2014/04/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.996
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
recursive decoding,  iterative decoding,  bounded-distance decoding,  u|u+v-construction,  Reed-Muller code,  

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Summary: 
A soft-decision recursive decoding algorithm (RDA) for the class of the binary linear block codes recursively generated using a u|u+v-construction method is proposed. It is well known that Reed-Muller (RM) codes are in this class. A code in this class can be decomposed into left and right components. At a recursive level of the RDA, if the component is decomposable, the RDA is performed for the left component and then for the cosets generated from the left decoding result and the right component. The result of this level is obtained by concatenating the left and right decoding results. If the component is indecomposable, a proposed iterative bounded-distance decoding algorithm is performed. Computer simulations were made to evaluate the RDA for RM codes over an additive white Gaussian-noise channel using binary phase-shift keying modulation. The results show that the block error rates of the RDA are relatively close to those of the maximum-likelihood decoding for the third-order RM code of length 26 and better than those of the Chase II decoding for the third-order RM codes of length 26 and 27, and the fourth-order RM code of length 28.