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Title: On the reliability-order-based decoding algorithms for binary linear block codes
Authors: Tang, Y.
Ling, S. 
Fu, F.-W. 
Keywords: Asymptotic optimality
Bounded-distance decoding
Error performance
Linear block codes
Maximum-likelihood (ML) decoding
Reliability-order-based decoding
Issue Date: Jan-2006
Citation: Tang, Y., Ling, S., Fu, F.-W. (2006-01). On the reliability-order-based decoding algorithms for binary linear block codes. IEEE Transactions on Information Theory 52 (1) : 328-336. ScholarBank@NUS Repository.
Abstract: In this correspondence, we consider the decoding of binary block codes over the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) signaling. By a reliability-order-based decoding algorithm (ROBDA), we mean a soft-decision decoding algorithm which decodes to the best (most likely) codeword of the form that is the sum of the hard-decision tuple and an error pattern in a set determined only by the order of the reliabilities of the hard decisions. Examples of ROBDAs include many well-known decoding algorithms, such as the generalized-minimum-distance (GMD) decoding algorithm, Chase decoding algorithms, and the reliability-based decoding algorithms proposed by Fossorier and Lin. It is known that the squared error-correction-radii of ROBDAs can be computed from the minimal squared Euclidean distances (MSEDs) between the all-one sequence and the polyhedra corresponding to the error patterns. For the computation of such MSEDs, we give a new method which is more compact than the one proposed by Fossorier and Lin. These results are further used to show that any bounded-distance ROBDA is asymptotically optimal: The ratio between the probability of decoding error of a bounded-distance ROBDA and that of the maximum-likelihood (ML) decoding approaches 1 when the signal-to-noise ratio (SNR) approaches infinity, provided that the minimum Hamming distance of the code is greater than 2. © 2006 IEEE.
Source Title: IEEE Transactions on Information Theory
ISSN: 00189448
DOI: 10.1109/TIT.2005.860451
Appears in Collections:Staff Publications

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