Computing upper bounds to error probability of soft-decision decoding of Reed-Solomon codes based on the ordered statistics algorithm

This correspondence presents performance analysis of symbol-level soft-decision decoding of q-ary maximum-distance-separable (MDS) codes based on the ordered statistics algorithm. The method we present is inspired by the one recently proposed by Agrawal and Vardy (2000), who approximately evaluate t...

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Bibliographic Details
Published in:IEEE transactions on information theory 2004-02, Vol.50 (2), p.337-344
Main Authors: Albanese, M., Spalvieri, A.
Format: Article
Language:English
Subjects:
Algorithms
Block codes
Codes
Error analysis
Error probability
Maximum likelihood decoding
Modulation coding
Partitioning algorithms
Performance analysis
Probability
Statistical analysis
Statistics
Viterbi algorithm
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Summary:This correspondence presents performance analysis of symbol-level soft-decision decoding of q-ary maximum-distance-separable (MDS) codes based on the ordered statistics algorithm. The method we present is inspired by the one recently proposed by Agrawal and Vardy (2000), who approximately evaluate the performance of generalized minimum-distance decoding. The correspondence shows that in our context, the method allows us to compute the exact value of the probability that the transmitted codeword is not one of the candidate codewords. This leads to a close upper bound on the performance of the decoding algorithm. Application of the ordered statistics algorithm to MDS codes is not new. Nevertheless, its advantages seem not to be fully explored. We show an example where the decoding algorithm is applied to singly extended 16-ary Reed-Solomon (RS) codes in a 128-dimensional multilevel coded-modulation scheme that approaches the sphere lower bound within 0.5 dB at the word error probability of 10/sup -4/ with manageable decoding complexity.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2003.822605