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On Multiple Decoding Attempts for Reed-Solomon Codes | | Phong S. Nguyen
; Henry D. Pfister
; Krishna R. Narayanan
; | | Date: |
25 May 2010 | | Abstract: | One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is
based on the idea of using multiple trials of a simple RS decoding algorithm in
combination with successively erasing or flipping a set of symbols or bits in
each trial. In this paper, we present an framework based on rate-distortion
(RD) theory to analyze such multiple-decoding algorithms for RS codes. By
defining an appropriate distortion measure between an error pattern and an
erasure pattern, it is shown that, for a single errors-and-erasures decoding
trial, the condition for successful decoding is equivalent to the condition
that the distortion is smaller than a fixed threshold. Finding the best set of
erasure patterns for multiple decoding trials then turns out to be a covering
problem which can be solved asymptotically by rate-distortion theory. Thus, the
proposed approach can be used to understand the asymptotic
performance-versus-complexity trade-off of multiple errors-and-erasures
decoding of RS codes. We also consider an analysis, based on the
rate-distortion exponent (RDE), that directly minimizes the probability that an
error pattern cannot be covered by any erasure patterns from a chosen set. The
framework is also extended to analyze multiple trials of algebraic
soft-decision (ASD) decoding of RS codes. As a byproduct, both analytical and
numerical computations of the RD and RDE functions for the corresponding
distortion measures are discussed. Simulation results show that sets of erasure
patterns designed using the proposed methods perform better than other
algorithms with the same number of decoding trials. | | Source: | arXiv, 1005.4461 | | Services: | Forum | Review | PDF | Favorites | |
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