  One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is
based on using multiple trials of a simple RS decoding algorithm in combination
with erasing or flipping a set of symbols or bits in each trial. This paper
presents a framework based on rate-distortion (RD) theory to analyze these
multiple-decoding algorithms. By defining an appropriate distortion measure
between an error pattern and an erasure pattern, the successful decoding
condition, for a single errors-and-erasures decoding trial, becomes equivalent
to distortion being less than a fixed threshold. Finding the best set of
erasure patterns also turns into 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.
  This initial result is also extended a few directions. The rate-distortion
exponent (RDE) is computed to give more precise results for moderate
blocklengths. Multiple trials of algebraic soft-decision (ASD) decoding are
analyzed using this framework. Analytical and numerical computations of the RD
and RDE functions are also presented. Finally, simulation results show that
sets of erasure patterns designed using the proposed methods outperform other
algorithms with the same number of decoding trials.
