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 talk 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.