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This paper is concerned with bounds on the maximum-likelihood (ML) decodingerror probability of Reed-Solomon (RS) codes over additive white Gaussian noise(AWGN) channels. To resolve the difficulty caused by the dependence of theEuclidean distance spectrum on the way of signal mapping, we propose to userandom mapping, resulting in an ensemble of RS-coded modulation (RS-CM)systems. For this ensemble of RS-CM systems, analytic bounds are derived, whichcan be evaluated from the known (symbol-level) Hamming distance spectrum. Alsopresented in this paper are simulation-based bounds, which are applicable toany specific RS-CM system and can be evaluated by the aid of a list decoding(in the Euclidean space) algorithm. The simulation-based bounds do not needdistance spectrum and are numerically tight for short RS codes in the regimewhere the word error rate (WER) is not too low. Numerical comparison resultsare relevant in at least three aspects. First, in the short code length regime,RS-CM using BPSK modulation with random mapping has a better performance thanbinary random linear codes. Second, RS-CM with random mapping (time varying)can have a better performance than with specific mapping. Third, numericalresults show that the recently proposed Chase-type decoding algorithm isessentially the ML decoding algorithm for short RS codes.

Bounds on the ML Decoding Error Probability of RS-Coded Modulation over AWGN Channels