Error Bounds for Algebraic Soft-Decision Decoding of Reed-Solomon Codes over Additive-Noise Channels

We bound the probability of error of Algebraic Soft-Decision Decoding (ASD) of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. First, we derive an exponential error bound on the probability of list-decoding error that improves on the bound presented in [9]. However, our previous work [1] has shown that list-decoding error is not sufficient to adequately characterize ASD´s performance. Thus, we redefine an error as the event that the decoder selects an erroneous codeword from its list, and we derive an exponential error bound for the probability of selection error.