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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.