Simplified Erasure/List Decoding

It was previously shown by Hashimoto that Forney's optimal erasure decoder can be significantly simplified, in the sense that a simplified decoder achieves the same random coding bounds, for the ensemble of independent and identically distributed codewords. In this paper, the analysis of simplified decoders is refined and generalized in several aspects. First, tighter random coding bounds for simplified decoders are derived, which equal the exact exponential behavior of the fixed composition ensemble average. Second, the exponential bounds are valid both in the erasure mode and in the list mode. Third, the analysis pertains to a rather general class of simplified decoders, including the case of mismatch in the threshold function of the decoder. Fourth, expurgated exponents, which are larger than the random coding exponents at low rates, are shown to be achievable using a significantly simpler decoder than Forney's optimal decoder. It is shown numerically that, from the aspect of exact random coding exponents, a decoder in the spirit of Hashimoto's is as good as Forney's in the erasure mode, as well as in the list mode.