Abstract

An important quantity in the analysis of MAP decoding for LDPC codes is the conditional entropy of the input given the output. There exist conjectured formulas for this entropy derived from the replica technique and one sided bounds derived with the help of the interpolation method. In this paper we compute exactly such a quantity for a simpler spin model which retains the essential features of the communications problem. The result is a step towards a proof of the conjectured replica formula for the conditional entropy under MAP decoding.

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