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Register a new userProof of Convergence for Correct-Decoding Exponent Computation
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Added by
Sergey Tridenski
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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For a discrete memoryless channel with finite input and output alphabets, we prove convergence of a parametric family of iterative computations of the optimal correct-decoding exponent. The exponent, as a function of communication rate, is computed for a fixed rate and for a fixed slope.
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`Tree pruning (TP) is an algorithm for probabilistic inference on binary Markov random fields. It has been recently derived by Dror Weitz and used to construct the first fully polynomial approximation scheme for counting independent sets up to the `tree uniqueness threshold. It can be regarded as a clever method for pruning the belief propagation computation tree, in such a way to exactly account for the effect of loops. In this paper we generalize the original algorithm to make it suitable for decoding linear codes, and discuss various schemes for pruning the computation tree. Further, we present the outcomes of numerical simulations on several linear codes, showing that tree pruning allows to interpolate continuously between belief propagation and maximum a posteriori decoding. Finally, we discuss theoretical implications of the new method.
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