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A Neyman–Pearson Approach to Universal Erasure and List Decoding

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1 Author(s)
Pierre Moulin ; Electr. & Comput. Eng. Dept., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA

When information is to be transmitted over an unknown, possibly unreliable channel, an erasure option at the decoder is desirable. Using constant-composition random codes, we propose a generalization of Csiszar and Korner's maximum mutual information (MMI) decoder with an erasure option for discrete memoryless channels. The new decoder is parameterized by a weighting function that is designed to optimize the fundamental tradeoff between undetected-error and erasure exponents for a compound class of channels. The class of weighting functions may be further enlarged to optimize a similar tradeoff for list decodersin that case, undetected-error probability is replaced with average number of incorrect messages in the list. Explicit solutions are identified. The optimal exponents admit simple expressions in terms of the sphere-packing exponent, at all rates below capacity. For small erasure exponents, these expressions coincide with those derived by Forney (1968) for symmetric channels, using maximum a posteriori decoding. Thus, for those channels at least, ignorance of the channel law is inconsequential. Conditions for optimality of the Csiszar-Korner rule and of the simpler empirical-mutual-information thresholding rule are identified. The error exponents are evaluated numerically for the binary symmetric channel.

Published in:

IEEE Transactions on Information Theory  (Volume:55 ,  Issue: 10 )