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A Neyman-Pearson approach to universal erasure and list decoding

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1 Author(s)
Moulin, P. ; Coord. Sci. Lab. & ECE Dept., Univ. of Illinois at Urbana-Champaign, Urbana, IL

We study communication over an unknown, possibly unreliable, discrete memoryless channel. For such problems, an erasure option at the decoder is desirable. We use constant-composition random codes and propose a generalization of the Maximum Mutual Information decoder. The proposed decoder is parameterized by a weighting function that can be designed to optimize the fundamental tradeoff between undetected-error and erasure exponents. Explicit solutions are identified. The class of functions can be further enlarged to optimize a similar tradeoff for list decoders. 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.

Published in:

Information Theory, 2008. ISIT 2008. IEEE International Symposium on

Date of Conference:

6-11 July 2008

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