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A Neyman-Pearson Approach to Universal Erasure and List Decoding
- Publication Year :
- 2008
-
Abstract
- 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 decoder with 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 decoders -- in 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.<br />Comment: 31 pages, submitted to IEEE Transactions on Information Theory
- Subjects :
- Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0801.4544
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1109/ISIT.2008.4594948