A distance between channels: the average error of mismatched channels

Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding distance between channels in terms of their ML-decoders whic...

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Bibliographic Details
Published inDesigns, codes, and cryptography Vol. 87; no. 2-3; pp. 481 - 493
Main Authors D’Oliveira, Rafael G. L., Firer, Marcelo
Format Journal Article
LanguageEnglish
Published New York Springer US 15.03.2019
Springer Nature B.V
Subjects
Channels
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Decoders
Decoding
Discrete Mathematics in Computer Science
Equivalence
Hyperplanes
Information and Communication
Maximum likelihood decoding
Special Issue: Coding and Cryptography
68P30
52C35
51E22
Mismatched channels
Space of channels
Maximum likelihood decoding
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Summary:Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding distance between channels in terms of their ML-decoders which is meaningful from the decoding point of view, in the sense that the closer two channels are, the larger is the probability of them sharing the same ML-decoder. We give explicit formulas for these probabilities.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-018-0557-3