A distance between channels: the average error of mismatched channels
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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.
KeywordsMismatched channels Maximum likelihood decoding Space of channels
Mathematics Subject Classification68P30 51E22 52C35
Rafael G. L. D’Oliveira was supported by CAPES. Marcelo Firer was partially supported by São Paulo Research Foundation, (FAPESP Grant 2013/25977-7).
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