Designs, Codes and Cryptography

, Volume 87, Issue 2–3, pp 481–493 | Cite as

A distance between channels: the average error of mismatched channels

  • Rafael G. L. D’Oliveira
  • Marcelo FirerEmail author
Part of the following topical collections:
  1. Special Issue: Coding and Cryptography


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.


Mismatched channels Maximum likelihood decoding Space of channels 

Mathematics Subject Classification

68P30 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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Rutgers UniversityNew BrunswickUSA
  2. 2.University of CampinasCampinasBrazil

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