2018/02/06 by D'Oliveira, Rafael G. L., Firer, Marcelo
#1E22 #52C35 #68P30 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1802.02049
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.