  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.
