Universal Decoding for Arbitrary Channels Relative to a Given Class of Decoding Metrics

We consider the problem of universal decoding
for arbitrary, finite–alphabet unknown channels in the random
coding regime. For a given random coding distribution and a
given class of metric decoders, we propose a generic universal
decoder whose average error probability is, within a sub–
exponential multiplicative factor, no larger than that of the
best decoder within this class of decoders. Since the optimal,
maximum likelihood (ML) decoder of the underlying channel is
not necessarily assumed to belong to the given class of decoders,
this setting suggests a common generalized framework for: (i)
mismatched decoding, (ii) universal decoding for a given family of
channels, and (iii) universal coding and decoding for deterministic
channels using the individual–sequence approach. The proof of
our universality result is fairly simple, and it is demonstrated how
some earlier results on universal decoding are obtained as special
cases. We also demonstrate how our method extends to more
complicated scenarios, like incorporation of noiseless feedback,
the multiple access channel, and continuous alphabet channels.