SPCoding School

Matching Channels and Metrics.pdf

A short description of the project

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The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel.

Back over 40 years, in a paper from 1971. Chiang and Wolf attribute the general question of matching metrics and channels to notes from a 1967 course given by Massey. The most significant work on this question was done by Seguin in 1980, in a paper where he studies necessary and sufficient conditions for a discrete memoryless channel to be matched to an additive metric.

Considering non-additive metrics, this question is widely open, some possible approaches for binnary asymmetric channels are proposed here.