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Partial ordering of communication channels has applications in performanceanalysis, and goes beyond comparisons of channels just on the basis of theirShannon capacity or error probability. Shannon defined a partial order ofchannel inclusion based on convex mixture of input/output degradations of adiscrete memoryless channel (DMC). In this paper, extensions to channels otherthan DMCs are considered. In particular, additive noise channels and phasedegraded channels, and multiple input multiple output (MIMO) linear Gaussianchannels (LGC) are considered. For each of these models, the conditions underwhich the partial order becomes a lattice are also discussed.

Channel Inclusion Beyond Discrete Memoryless Channels