Abstract
The single-user source-channel separation theorem has been proved for many classes of sources and channels, including sources with finite or countably infinite alphabets. Typically, the source-channel separation theorem is first proved for sources with a finite alphabet, and then the results are extended to sources with a countably infinite alphabet. This paper considers the direct extension of the source-channel separation theorem for some classes of sources with a finite alphabet to a countably infinite alphabet. Specifically, we provide a solution for memoryless sources and arbitrary channels. It is then discussed how this approach may be extended to the case of general sources and arbitrary channels.
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