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The idea of Typical sequences( is a crucial concept in Shannon's proof of the Noisy channel coding theorem. Unfortunately the notion is not sufficient to settle the capacity of transmission of non-communicating correlated sources over independent channels to a common noisy receiver? Even the problem of two-user interference channel capacity with uncorrelated sources is open. What makes it hard to apply typicality to these cases?

Is it possible to associate a geometry/topology to easily visualize typical sequences(atleast when the alphabets are $1$-dimensional reals - more complicated cases include matrix or non-commutatitve alphabets such as in Multiple Input and Multiple Output systems)? Shannon's proof( is geometry-less and very abstract.

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yes,there is an illustrative proof here : Network information theory by Abbas El gammal and

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