The idea of Typical sequences(http://en.wikipedia.org/wiki/Typical_set) 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(http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf) is geometry-less and very abstract.