6
$\begingroup$

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.

$\endgroup$

1 Answer 1

2
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.