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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.

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? Shannon's proof(http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf) is geometry-less and very abstract.

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.

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user16007
user16007
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A geometric/topology notion of Typical Sequences? Power of typical sequences in multiuser channels?

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? Shannon's proof(http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf) is geometry-less and very abstract.

A geometric notion of Typical Sequences? Power of typical sequences in multiuser channels?

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 to easily visualize typical sequences? Shannon's proof(http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf) is geometry-less and very abstract.

A geometric/topology notion of Typical Sequences? Power of typical sequences in multiuser channels?

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? Shannon's proof(http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf) is geometry-less and very abstract.

Source Link
user16007
user16007
  • 800
  • 1
  • 7
  • 15

A geometric notion of Typical Sequences? Power of typical sequences in multiuser channels?

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 to easily visualize typical sequences? Shannon's proof(http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf) is geometry-less and very abstract.