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2008

Communication Requirements for Generating Correlated Random Variables

Cuff, Paul

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Two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel, in which a channel output is generated based only on a description of the channel input.

Wyner's "common information" coincides with the minimum description rate needed.
However, when common randomness independent of the input is available, the necessary description rate reduces to Shannon's mutual information.
This work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description.

Communication Requirements for Generating Correlated Random Variables · Around

Built on

P. Gács and J. Körner, “Common Information is Far Less Than Mutual Information,” Problems of Control and Info. Theory , vol. 2, pp. 149-162, 1973
1973
Earlier work this paper cites.
A. Wyner, “The Common Information of Two Dependent Random Variables,” IEEE Trans. Info. Theory , vol. IT-21, no. 2, March 1975
1975
Earlier work this paper cites.
I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems
1981
Earlier work this paper cites.

Similar

T. S. Han and S. Verdú, “Approximation Theory of Output Statistics,” IEEE Trans. Info. Theory , vol. 39, no. 3, May 1993
Original
1993
Cited alongside, same era.
C. H. Bennett and P. W. Shor, “Entanglement-Assisted Capacity of a Quantum Channel and the Reverse Shannon Theorem,” IEEE Trans. Info. Theory , vol. 48, no. 10, Oct. 2002
2002
Cited alongside, same era.

Then

T. Cover and H. Permuter, “Capacity of Coordinated Actions,” ISIT 2007, Nice, France
2007
Later among the works it cites.
V. Anantharam and V. Borkar, “Common Randomness and Distributed Control: A Counterexample,” Systems and Control Letters , vol. 56, no. 7-8, July 2007
2007
Later among the works it cites.

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