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25th Annual Symposium on Foundations of Computer Science (FOCS 1984)
Singer Island, FL
October 24-October 26
ISBN: 0-8186-0591-X
A. El Gamal, Stanford University
Let X and Y be two random variables with probability distribution p(x,y), joint entropy H(X,Y) and conditional entropies H(X \ Y) and H(Y \ X) . Person P/sub x/ knows X and person P/sub Y/ knows Y. They communicate over a noiseless two-way channel so that both know X and Y. It is proved that, on the average, at least H(X \ Y) + H(Y \ X) bits must be exchanged and that H(X,Y) + 2 bits are sufficient. If p(x.y) > 0 for all (x.y), then at least H(X,Y) bits must be communicated on the average. However, if p (x,y) is uniform over its support set, the average number of bits needed is close to H(X \ Y) + H (Y \ X). Randomized protocols can reduce the amount of communication considerably but only when some probability of error is acceptable.
A. El Gamal, A. Orlitsky, "Interactive Data Compression," focs, pp.100-108, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984
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