Improved bounds for asymmetric communication protocols

Authors:
Eduardo Sany Laber;Leonardo Gomes Holanda
Affiliations:
Departamento e Informática da PUC-Rio, Rua Marquês de São Vicente 225, RDC Andar 5, PESC/COPPE/UFRJ, P.O. Box 68511, CEP 21945.970, Rio de Janeiro, RJ, Brazil;Departamento e Informática da PUC-Rio, Rua Marquês de São Vicente 225, RDC Andar 5, PESC/COPPE/UFRJ, P.O. Box 68511, CEP 21945.970, Rio de Janeiro, RJ, Brazil
Venue:
Information Processing Letters
Year:
2002

Citing 1
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Abstract

Adler and Maggs [FOCS'98, 1998, 522] introduced some protocols for asymmetric communication channels. For one of them, the "computational efficient" one, they prove that the expected number of bits sent by the client to the server is at most 1.71H(D) + 1, where H(D) is the entropy of the distribution of probability D maintained by the server. In this paper, we show that their protocol is much better. In fact, we prove that the expected number of bits sent by the client is at most H(D)/(log2 3 - 2/3) + 1 ≈ 1.089H(D) + 1. We also argue that this upper bound is tight in the sense that there is a distribution for which this protocol does not perform any better.