Improved bounds for asymmetric communication protocols.
\textit{M. Adler} and \textit{B. M. Maggs} [FOCS'98, 522 (1998)] 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 \(H(D)/(\log_{2}3\frac23)+ 1\approx1.089H(D)+1\). 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.
scientific article; zbMATH DE number 1856411