New Protocols for Asymmetric Communication Channels

In this paper, we study the problem of sending an n-bit binary string drawn from a probability distribution D across a communication channel connecting a client and a server, where the bandwidth from the client to the server is much smaller than the bandwidth from the server to the client. We assume that the client knows the string x but not the distribution D, and the server knows the distribution D, but not the string x. Adler and Maggs demonstrated protocols for this problem where the expected number of bits sent by the client is O(H(D)), and the expected number of bits sent by the server is O(n). Here, H(D) is the binary entropy of the distribution and a lower bound on the expected number of bits that the client must send. In this paper, a new protocol is presented in which the expected number of bits sent by the client is H(D)+2, and the expected number of bits sent by the server is n(H(D)+2). This protocol is then generalized so as to reduce the number of rounds of communication at the expense of computation and bits sent by the server.