Coding for distributed computation

Abstract

The author describes analogous coding theorems for the more general, interactive, communications required in computation. In this case the bits transmitted in the protocol are not known to the processors in advance but are determined dynamically. First he shows that any interactive protocol of length T between two processors connected by a noiseless channel can be simulated, if the channel is noisy (a binary symmetric channel of capacity C), in time proportional to T 1/C, and with error probability exponentially small in T. He then shows that this result can be extended to arbitrary distributed network protocols. He shows that any distributed protocol which runs in time T on a network of degree d having noiseless communication channels, can, if the channels are in fact noisy, be simulated on that network in time proportional to T 1/C log d. The probability of failure of the protocol is exponentially small in T.