Deterministic simulation of randomized protocols over arbitrary networks of noisy channels*

Suppose the input to a function is split between several processors connected by a network of binary channels, and the processors know an interactive protocol by which they can compute the function in N steps of communication, provided the channels are all noiseless. Since all practical channels are noisy, it is important, to study the effect of channel noise on the complexity and reliability of the protocol. In this direction, Rajagopalan and Schulman recently proved that any Ar-step noiseless-network protocol can be simulated over a network of identical and independent binary symmetric channels (with the same topology) in O ((N/C) logrf) steps, while incurring a simulation failure probability of 2~n(N), Here, d is the maximum in-degree of any pro cessor in the network, and C is the capacity of each channel. We show that this result can be strengthened in the following way: any Af-step private-coin randomized protocol that computes a function correctly with probability at least 1 —e (in the noiseless case) can be deterministically simulated over the noisy network in Ofyr^J + Of—^-J steps, while incurring an error probability in computing the function of at most e + 2~nf>NK Here, m is the number of channels in the network. •Research supported by NSF IRI 9005849, IRl 9310670, NCR 9422513, and the AT&T Foundation. 1Cornell University and U.C Berkeley. *Univ. of California, Berkeley. sAddress all correspondence to the second author: 570 Cory Hall, Dept. of EECS, U.C. Berkeley, Berkeley, CA 94720.