Efficient Coding for Interactive Communication

We revisit the problem of reliable interactive communication over a noisy channel, and obtain the first fully (randomized) efficient constant-rate emulation procedure for reliable interactive communication. Our protocol works for any discrete memoryless noisy channel with constant capacity, and fails with exponentially small probability in the total length of the protocol. Following a work by Schulman (1993) our simulation uses a tree-code, yet as opposed to the non-efficient construction of absolute tree-code used by Schulman, we introduce a relaxation in the notion of goodness for a tree code and define a potent tree code. This relaxation allows us to construct an efficient emulation procedure for any two-party protocol. Our results also extend to the case of interactive multiparty communication. We show that a randomly generated tree code (with suitable constant alphabet size) is an efficiently decodable potent tree code with overwhelming probability. Furthermore we are able to partially derandomize this result by means of epsilon-biased distributions using only O(N) random bits, where N is the depth of the tree