Coding for interactive communication

Let the input to a computation problem be split between two processors connected by a commu nication link and let an interactive protocol be known by which on any input the processors can solve the problem using no more than T transmissions of bits between them provided the channel is noiseless in each direction We study the following question if in fact the channel is noisy what is the e ect upon the number of transmissions needed in order to solve the computation problem reliably Technologically this concern is motivated by the increasing importance of communication as a re source in computing and by the tradeo in communications equipment between bandwidth reliability and expense We treat a model with random channel noise We describe a deterministic method for simulating noiseless channel protocols on noisy channels with only a constant slow down This is an analog for general interactive protocols of Shannon s coding theorem which deals only with data transmission i e one way protocols We cannot use Shannon s block coding method because the bits exchanged in the protocol are determined only one at a time dynamically in the course of the interaction Instead we describe a simulation protocol using a new kind of code explicit tree codes