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Coding for Interactive Communication \Lambda Leonard J. Schulman

Summary: Coding for Interactive Communication \Lambda
Leonard J. Schulman
Computer Science Division
U. C. Berkeley
Let the input to a computation problem be split between two processors connected by a commu­
nication link; and let an interactive protocol ß 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
effect 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 tradeoff in communications equipment between bandwidth, reliability
and expense.
We treat a model with random channel noise. We describe a deterministic method for simulating
noiseless­channel protocols on noisy channels, with only a constant slow­down. This is an analog for
general interactive protocols of Shannon's coding theorem, which deals only with data transmission, i.e.
one­way 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.


Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology


Collections: Computer Technologies and Information Sciences