Coding for interactive communication
Schulman, L.J.
Information Theory, IEEE Transactions on
Volume 42, Issue 6, Nov 1996 Page(s):1745 - 1756
Digital Object Identifier 10.1109/18.556671
Summary:Let the input to a computation problem be split between two
processors connected by a communication link; and let an interactive
protocol π 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 resource 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
noiseless-channel 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.,
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
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