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Summary: A Coding Theorem for Distributed Computation
Sridhar Rajagopalan \Lambda Leonard J. Schulman y
University of California, Berkeley.
Abstract
Shannon's Coding Theorem shows that in order to reliably
transmit a message of T bits over a noisy communication
channel, only a constant slowdown factor is necessary in the
case when the channel is noisy, relative to the case in which
the channel is noiseless. (The time required is asymptotically
T 1
C , where 0 ! C Ÿ 1 is the ``Shannon capacity'', a function
only of the noise characteristics.) The theorem ensures that
the probability of a decoding error is exponentially small in
the message length T . Recently the second author obtained
an analogous result for arbitrary interactive communication
protocols between two processors.
In the present paper we provide a coding theorem for all
distributed protocols on static topology networks. We prove
that any protocol which runs in time T on a network of de
gree d having noiseless communication channels, can, if the
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