A coding theorem for distributed computation

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 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 degree d having noiseless communication channels, can, if the channels are in fact noisy (each a binary symmetric channel of capacity C), be simulated on that network in time propo...

• Type: Conference
• Year: 1994
• Where: STOC
• Authors: Sridhar Rajagopalan, Leonard J. Schulman
• Keywords: Algorithms, Coding Theorem, Noisy Communication Channel, Shannon's Coding Theorem, STOC 1994