Speaker Mark Braverman
Host Jennifer Chayes
Affiliation University of Toronto
Date recorded 10 February 2011
Notions of entropy and information, pioneered by Shannon, have been very powerful tools in coding theory. Coding theory aims to solve the problem of one-way communication: sending a message from Alice to Bob using as little communication as possible, sometimes over a noisy channel.
Communication complexity aims to solve the problem of two-way communication: Alice and Bob aim to implement a functionality f that depends on both parties’ inputs. We will discuss several extensions of information-theoretic notions to the two-way communication setting. We use them to prove a direct sum theorem for randomized communication complexity, showing that implementing k copies of a functionality requires substantially more communication than just one copy, partially settling a long-standing open problem.
More generally, we will show that information cost I(f) can be defined as a natural fundamental property of a functionality f. We will describe several new tight connections between I(f), direct sum theorems, interactive compression schemes, and amortized communication complexity.
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