A Candidate for a Strong Separation of Information and Communication

Abstract

The weak interactive compression conjecture asserts that any two-party communication protocol with communication complexity C and information complexity I can be compressed to a protocol with communication complexity poly(I)polylog(C). We describe a communication problem that is a candidate for refuting that conjecture. Specifically, while we show that the problem can be solved by a protocol with communication complexity C and information complexity I=polylog(C), the problem seems to be hard for protocols with communication complexity poly(I)polylog(C)=polylog(C).