Rounds in communication complexity revisited
SIAM Journal on Computing
Amortized Communication Complexity
SIAM Journal on Computing
Communication complexity
The communication complexity of pointer chasing
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
An Information Statistics Approach to Data Stream and Communication Complexity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A property of quantum relative entropy with an application to privacy in quantum communication
Journal of the ACM (JACM)
Communication lower bounds via the chromatic number
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
How to compress interactive communication
Proceedings of the forty-second ACM symposium on Theory of computing
The communication complexity of correlation
IEEE Transactions on Information Theory
An Optimal Randomized Cell Probe Lower Bound for Approximate Nearest Neighbor Searching
SIAM Journal on Computing
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
Interactive information complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Direct sum fails for zero error average communication
Proceedings of the 5th conference on Innovations in theoretical computer science
Choosing, Agreeing, and Eliminating in Communication Complexity
Computational Complexity
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We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti et al. [CSWY01] and refined further by Bar-Yossef et al. [BJKS02]. Our main technical result is a 'compression' theorem saying that, for any probability distribution µ over the inputs, a k-round private coin bounded error protocol for a function f with information cost c can be converted into a k-round deterministic protocol for f with bounded distributional error and communication cost O(kc). We prove this result using a Substate Theorem about relative entropy and a rejection sampling argument. Our direct sum result follows from this 'compression' result via elementary information theoretic arguments. We also consider the direct sum problem in quantum communication. Using a probabilistic argument, we show that messages cannot be compressed in this manner even if they carry small information.