A Direct Sum Theorem in Communication Complexity via Message Compression

We prove lower bounds for the direct sum problem for two-party bounded error randomised multipleround 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 probabilitydistribution£ over the inputs, a ¤ -round private coin bounded error protocol for a function ¥ with information cost ¦ can be converted into a ¤ round deterministic protocol for ¥ with bounded distributionalerror and communication cost §©¨¤¦ . 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 probabilisticargument, we show that messages cannot be compressed in this man...

• Type: Conference
• Year: 2003
• Where: ICALP
• Authors: Rahul Jain, Jaikumar Radhakrishnan, Pranab Sen
• Keywords: Direct Sum Problem, Et Al, ICALP 2003, Theoretical Computer Science, Two-party Bounded Error