Information equals amortized communication

Mark Braverman, Anup Rao

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

We show how to efficiently simulate the sending of a single message \(M\) to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information that the message reveals to the receiver. This is a generalization and strengthening of the Slepian-Wolf theorem, which shows how to carry out such a simulation with low amortized communication in the case that \(M\) is a deterministic function of \(X\). A caveat is that our simulation is interactive. As a consequence, we prove that the internal information cost (namely the information revealed to the parties) involved in computing any relation or function using a two party interactive protocol is exactly equal to the amortized communication complexity of computing independent copies of the same relation or function. We also show that the only way to prove a strong direct sum theorem for randomized communication complexity is by solving a particular variant of the pointer jumping problem that we define. This paper implies that a strong direct sum theorem for communication complexity holds if and only if efficient compression of communication protocols is possible. In particular, together with our result, a recent result of Ganor, Kol, and Raz implies that the strongest version of direct sum for randomized communication complexity is false.

Original languageEnglish (US)
Article number6877708
Pages (from-to)6058-6069
Number of pages12
JournalIEEE Transactions on Information Theory
Volume60
Issue number10
DOIs
StatePublished - Oct 1 2014

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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