TY - GEN

T1 - Information equals amortized communication

AU - Braverman, Mark

AU - Rao, Anup

PY - 2011

Y1 - 2011

N2 - We show how to efficiently simulate the sending of a message 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 who has some information about the message. 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 the message is a deterministic function of an input. 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. Our work implies that a strong direct sum theorem for communication complexity holds if and only if efficient compression of communication protocols is possible.

AB - We show how to efficiently simulate the sending of a message 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 who has some information about the message. 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 the message is a deterministic function of an input. 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. Our work implies that a strong direct sum theorem for communication complexity holds if and only if efficient compression of communication protocols is possible.

KW - Communication Complexity

KW - Compression

KW - Direct Sum

UR - http://www.scopus.com/inward/record.url?scp=84863322607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863322607&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2011.86

DO - 10.1109/FOCS.2011.86

M3 - Conference contribution

AN - SCOPUS:84863322607

SN - 9780769545714

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 748

EP - 757

BT - Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011

T2 - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011

Y2 - 22 October 2011 through 25 October 2011

ER -