Interactive information complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
From information to exact communication
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Direct product via round-preserving compression
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Deterministic compression with uncertain priors
Proceedings of the 5th conference on Innovations in theoretical computer science
Direct sum fails for zero error average communication
Proceedings of the 5th conference on Innovations in theoretical computer science
| Hi-index | 0.00 |
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.