### Abstract

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.

Original language | English (US) |
---|---|

Title of host publication | Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |

Pages | 748-757 |

Number of pages | 10 |

DOIs | |

State | Published - Dec 1 2011 |

Externally published | Yes |

Event | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States Duration: Oct 22 2011 → Oct 25 2011 |

### Publication series

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

ISSN (Print) | 0272-5428 |

### Other

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

Country | United States |

City | Palm Springs, CA |

Period | 10/22/11 → 10/25/11 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)

### Keywords

- Communication Complexity
- Compression
- Direct Sum

## Fingerprint Dive into the research topics of 'Information equals amortized communication'. Together they form a unique fingerprint.

## Cite this

*Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011*(pp. 748-757). [6108245] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). https://doi.org/10.1109/FOCS.2011.86