### Abstract

Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We propose a new interactive protocol for data exchange, which increases the communication size in steps until the task is done. We also derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Our single-shot analysis applies to all discrete random variables and yields upper and lower bounds of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general source sequence, such as a mixture of independent and identically distributed (IID) random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.

Original language | English (US) |
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Pages (from-to) | 26-37 |

Number of pages | 12 |

Journal | IEEE Transactions on Information Theory |

Volume | 64 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2018 |

### Keywords

- Data exchange
- Interactive communication
- Omniscience
- Secret key agreement

### ASJC Scopus subject areas

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

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## Cite this

*IEEE Transactions on Information Theory*,

*64*(1), 26-37. https://doi.org/10.1109/TIT.2017.2769124