### Abstract

Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical distance of the joint distribution of the input and the transcript of the original protocol? We present an information spectrum approach for this problem whereby the information complexity of the protocol is replaced by its information complexity density. Our single-shot bounds relate the communication complexity of simulating a protocol to tail bounds for information complexity density. As a consequence, we obtain a strong converse and characterize the second-order asymptotic term in communication complexity for independent and identically distributed observation sequences. Furthermore, we obtain a general formula for the rate of communication complexity, which applies to any sequence of observations and protocols. Connections with results from theoretical computer science and implications for the function computation problem are discussed.

Original language | English (US) |
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Article number | 8022868 |

Pages (from-to) | 6979-7002 |

Number of pages | 24 |

Journal | IEEE Transactions on Information Theory |

Volume | 63 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2017 |

### Keywords

- Compression of protocols
- Information complexity
- Interactive communication
- 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*,

*63*(11), 6979-7002. [8022868]. https://doi.org/10.1109/TIT.2017.2746859