### Abstract

We characterize second-order coding rates (or dispersions) for distributed lossless source coding (the Slepian-Wolf problem). We introduce a fundamental quantity known as the entropy dispersion matrix, which is analogous to scalar dispersion quantities. We show that if this matrix is positive-definite, the optimal rate region under the constraint of a fixed blocklength and non-zero error probability has a curved boundary compared to being polyhedral for the Slepian-Wolf case. In addition, the entropy dispersion matrix governs the rate of convergence of the non-asymptotic region to the asymptotic one. As a by-product of our analyses, we develop a general universal achievability procedure for dispersion analysis of some other network information theory problems such as the multiple-access channel. Numerical examples show how the region given by Gaussian approximations compares to the Slepian-Wolf region.

Original language | English (US) |
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Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Pages | 915-919 |

Number of pages | 5 |

DOIs | |

State | Published - 2012 |

Externally published | Yes |

Event | 2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States Duration: Jul 1 2012 → Jul 6 2012 |

### Other

Other | 2012 IEEE International Symposium on Information Theory, ISIT 2012 |
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Country | United States |

City | Cambridge, MA |

Period | 7/1/12 → 7/6/12 |

### Fingerprint

### Keywords

- Dispersion
- Second-order Rates
- Slepian-Wolf

### ASJC Scopus subject areas

- Applied Mathematics
- Modeling and Simulation
- Theoretical Computer Science
- Information Systems

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*(pp. 915-919). [6284695] https://doi.org/10.1109/ISIT.2012.6284695

**The dispersion of Slepian-Wolf coding.** / Tan, Vincent Y F; Kosut, Oliver.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE International Symposium on Information Theory - Proceedings.*, 6284695, pp. 915-919, 2012 IEEE International Symposium on Information Theory, ISIT 2012, Cambridge, MA, United States, 7/1/12. https://doi.org/10.1109/ISIT.2012.6284695

}

TY - GEN

T1 - The dispersion of Slepian-Wolf coding

AU - Tan, Vincent Y F

AU - Kosut, Oliver

PY - 2012

Y1 - 2012

N2 - We characterize second-order coding rates (or dispersions) for distributed lossless source coding (the Slepian-Wolf problem). We introduce a fundamental quantity known as the entropy dispersion matrix, which is analogous to scalar dispersion quantities. We show that if this matrix is positive-definite, the optimal rate region under the constraint of a fixed blocklength and non-zero error probability has a curved boundary compared to being polyhedral for the Slepian-Wolf case. In addition, the entropy dispersion matrix governs the rate of convergence of the non-asymptotic region to the asymptotic one. As a by-product of our analyses, we develop a general universal achievability procedure for dispersion analysis of some other network information theory problems such as the multiple-access channel. Numerical examples show how the region given by Gaussian approximations compares to the Slepian-Wolf region.

AB - We characterize second-order coding rates (or dispersions) for distributed lossless source coding (the Slepian-Wolf problem). We introduce a fundamental quantity known as the entropy dispersion matrix, which is analogous to scalar dispersion quantities. We show that if this matrix is positive-definite, the optimal rate region under the constraint of a fixed blocklength and non-zero error probability has a curved boundary compared to being polyhedral for the Slepian-Wolf case. In addition, the entropy dispersion matrix governs the rate of convergence of the non-asymptotic region to the asymptotic one. As a by-product of our analyses, we develop a general universal achievability procedure for dispersion analysis of some other network information theory problems such as the multiple-access channel. Numerical examples show how the region given by Gaussian approximations compares to the Slepian-Wolf region.

KW - Dispersion

KW - Second-order Rates

KW - Slepian-Wolf

UR - http://www.scopus.com/inward/record.url?scp=84867527299&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867527299&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2012.6284695

DO - 10.1109/ISIT.2012.6284695

M3 - Conference contribution

SN - 9781467325790

SP - 915

EP - 919

BT - IEEE International Symposium on Information Theory - Proceedings

ER -