### Abstract

We consider the problem of distributed compression of the difference *Z* = *Y*_{1} c*Y*_{2} of two jointly Gaussian sources *Y*_{1} and *Y*_{2} (with positive correlation coefficient ρ and positive *c*) under an MSE distortion constraint *D* on *Z*. The rate region for this problem is unknown. We provide a new lower bound on the minimum sum-rate by utilizing the connection of the above problem with the two-terminal source coding problem with matrix-distortion constraint. Our lower bound not only improves existing bounds in many cases, but also allows us to prove sum-rate tightness of the Berger-Tung scheme when c is either relatively small or large and *D* is larger than some threshold. Furthermore, our lower bound enables us to show that the improved lattice-based scheme recently introduced in [1] (with the smallest achievable sum-rate) performs within 1.18 b/s from the optimal sum-rate for all values of ρ, *c*, and *D*.

Original language | English |
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Title of host publication | 2011 IEEE International Symposium on Information Theory Proceedings (ISIT 2011) |

Subtitle of host publication | St. Petersburg, Russia, 31 July – 5 August 2011 |

Publisher | IEEE, Institute of Electrical and Electronics Engineers |

Pages | 2766-2770 |

Number of pages | 5 |

ISBN (Print) | 9781457705953, 9781457705960 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

Event | IEEE International Symposium on Information Theory 2011 - St. Petersburg, Russian Federation Duration: 31 Jul 2011 → 5 Aug 2011 https://www.ieee.org/conferences_events/conferences/conferencedetails/index.htm?Conf_ID=15138 |

### Conference

Conference | IEEE International Symposium on Information Theory 2011 |
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Abbreviated title | ISIT 2011 |

Country | Russian Federation |

City | St. Petersburg |

Period | 31/07/11 → 5/08/11 |

Internet address |

## Cite this

*2011 IEEE International Symposium on Information Theory Proceedings (ISIT 2011): St. Petersburg, Russia, 31 July – 5 August 2011*(pp. 2766-2770). [6034077] IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT.2011.6034077