### Abstract

In this paper we show tightness of the Berger-Tung (BT) sumrate bound for a new class of quadratic Gaussian multiterminal (MT) source coding problems dubbed bi-eigen equal-variance with equal distortion (BEEV-ED), where the L X L source covariance matrix has equal diagonal elements with two distinct eigenvalues, and the L target distortions are equal. Let K(K < L) be the number of larger eigenvalues, the BEEV covariance structure allows us to connect K i.i.d virtual Gaussian sources with the L given MT sources via an LXK semiorthogonal transform whose rows have equal Euclidean norm plus additive i.i.d. Gaussian noises, resulting in the two sets of sources being mutually conditional i.i.d. By relating the given MT source coding problem to a generalized Gaussian CEO problem with the K virtual sources as remote sources and the L MT sources as observations, we obtain a lower bound on the MT sum-rate, and show its achievability by BT schemes under the equal distortion constraints. Our BEEV-ED class of quadratic Gaussian MT source coding problems subsumes both the positive-symmetric case considered by Wagner et al. and the negative-symmetric case. Other examples, including a subclass of sources with BE circulant symmetric covariance matrices and equal distortion constraints, are also provided to highlight tightness of the sum-rate bound.

Original language | English |
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Title of host publication | 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 |

Subtitle of host publication | Monticello, Illinois, USA, September 30 - October 2, 2009 |

Publisher | IEEE, Institute of Electrical and Electronics Engineers |

Pages | 1554-1561 |

Number of pages | 8 |

ISBN (Print) | 9781424458714, 9781424458707 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States of America Duration: 30 Sep 2009 → 2 Oct 2009 |

### Conference

Conference | 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 |
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Country | United States of America |

City | Monticello, IL |

Period | 30/09/09 → 2/10/09 |

### Cite this

*2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009: Monticello, Illinois, USA, September 30 - October 2, 2009*(pp. 1554-1561). [5394491; FrA5.5] IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ALLERTON.2009.5394491