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A New Sufficient Condition for Sum-Rate Tightness in Quadratic Gaussian Multiterminal Source Coding

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3 Author(s)
Yang Yang ; Dept. of Electr. & Comput. Eng., Texas A&M Univ., College Station, TX, USA ; Yifu Zhang ; Zixiang Xiong

This paper considers the quadratic Gaussian multiterminal (MT) source coding problem and provides a new sufficient condition for the Berger-Tung (BT) sum-rate bound to be tight. The converse proof utilizes a set of virtual remote sources given which the observed sources are block independent with a maximum block size of 2. The given MT source coding problem is then related to a set of two-terminal problems with matrix-distortion constraints, for which a new lower bound on the sum-rate is given. By formulating a convex optimization problem over all distortion matrices, a sufficient condition is derived for the optimal BT scheme to satisfy the subgradient-based Karush-Kuhn-Tucker condition. The subset of the quadratic Gaussian MT problem satisfying our new sufficient condition subsumes all previously known tight cases, and our proof technique opens a new direction for more general partial solutions.

Published in:

IEEE Transactions on Information Theory  (Volume:59 ,  Issue: 1 )