A new sufficient condition for sum-rate tightness of quadratic Gaussian MT source coding
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This work considers the quadratic Gaussian multiterminal source coding problem and provides a new sufficient condition for the Berger-Tung sum-rate bound to be tight. The converse proof utilizes a generalized CEO problem where the observation noises are correlated Gaussian with a block-diagonal covariance matrix. First, the given multiterminal source coding problem is related to a set of two-terminal problems with matrix distortion constraints, for which a new lower bound on the sum-rate is given. Then, a convex optimization problem is formulated and a sufficient condition derived for the optimal BT scheme to satisfy the subgradient based Karush-Kuhn-Tucker condition. The set of sum-rate tightness problems defined by our new sufficient condition subsumes all previously known tight cases, and opens new direction for a more general partial solution.
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2010 Information Theory and Applications Workshop (ITA)