The conventional enhancement-and-perturbation approach to establishing gaussian extremal inequalities is refined via a novel monotone path argument in the product probability space. This refined approach is illustrate...
详细信息
The conventional enhancement-and-perturbation approach to establishing gaussian extremal inequalities is refined via a novel monotone path argument in the product probability space. This refined approach is illustrated with simplified/corrected proofs of the Liu-Viswanath extremal inequality and a vector generalization of Costa's entropy power inequality. The power of this refinement is further demonstrated by characterizing two information-theoretic limits, namely, the capacity region of the multiple-input multiple-output (MIMO) gaussian broadcast channel with private and common messages and the rate-distortion-equivocation function of vectorgaussian secure sourcecoding, which have previously resisted the attack of the conventional approach.
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