New Proofs of Extremal Inequalities With Applications

2021/09/01 by Xu, Yinfei, Chen, Guojun
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2109.00377

Abstract

The extremal inequality approach plays a key role in network information theory problems. In this paper, we propose a novel monotone path construction in product probability space. The optimality of Gaussian distribution is then established by standard perturbation arguments. The proofs of Liu-Viswanath extremal and vector Generalization of Costa's entropy power inequality are illustrated into the unified framework. As applications, capacity region of the multiple-input multiple-output (MIMO) Gaussian broadcast channel and rate-distortion-equivocation function of the vector Gaussian secure source coding are revisited through our proposed extremal inequality approach.

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