2011/09/25 by Neri Merhav, Merhav, Neri
Computer Science · Engineering · Physics and Astronomy · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques #Statistical Mechanics and Entropy #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1109.5351
openalex publication_date 2011/09/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We study data processing inequalities that are derived from a certain class\nof generalized information measures, where a series of convex functions and\nmultiplicative likelihood ratios are nested alternately. While these\ninformation measures can be viewed as a special case of the most general\nZakai-Ziv generalized information measure, this special nested structure calls\nfor attention and motivates our study. Specifically, a certain choice of the\nconvex functions leads to an information measure that extends the notion of the\nBhattacharyya distance (or the Chernoff divergence): While the ordinary\nBhattacharyya distance is based on the (weighted) geometric mean of two\nreplicas of the channel's conditional distribution, the more general\ninformation measure allows an arbitrary number of such replicas. We apply the\ndata processing inequality induced by this information measure to a detailed\nstudy of lower bounds of parameter estimation under additive white Gaussian\nnoise (AWGN) and show that in certain cases, tighter bounds can be obtained by\nusing more than two replicas. While the resulting lower bound may not compete\nfavorably with the best bounds available for the ordinary AWGN channel, the\nadvantage of the new lower bound, relative to the other bounds, becomes\nsignificant in the presence of channel uncertainty, like unknown fading. This\ndifferent behavior in the presence of channel uncertainty is explained by the\nconvexity property of the information measure.\n