2014/04/28 by Thomas A. Courtade, Jiantao Jiao, Courtade, Thomas +1 · 1 citation
Engineering · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1404.6984
openalex publication_date 2014/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X,Y be jointly Gaussian vectors, and consider random variables U,V that satisfy the Markov constraint U-X-Y-V. We prove an extremal inequality relating the mutual informations between all 4 \choose 2 pairs of random variables from the set (U,X,Y,V). As a first application, we show that the rate region for the two-encoder quadratic Gaussian source coding problem follows as an immediate corollary of the the extremal inequality. In a second application, we establish the rate region for a vector-Gaussian source coding problem where Löwner-John ellipsoids are approximated based on rate-constrained descriptions of the data.