Vector Gaussian Multiple Description With Two Levels of Receivers

• Published in: IEEE transactions on information theory Vol. 55; no. 1; pp. 401 - 410
• Main Authors: Hua Wang, Viswanath, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Binning; Communication channels; Communications networks; Constraint theory; Counters; Covariance matrix; Decoding; Derivation; Distortion; Distortion measurement; Exact sciences and technology; Gaussian; Gaussian source; Information science; Information theory; Information, signal and communications theory; inner bound; Mathematical analysis; multiple description problem; Normal distribution; outer bound; Problem solving; Quality of service; Rate-distortion; Receivers; Receivers & amplifiers; Reconstruction; Sampling, quantization; Signal and communications theory; Source coding; Symmetric matrices; Telecommunications and information theory; Vectors (mathematics); inner bound; rate distortion; Binning; Vector quantization; outer bound; Gaussian source; Rate distortion theory; Ergodicity; multiple description problem
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2008.2008146

The problem of L multiple descriptions of a stationary and ergodic Gaussian source with two levels of receivers is investigated. Each of the first-level receivers receive (an arbitrary subset) k of the L descriptions,(k<L). The second-level receiver receives all L descriptions. All the receivers, both at the first level and the second level, reconstruct the source using the subset of descriptions they receive. The corresponding reconstructions are subject to quadratic distortion constraints. Our main result is the derivation of an outer bound on the sum rate of the descriptions so that the distortion constraints are met. We show that an analog-digital separation architecture involving joint Gaussian vector quantizers and a binning scheme meets this outer bound with equality for several scenarios. These scenarios include the case when the distortion constraints are symmetric and the case for general distortion constraints with k=2 and L=3.