n-channel entropy-constrained multiple-description lattice vector quantization

• Published in: IEEE transactions on information theory Vol. 52; no. 5; pp. 1956 - 1973
• Main Authors: Ostergaard, J., Jensen, J., Heusdens, R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Centralized control; Coding, codes; Communication channels; Counters; Data compression; Descriptions; Distortion; Entropy; Exact sciences and technology; High-rate quantization; Information systems; Information, signal and communications theory; lattice quantization; Lattices; Materials science and technology; Mathematical analysis; Mathematical models; multiple-description coding (MDC); Numerical simulation; Packet switched networks; Probability; Sampling, quantization; Signal and communications theory; Simulation; Source coding; Switching and signalling; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Vector quantization; Performance evaluation; Packet switching; State of the art; High resolution; Vector quantization; Redundancy; Data compression; Two channel system; Loss rate; Data transmission; n channel; Entropy; multiple-description coding (MDC); Analytical method; Numerical simulation; Quantifier; Transmission loss; Multiple channel; lattice quantization; High-rate quantization
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2006.872847

In this paper, we derive analytical expressions for the central and side quantizers which, under high-resolution assumptions, minimize the expected distortion of a symmetric multiple-description lattice vector quantization (MD-LVQ) system subject to entropy constraints on the side descriptions for given packet-loss probabilities. We consider a special case of the general n-channel symmetric multiple-description problem where only a single parameter controls the redundancy tradeoffs between the central and the side distortions. Previous work on two-channel MD-LVQ showed that the distortions of the side quantizers can be expressed through the normalized second moment of a sphere. We show here that this is also the case for three-channel MD-LVQ. Furthermore, we conjecture that this is true for the general n-channel MD-LVQ. For given source, target rate, and packet-loss probabilities we find the optimal number of descriptions and construct the MD-LVQ system that minimizes the expected distortion. We verify theoretical expressions by numerical simulations and show in a practical setup that significant performance improvements can be achieved over state-of-the-art two-channel MD-LVQ by using three-channel MD-LVQ.