TY - JOUR

T1 - Successive refinement of vector sources under individual distortion criteria

AU - Nayak, Jayanth

AU - Tuncel, Ertem

AU - Gündüz, Deniz

AU - Erkip, Elza

N1 - Funding Information:
Manuscript received August 19, 2008; revised September 01, 2009. Current version published March 17, 2010. This work was supported in part by the National Science Foundation under Grant CNS-06-35177. The material in this paper was presented in part at the Information Theory Workshop, Lake Tahoe, CA, September 2007.

PY - 2010/4

Y1 - 2010/4

N2 - The successive refinement problem is extended to vector sources where individual distortion constraints are posed on each vector component. For vector Gaussian sources with squared-error distortion, a single-letter rate-distortion characterization is inherited from the previously studied Gaussian multiple descriptions problem with covariance distortion constraints. Though this characterization is amenable to well-known numerical convex optimization techniques, an analytical solution is difficult to obtain in full generality even for 2-D sources. In this work, the special case of successive refinability is addressed analytically. Specifically, vector Gaussian sources are shown to be not successively refinable everywhere unlike scalar Gaussian sources. It is also shown that, for 2-D Gaussian sources, the rate loss at the second stage can be as high as 0.5 b/sample in a degenerate scenario corresponding to what is known as sequential coding of correlated sources. Finally, analysis of 2-D binary symmetric sources with Hamming distortion reveals that the behavior of these sources with respect to successive refinability exhibits remarkable similarity to their 2-D Gaussian counterparts.

AB - The successive refinement problem is extended to vector sources where individual distortion constraints are posed on each vector component. For vector Gaussian sources with squared-error distortion, a single-letter rate-distortion characterization is inherited from the previously studied Gaussian multiple descriptions problem with covariance distortion constraints. Though this characterization is amenable to well-known numerical convex optimization techniques, an analytical solution is difficult to obtain in full generality even for 2-D sources. In this work, the special case of successive refinability is addressed analytically. Specifically, vector Gaussian sources are shown to be not successively refinable everywhere unlike scalar Gaussian sources. It is also shown that, for 2-D Gaussian sources, the rate loss at the second stage can be as high as 0.5 b/sample in a degenerate scenario corresponding to what is known as sequential coding of correlated sources. Finally, analysis of 2-D binary symmetric sources with Hamming distortion reveals that the behavior of these sources with respect to successive refinability exhibits remarkable similarity to their 2-D Gaussian counterparts.

KW - Individual distortion criteria

KW - Rate loss

KW - Successive refinement

KW - Vector sources

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U2 - 10.1109/TIT.2010.2040858

DO - 10.1109/TIT.2010.2040858

M3 - Article

AN - SCOPUS:77950210110

SN - 0018-9448

VL - 56

SP - 1769

EP - 1781

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 4

M1 - 5437437

ER -