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Improved bounds for the rate loss of multiresolution source codes

Feng, Hanying and Effros, Michelle (2003) Improved bounds for the rate loss of multiresolution source codes. IEEE Transactions on Information Theory, 49 (4). pp. 809-821. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:FENieeetit03

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Abstract

We present new bounds for the rate loss of multiresolution source codes (MRSCs). Considering an M-resolution code, the rate loss at the ith resolution with distortion D/sub i/ is defined as L/sub i/=R/sub i/-R(D/sub i/), where R/sub i/ is the rate achievable by the MRSC at stage i. This rate loss describes the performance degradation of the MRSC compared to the best single-resolution code with the same distortion. For two-resolution source codes, there are three scenarios of particular interest: (i) when both resolutions are equally important; (ii) when the rate loss at the first resolution is 0 (L/sub 1/=0); (iii) when the rate loss at the second resolution is 0 (L/sub 2/=0). The work of Lastras and Berger (see ibid., vol.47, p.918-26, Mar. 2001) gives constant upper bounds for the rate loss of an arbitrary memoryless source in scenarios (i) and (ii) and an asymptotic bound for scenario (iii) as D/sub 2/ approaches 0. We focus on the squared error distortion measure and (a) prove that for scenario (iii) L/sub 1/<1.1610 for all D/sub 2/<0.7250; (c) tighten the Lastras-Berger bound for scenario (i) from L/sub i//spl les/1/2 to L/sub i/<0.3802, i/spl isin/{1,2}; and (d) generalize the bounds for scenarios (ii) and (iii) to M-resolution codes with M/spl ges/2. We also present upper bounds for the rate losses of additive MRSCs (AMRSCs). An AMRSC is a special MRSC where each resolution describes an incremental reproduction and the kth-resolution reconstruction equals the sum of the first k incremental reproductions. We obtain two bounds on the rate loss of AMRSCs: one primarily good for low-rate coding and another which depends on the source entropy.


Item Type:Article
Additional Information:“©2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received April 4, 2002; revised November 8, 2002. This work was supported in part by the National Science Foundation under Grant CCR-9909026 and in part by the Caltech’s Lee Center for Advanced Networking. The material in this paperwas presented in part at the IEEE International Symposium on Information Theory (ISIT), Washington, DC, June, 2001. Communicated by R. Zamir, Associate Editor for Source Coding. The authors are grateful to the Associate Editor and anonymous reviewers for their detailed suggestions and comments; in particular, Lemma 3 and the current improved result in Theorem 10 result from their insights.
Subject Keywords:Additive successive refinement code, progressive transmission, tree-structured vector quantizer, source coding theory, network information theory
Record Number:CaltechAUTHORS:FENieeetit03
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:FENieeetit03
Alternative URL:http://dx.doi.org/10.1109/TIT.2003.809604
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1180
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:02 Jan 2006
Last Modified:26 Dec 2012 08:43

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