On Multistage Successive Refinement for Wyner-Ziv Source Coding with Degraded Side Informations

Chao Tian; Suhas Diggavi

Home/Archive/arXiv

arXiv · cs/0605001

On Multistage Successive Refinement for Wyner-Ziv Source Coding with Degraded Side Informations

Chao Tian·Suhas Diggavi

View original source ↗Read source document ↗Export metadata ↓

Abstract

We provide a complete characterization of the rate-distortion region for the multistage successive refinement of the Wyner-Ziv source coding problem with degraded side informations at the decoder. Necessary and sufficient conditions for a source to be successively refinable along a distortion vector are subsequently derived. A source-channel separation theorem is provided when the descriptions are sent over independent channels for the multistage case. Furthermore, we introduce the notion of generalized successive refinability with multiple degraded side informations. This notion captures whether progressive encoding to satisfy multiple distortion constraints for different side informations is as good as encoding without progressive requirement. Necessary and sufficient conditions for generalized successive refinability are given. It is shown that the following two sources are generalized successively refinable: (1) the Gaussian source with degraded Gaussian side informations, (2) the doubly symmetric binary source when the worse side information is a constant. Thus for both cases, the failure of being successively refinable is only due to the inherent uncertainty on which side information will occur at the decoder, but not the progressive encoding requirement.

Explore related subjects

cs.IT math.IT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Chao Tian, Suhas Diggavi. 2006-05-02. On Multistage Successive Refinement for Wyner-Ziv Source Coding with Degraded Side Informations. https://arxiv.org/abs/cs/0605001

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bistatic Target Detection by Exploiting Both Deterministic Pilots and Unknown Random Data Payloads

Integrated sensing and communication (ISAC) plays a crucial role in 6G, to enable innovative applications such as drone surveillance, urban air mobility, and low-altitude logistics. However, the hybrid ISAC signal, which comprises deterministic pilot and random data payload components, poses challenges for target detection due to two reasons: 1) these two components cause coupled shifts in both the mean and variance of the received signal, and 2) the random data payloads are typically unknown to the sensing receiver in the bistatic setting. Unfortunately, these challenges could not be tackled by existing target detection algorithms. In this paper, a generalized likelihood ratio test (GLRT)-based detector is derived, by leveraging the known deterministic pilots and the statistical characteristics of the unknown random data payloads. Due to the analytical intractability of exact performance characterization, we perform an asymptotic analysis for the false alarm probability and detection probability of the proposed detector. The results highlight a critical trade-off: both deterministic and random components improve detection reliability, but the latter also brings statistical uncertainty that hinders detection performance. Simulations validate the theoretical findings and demonstrate the effectiveness of the proposed detector, which highlights the necessity of designing a dedicated detector to fully exploited the signaling resources assigned to random data payloads.

cs.IT↗

arXiv2026

On Unbiased Parameter Estimation and Signal Reconstruction

In this paper, we extend the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction for an arbitrary number of non-zero parameters. The topic touches on exact reconstructibility, most commonly studied in compressed sensing and multisource estimation across various imaging problems. The theoretical results derive upper bounds on the number of recoverable parameters in the noiseless case, and define a probability measure to assess the likelihood of recovering all non-zero parameters with correct magnitude order. The work provides a mathematical explanation of the open question regarding the noise robustness of standardized and unbiased methods. The paper also reveals a trade-off between the number of sensors and the signal-to-noise ratio. Numerical experiments demonstrate the theoretical findings.

cs.IT↗

arXiv2026

Minimum enclosing Bregman balls made easy

In this work, we revisit the problem of computing minimum enclosing Bregman balls (Bregman MEBs) of finite sets of parameters. First, we show that Bregman MEBs are equivalent to MEBs of corresponding weighted point sets with respect to the power distance. We then report an efficient Frank--Wolfe $(1+ε)$-approximation algorithm for computing power MEBs, for any $ε>0$. This power MEB approximation algorithm coincides with the Bregman MEB approximation algorithm of Nock and Nielsen (2005) when expressed in the dual gradient space. Finally, we show that the Bregman potential lifting transforms used to construct Bregman Voronoi diagrams can be reinterpreted as the classical paraboloid lifting transform applied to corresponding weighted point sets. In particular, Bregman MEB circumcenters lie on the farthest Bregman Voronoi diagrams or equivalently on the corresponding farthest power diagrams.

cs.IT↗