Successive Refinement of Abstract Sources

In successive refinement of information, the decoder refines its representation of the source progressively as it receives more encoded bits. The rate-distortion region of successive refinement describes the minimum rates required to attain the target distortions at each decoding stage. In this paper, we derive a parametric characterization of the rate-distortion region for successive refinement of abstract sources. Our characterization extends Csiszar's result to successive refinement, and generalizes a result by Tuncel and Rose, applicable for finite alphabet sources, to abstract sources. This characterization spawns a family of outer bounds to the rate-distortion region. It also enables an iterative algorithm for computing the rate-distortion region, which generalizes Blahut's algorithm to successive refinement. Finally, it leads a new nonasymptotic converse bound. In all the scenarios where the dispersion is known, this bound is second-order optimal. In our proof technique, we avoid Karush-Kuhn-Tucker conditions of optimality, and we use basic tools of probability theory. We leverage the Donsker-Varadhan lemma for the minimization of relative entropy on abstract probability spaces.Comment: Extended version of a paper presented at ISIT 201

Successive Wyner-Ziv Coding Scheme and its Application to the Quadratic Gaussian CEO Problem

We introduce a distributed source coding scheme called successive Wyner-Ziv coding. We show that any point in the rate region of the quadratic Gaussian CEO problem can be achieved via the successive Wyner-Ziv coding. The concept of successive refinement in the single source coding is generalized to the distributed source coding scenario, which we refer to as distributed successive refinement. For the quadratic Gaussian CEO problem, we establish a necessary and sufficient condition for distributed successive refinement, where the successive Wyner-Ziv coding scheme plays an important role.Comment: 28 pages, submitted to the IEEE Transactions on Information Theor

Polar Codes for Distributed Hierarchical Source Coding

We show that polar codes can be used to achieve the rate-distortion functions in the problem of hierarchical source coding also known as the successive refinement problem. We also analyze the distributed version of this problem, constructing a polar coding scheme that achieves the rate distortion functions for successive refinement with side information.Comment: 14 page

Multiuser Successive Refinement and Multiple Description Coding

We consider the multiuser successive refinement (MSR) problem, where the users are connected to a central server via links with different noiseless capacities, and each user wishes to reconstruct in a successive-refinement fashion. An achievable region is given for the two-user two-layer case and it provides the complete rate-distortion region for the Gaussian source under the MSE distortion measure. The key observation is that this problem includes the multiple description (MD) problem (with two descriptions) as a subsystem, and the techniques useful in the MD problem can be extended to this case. We show that the coding scheme based on the universality of random binning is sub-optimal, because multiple Gaussian side informations only at the decoders do incur performance loss, in contrast to the case of single side information at the decoder. We further show that unlike the single user case, when there are multiple users, the loss of performance by a multistage coding approach can be unbounded for the Gaussian source. The result suggests that in such a setting, the benefit of using successive refinement is not likely to justify the accompanying performance loss. The MSR problem is also related to the source coding problem where each decoder has its individual side information, while the encoder has the complete set of the side informations. The MSR problem further includes several variations of the MD problem, for which the specialization of the general result is investigated and the implication is discussed.Comment: 10 pages, 5 figures. To appear in IEEE Transaction on Information Theory. References updated and typos correcte

The rate-distortion function for successive refinement of abstract sources

In successive refinement of information, the decoder refines its representation of the source progressively as it receives more encoded bits. The rate-distortion region of successive refinement describes the minimum rates required to attain the target distortions at each decoding stage. In this paper, we derive a parametric characterization of the rate-distortion region for successive refinement of abstract sources. Our characterization extends Csiszar's result [1] to successive refinement, and generalizes a result by Tuncel and Rose [2], applicable for finite alphabet sources, to abstract sources. The new characterization leads to a family of outer bounds to the rate-distortion region. It also enables new nonasymptotic converse bounds

Distortion Minimization in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.Comment: Accepted for publication in IEEE Transactions on Information Theor