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

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

Event Systems and Access Control

We consider the interpretations of notions of access control (permissions, interdictions, obligations, and user rights) as run-time properties of information systems specified as event systems with fairness. We give proof rules for verifying that an access control policy is enforced in a system, and consider preservation of access control by refinement of event systems. In particular, refinement of user rights is non-trivial; we propose to combine low-level user rights and system obligations to implement high-level user rights

On rate-distortion with mixed types of side information

In this correspondence, we consider rate-distortion examples in the presence of side information. For a system with some side information known at both the encoder and decoder, and some known only at the decoder, we evaluate the rate distortion function for both Gaussian and binary sources. While the Gaussian example is a straightforward generalization of the corresponding result by Wyner, the binary example proves more difficult and is solved using a multidimensional optimization approach. Leveraging the insights gained from the binary example, we then solve the more complicated binary Heegard and Berger problem of decoding when side information may be present. The results demonstrate the existence of a new type of successive refinement in which the refinement information is decoded together with side information that is not available for the initial description

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

Side-information Scalable Source Coding

The problem of side-information scalable (SI-scalable) source coding is considered in this work, where the encoder constructs a progressive description, such that the receiver with high quality side information will be able to truncate the bitstream and reconstruct in the rate distortion sense, while the receiver with low quality side information will have to receive further data in order to decode. We provide inner and outer bounds for general discrete memoryless sources. The achievable region is shown to be tight for the case that either of the decoders requires a lossless reconstruction, as well as the case with degraded deterministic distortion measures. Furthermore we show that the gap between the achievable region and the outer bounds can be bounded by a constant when square error distortion measure is used. The notion of perfectly scalable coding is introduced as both the stages operate on the Wyner-Ziv bound, and necessary and sufficient conditions are given for sources satisfying a mild support condition. Using SI-scalable coding and successive refinement Wyner-Ziv coding as basic building blocks, a complete characterization is provided for the important quadratic Gaussian source with multiple jointly Gaussian side-informations, where the side information quality does not have to be monotonic along the scalable coding order. Partial result is provided for the doubly symmetric binary source with Hamming distortion when the worse side information is a constant, for which one of the outer bound is strictly tighter than the other one.Comment: 35 pages, submitted to IEEE Transaction on Information Theor

Plumbophyllite, a new species from the Blue Bell claims near Baker, San Bernardino County, California

The new mineral plumbophyllite, Pb2Si4O10·H2O, orthorhombic with space group Pbcn and cell parameters a = 13.2083(4), b = 9.7832(3), c = 8.6545(2) Å, V = 1118.33(5) Å^3, and Z = 4. It occurs as colorless to pale blue prismatic crystals to 3 mm, with wedge-shaped terminations at the Blue Bell claims, about 11 km west of Baker, San Bernardino County, California. It is found in narrow veins in a highly siliceous hornfels in association with cerussite, chrysocolla, fluorite, goethite, gypsum, mimetite, opal, plumbotsumite, quartz, sepiolite, and wulfenite. The streak is white, the luster is vitreous, the Mohs hardness is about 5, and there is one perfect cleavage, {100}. The measured density is 3.96(5) g/cm^3 and the calculated density is 3.940 g/cm^3. Optical properties (589 nm): biaxial (+), {alpha} = 1.674(2), β = 1.684(2), {gamma} = 1.708(2), 2V = 66(2)°, dispersion r > v (strong); X = b, Y = c, Z = a. Electron microprobe analysis provided PbO 60.25, CuO 0.23, SiO_2 36.22 wt%, and CHN analysis provided H_2O 3.29 wt% for a total of 99.99 wt%. Powder IR spectroscopy confirmed the presence of H_2O and single-crystal IR spectroscopy indicated the H_2O to be oriented perpendicular to the b axis. Raman spectra were also obtained. The strongest powder X-ray diffraction lines are [d (hkl) I]: 7.88(110)97, 6.63(200)35, 4.90(020)38, 3.623(202)100, 3.166(130)45, 2.938(312/411/222)57, 2.555(132/213)51, and 2.243(521/332)50. The atomic structure (R1 = 2.04%) consists of undulating sheets of silicate tetrahedra between which are located Pb atoms and channels containing H_2O (and Pb^(2+) lone-pair electrons). The silicate sheets can be described as consisting of zigzag pyroxene-like (SiO_3)_n chains joined laterally into sheets with the unshared tetrahedral apices in successive chains pointed alternately up and down, a configuration also found in pentagonite

A fast and robust patient specific Finite Element mesh registration technique: application to 60 clinical cases

Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially digitized at intraoperative stage, and 50 CT volumes of patients' heads. The MMRep algorithm succeeded in all 60 cases, yielding for each patient a hex-dominant, Atlas based, Finite Element mesh with submillimetric surface representation accuracy, directly exploitable within a commercial FE software