Multiple-Description Coding by Dithered Delta-Sigma Quantization

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has been fixed. Accepted for publication in the IEEE Transactions on Information Theor

Graded quantization for multiple description coding of compressive measurements

Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics

Three-Description Scalar And Lattice Vector Quantization Techniques For Efficient Data Transmission

In twenty-first century, it has been witness the tremendous growth of communication technology and has had a profound impact on our daily life. Throughout history, advancements in technology and communication have gone hand-in-hand, and the most recent technical developments such as the Internet and mobile devices have achieved in the development of communication to a new phase. Majority of researches who work in Multiple Description Coding (MDC) are interested with only two description coding. However, most of the practical applications necessitate more than two packets of transmission to acquire preferable quality. The goals of this work are to develop three description coding system of scalar quantizers using modified nested index assignment technique at the number of diagonals used in the index assignment of two. Furthermore, this work aims to develop three description lattice vector quantizers using designed labeling function in the four dimensional lattice 4 since it offers more lattice points as neighbours that lead the central decoder to achieve better reconstruction quality. This thesis put emphasis on exploiting three description MDC system using scalar quantizers and lattice vector quantizers. The proposed three description system consists of three encoders and seven decoders (including of one central decoder). A three dimensional modified nested index assignment is implemented in the proposed three description scalar quantization scheme. The index assignment algorithm utilizes a matrix, to indicate the mapping process in the proposed three description scalar quantization scheme. As this thesis suggests a new labeling algorithm that uses lattice 4 for three description MDC system. Projection of a tesseract in four-dimensional space of lattice 4 yields four outputs and the data are transmitted via three channels where one of the outputs is defined as time. The three description quantization system is efficient that provides low distortion and good peak signal-to-noise ratio (PSNR) reconstruction quality. The greater the number of diagonals used in the index assignment, k in MDSQ scheme, the higher quality of the central reconstruction can be accomplished. Simulation results show that the central PSNR is promoted to 34.53 dB at rate of 0.1051 bpp and 38.07 dB at 0.9346 bpp for the proposed three description with 2k= Multiple Description Scalar Quantization (MDSQ) scheme. The percentage gain for the central reconstruction quality is improved from 6.36 % to 18.97 % by the proposed three description scalar quantizer which is at 2k= compared to the renownedMDSQ schemes.Moreover, the proposed three description lattice vector quantization (3DLVQ- 4) scheme outperforms the renowned MDC schemes from 4.4 % to 11.43 %. The central reconstruction quality is promoted to 42.63 dB and the average side reconstruction quality inaugurates 32.13 dB, both at bit rate of 1.0 bpp for the proposed 3DLVQ- 4 scheme

State of the art in 2D content representation and compression

Livrable D1.3 du projet ANR PERSEECe rapport a été réalisé dans le cadre du projet ANR PERSEE (n° ANR-09-BLAN-0170). Exactement il correspond au livrable D3.1 du projet

Geometry Compression of 3D Static Point Clouds based on TSPLVQ

International audienceIn this paper, we address the challenging problem of the 3D point cloud compression required to ensure efficient transmission and storage. We introduce a new hierarchical geometry representation based on adaptive Tree-Structured Point-Lattice Vector Quantization (TSPLVQ). This representation enables hierarchically structured 3D content that improves the compression performance for static point cloud. The novelty of the proposed scheme lies in adaptive selection of the optimal quantization scheme of the geometric information, that better leverage the intrinsic correlations in point cloud. Based on its adaptive and multiscale structure, two quantization schemes are dedicated to project recursively the 3D point clouds into a series of embedded truncated cubic lattices. At each step of the process, the optimal quantization scheme is selected according to a rate-distortion cost in order to achieve the best trade-off between coding rate and geometry distortion, such that the compression flexibility and performance can be greatly improved. Experimental results show the interest of the proposed multi-scale method for lossy compression of geometry

Vector space framework for unification of one- and multidimensional filter bank theory

A number of results in filter bank theory can be viewed using vector space notations. This simplifies the proofs of many important results. In this paper, we first introduce the framework of vector space, and then use this framework to derive some known and some new filter bank results as well. For example, the relation among the Hermitian image property, orthonormality, and the perfect reconstruction (PR) property is well-known for the case of one-dimensional (1-D) analysis/synthesis filter banks. We can prove the same result in a more general vector space setting. This vector space framework has the advantage that even the most general filter banks, namely, multidimensional nonuniform filter banks with rational decimation matrices, become a special case. Many results in 1-D filter bank theory are hence extended to the multidimensional case, with some algebraic manipulations of integer matrices. Some examples are: the equivalence of biorthonormality and the PR property, the interchangeability of analysis and synthesis filters, the connection between analysis/synthesis filter banks and synthesis/analysis transmultiplexers, etc. Furthermore, we obtain the subband convolution scheme by starting from the generalized Parseval's relation in vector space. Several theoretical results of wavelet transform can also be derived using this framework. In particular, we derive the wavelet convolution theorem

A vector quantization approach to universal noiseless coding and quantization

A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that “quantizes” the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n -1 log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n-1) when the universe of sources is countable, and as O(n-1+ϵ) when the universe of sources is infinite-dimensional, under appropriate conditions

n-Channel Asymmetric Entropy-Constrained Multiple-Description Lattice Vector Quantization

This paper is about the design and analysis of an index-assignment (IA) based multiple-description coding scheme for the n-channel asymmetric case. We use entropy constrained lattice vector quantization and restrict attention to simple reconstruction functions, which are given by the inverse IA function when all descriptions are received or otherwise by a weighted average of the received descriptions. We consider smooth sources with finite differential entropy rate and MSE fidelity criterion. As in previous designs, our construction is based on nested lattices which are combined through a single IA function. The results are exact under high-resolution conditions and asymptotically as the nesting ratios of the lattices approach infinity. For any n, the design is asymptotically optimal within the class of IA-based schemes. Moreover, in the case of two descriptions and finite lattice vector dimensions greater than one, the performance is strictly better than that of existing designs. In the case of three descriptions, we show that in the limit of large lattice vector dimensions, points on the inner bound of Pradhan et al. can be achieved. Furthermore, for three descriptions and finite lattice vector dimensions, we show that the IA-based approach yields, in the symmetric case, a smaller rate loss than the recently proposed source-splitting approach.Comment: 49 pages, 4 figures. Accepted for publication in IEEE Transactions on Information Theory, 201

Graded quantization for multiple description coding of compressive measurements

Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics