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125
Quantization
 IEEE TRANS. INFORM. THEORY
, 1998
"... The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analogtodigital conversion was first recognized during the early development of pulsecode modula ..."
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Cited by 872 (12 self)
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The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analogtodigital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first highresolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for quantization as analogtodigital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.
Multiple Description Coding: Compression Meets the Network
, 2001
"... This article focuses on the compressed representations of the pictures ..."
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Cited by 433 (9 self)
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This article focuses on the compressed representations of the pictures
Successive refinement of information
 Applications
, 1989
"... AbstrocrThe successive refinement of information consists of first approximating data using a few bits of information, then iteratively improving the approximation as more and more information is supplied. The god is to achieve an optimal description at each stage. In general an ongoing description ..."
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Cited by 217 (0 self)
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AbstrocrThe successive refinement of information consists of first approximating data using a few bits of information, then iteratively improving the approximation as more and more information is supplied. The god is to achieve an optimal description at each stage. In general an ongoing description is sought which is ratedistortion optimal whenever it is interrupted. It is shown that a rate distortion problem is successively refinable if and only if the individual solutions of the rate distortion problems can be written as a Markov chain. This implies in particular that tree structured descriptions are optimal if and only if the rate distortion problem is successively rethable. Successive refinement is shown to be possible for all fmite alphabet signals with Hamming distortion, for Gaussian signals with squarederror distortion, and for Laplacian signals with absoluteerror distortion. However, a simple counterexample witb absolute error distortion and a symmetric source distribution shows that successive refinement is not always achievable. lnder TermRate distortion, refinement, progressive transmission, multiuser information theory, squarederror distortion, tree structure. I.
Generalized multiple description coding with correlating transforms
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—Multiple description (MD) coding is source coding in which several descriptions of the source are produced such that various reconstruction qualities are obtained from different subsets of the descriptions. Unlike multiresolution or layered source coding, there is no hierarchy of descriptio ..."
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Cited by 80 (2 self)
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Abstract—Multiple description (MD) coding is source coding in which several descriptions of the source are produced such that various reconstruction qualities are obtained from different subsets of the descriptions. Unlike multiresolution or layered source coding, there is no hierarchy of descriptions; thus, MD coding is suitable for packet erasure channels or networks without priority provisions. Generalizing work by Orchard, Wang, Vaishampayan, and Reibman, a transformbased approach is developed for producing descriptions of antuple source,. The descriptions are sets of transform coefficients, and the transform coefficients of different descriptions are correlated so that missing coefficients can be estimated. Several transform optimization results are presented for memoryless Gaussian sources, including a complete solution of the aP, aPcase with arbitrary weighting of the descriptions. The technique is effective only when independent components of the source have differing variances. Numerical studies show that this method performs well at low redundancies, as compared to uniform MD scalar quantization. Index Terms—Erasure channels, integertointeger transforms, packet networks, robust source coding.
Multiple Description Coding with Many Channels
 IEEE TRANS. INFORM. THEORY
, 2003
"... An achievable region for thechannel multiple description coding problem is presented. This region generalizes twochannel results of El Gamal and Cover and of Zhang and Berger. It further generalizes threechannel results of Gray and Wyner and of Zhang and Berger. A source that is successively refi ..."
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Cited by 73 (1 self)
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An achievable region for thechannel multiple description coding problem is presented. This region generalizes twochannel results of El Gamal and Cover and of Zhang and Berger. It further generalizes threechannel results of Gray and Wyner and of Zhang and Berger. A source that is successively refinable on chains is shown to be successively refinable on trees. A new outer bound on the ratedistortion (RD) region for memoryless Gaussian sources with mean squared error distortion is also derived. The achievable region meets this outer bound for certain symmetric cases.
Multiple Description Coding via Polyphase Transform and Selective Quantization
, 1999
"... In this paper, we present an ecient Multiple Description Coding (MDC) technique to achieve robust communication over unreliable channels such as a lossy packet network. We first model such unreliable channels as erasure channels and then we present a MDC system using polyphase transform and selectiv ..."
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Cited by 72 (6 self)
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In this paper, we present an ecient Multiple Description Coding (MDC) technique to achieve robust communication over unreliable channels such as a lossy packet network. We first model such unreliable channels as erasure channels and then we present a MDC system using polyphase transform and selective quantization to recover channel erasures. Different from previous MDC work, our system explicitly separates description generation and redundancy addition which greatly reduces the implementation complexity specially for systems with more than two descriptions. Our system also realizes a Balanced Multiple Description Coding (BMDC) framework which can generate descriptions of statistically equal rate and importance. This property is well matched to communication systems with no priority mechanisms for data delivery, such as today's Internet.
Rate region of the quadratic Gaussian twoencoder sourcecoding problem
 IEEE Trans. Inf. Theory
, 2008
"... We determine the rate region of the quadratic Gaussian twoencoder sourcecoding problem. This rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression. Furthermore, this architecture requires higher rates to send a Gaussian source than it doe ..."
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Cited by 69 (6 self)
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We determine the rate region of the quadratic Gaussian twoencoder sourcecoding problem. This rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression. Furthermore, this architecture requires higher rates to send a Gaussian source than it does to send any other source with the same covariance. Our techniques can also be used to determine the sum rate of some generalizations of this classical problem. Our approach involves coupling the problem to a quadratic Gaussian “CEO problem.”
The RateDistortion Region for Multiple Descriptions without Excess Rate
 IEEE Trans. Inform. Theory
, 1985
"... During recent years there has been strong interest in a certain source coding problem, which some authors call the "problem of multiple descriptions". Old and new wringing techniques enable us to establish a singleletter characterization of the ratedistrotion region in the case of no e ..."
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Cited by 62 (1 self)
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During recent years there has been strong interest in a certain source coding problem, which some authors call the "problem of multiple descriptions". Old and new wringing techniques enable us to establish a singleletter characterization of the ratedistrotion region in the case of no excess rate for the joint description. 1 The Result Since the origin of the problem of multiple descriptiona and motivations for its study have already been described in an extensive literature [1][9], we present our result immediately. It goes considerably beyond those of [17], where the reader also will find a detailed discussion of previously known results. We are given the following. 1) A sequence (X t ) 1 t=1 of independent and identically distributed random variables with values in a finite set X , that is, a discrete memoryless source (DMS). 2) Three finite reconstruction spaces X 0 , X 1 , and X 2 , together with associated per letter distortion measures d i : X \Theta X i ! R ...
Optimal multiple description transform coding of Gaussian vectors
 In Proc. IEEE Data Compr. Conf
, 1998
"... Includes minor corrections. Multiple description coding (MDC) is source coding for multiple channels such that a decoder which receives an arbitrary subset of the channels may produce a useful reconstruction. Orchard et al. [1] proposed a transform coding method for MDC of pairs of independent Gaus ..."
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Cited by 54 (12 self)
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Includes minor corrections. Multiple description coding (MDC) is source coding for multiple channels such that a decoder which receives an arbitrary subset of the channels may produce a useful reconstruction. Orchard et al. [1] proposed a transform coding method for MDC of pairs of independent Gaussian random variables. This paper provides a general framework which extends multiple description transform coding (MDTC) to any number of variables and expands the set of transforms which are considered. Analysis of the general case is provided, which can be used to numerically design optimal MDTC systems. The case of two variables sent over two channels is analytically optimized in the most general setting where channel failures need not have equal probability or be independent. It is shown that when channel failures are equally probable and independent, the transforms used in [1] are in the optimal set, but many other choices are possible. A cascade structure is presented which facilitates lowcomplexity design, coding, and decoding for a system with a large number of variables. 1
Vector Gaussian multiple description with individual and central receivers
 IEEE Trans. Information Theory
, 2007
"... The problem of L multiple descriptions of a stationary and ergodic Gaussian source with two levels of receivers is investigated. Each of the first level receivers receive (an arbitrary subset) k of the L descriptions, (k < L). The second level receiver receives all L descriptions. All the receive ..."
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Cited by 41 (3 self)
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The problem of L multiple descriptions of a stationary and ergodic Gaussian source with two levels of receivers is investigated. Each of the first level receivers receive (an arbitrary subset) k of the L descriptions, (k < L). The second level receiver receives all L descriptions. All the receivers, both at the first level and the second level, reconstruct the source using the subset of descriptions they receive. The corresponding reconstructions are subject to quadratic distortion constraints. Our main result is the derivation of an outer bound on the sum rate of the descriptions so that the distortion constraints are met. We show that a natural analogdigital separation architecture involving joint Gaussian vector quantizers and a binning scheme meets this outer bound with equality for several scenarios. These scenarios include the case when the distortion constraints are symmetric and the case for general distortion constraints with k = 2 and L = 3. We also show the robustness of this architecture: the distortions achieved are no larger when used to describe any nonGaussian source with the same covariance matrix. 1