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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 878 (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.
Error Control and Concealment for Video Communication  A Review
 PROCEEDINGS OF THE IEEE
, 1998
"... The problem of error control and concealment in video communication is becoming increasingly important because of the growing interest in video delivery over unreliable channels such as wireless networks and the Internet. This paper reviews the techniques that have been developed for error control a ..."
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Cited by 436 (13 self)
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The problem of error control and concealment in video communication is becoming increasingly important because of the growing interest in video delivery over unreliable channels such as wireless networks and the Internet. This paper reviews the techniques that have been developed for error control and concealment in the past ten to fifteen years. These techniques are described in three categories according to the roles that the encoder and decoder play in the underlying approaches. Forward error concealment includes methods that add redundancy at the source end to enhance error resilience of the coded bit streams. Error concealment by postprocessing refers to operations at the decoder to recover the damaged areas based on characteristics of image and video signals. Finally, interactive error concealment covers techniques that are dependent on a dialog between the source and destination. Both current research activities and practice in international standards are covered.
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 218 (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.
Lossy Source Coding
 IEEE Trans. Inform. Theory
, 1998
"... Lossy coding of speech, highquality audio, still images, and video is commonplace today. However, in 1948, few lossy compression systems were in service. Shannon introduced and developed the theory of source coding with a fidelity criterion, also called ratedistortion theory. For the first 25 year ..."
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Cited by 104 (1 self)
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Lossy coding of speech, highquality audio, still images, and video is commonplace today. However, in 1948, few lossy compression systems were in service. Shannon introduced and developed the theory of source coding with a fidelity criterion, also called ratedistortion theory. For the first 25 years of its existence, ratedistortion theory had relatively little impact on the methods and systems actually used to compress real sources. Today, however, ratedistortion theoretic concepts are an important component of many lossy compression techniques and standards. We chronicle the development of ratedistortion theory and provide an overview of its influence on the practice of lossy source coding. Index TermsData compression, image coding, speech coding, rate distortion theory, signal coding, source coding with a fidelity criterion, video coding. I.
Multiple Description Coding Using Pairwise Correlating Transforms
 IEEE Trans. Image Processing
, 1999
"... The objective of multiple description coding (MDC) is to encode a source into two (or more) bitstreams supporting two quality levels of decoding. A highquality reconstruction should be decodable from the two bitstreams together, while lower, but still acceptable, quality reconstructions should b ..."
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Cited by 93 (1 self)
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The objective of multiple description coding (MDC) is to encode a source into two (or more) bitstreams supporting two quality levels of decoding. A highquality reconstruction should be decodable from the two bitstreams together, while lower, but still acceptable, quality reconstructions should be decodable from either of the two individual bitstreams. This paper describes techniques for meeting MDC objectives in the framework of standard transformbased image coding through the design of pairwise transforms.
A.: Video coding for streaming media delivery on the Internet
 IEEE Transactions on Circuits and Systems for Video Technology
"... ..."
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.
Filter Bank Frame Expansions with Erasures
, 2002
"... We study frames for robust transmission over the Internet. In our previous work, we used quantized finitedimensional frames to achieve resilience to packet losses; here, we allow the input to be a sequence in ` 2 (Z) and focus on a filterbank implementation of the system. We present results in par ..."
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Cited by 68 (4 self)
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We study frames for robust transmission over the Internet. In our previous work, we used quantized finitedimensional frames to achieve resilience to packet losses; here, we allow the input to be a sequence in ` 2 (Z) and focus on a filterbank implementation of the system. We present results in parallel, R N or C N versus ` 2 (Z), and show that uniform tight frames, as well as newly introduced strongly uniform tight frames, provide the best performance.
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 63 (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 55 (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