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75
Multiple Description Coding: Compression Meets the Network
, 2001
"... This article focuses on the compressed representations of the pictures ..."
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Cited by 288 (7 self)
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This article focuses on the compressed representations of the pictures
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 71 (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.
Vector Quantization of Image Subbands: A Survey
 IEEE Transactions on Image Processing
, 1996
"... Subband and wavelet decompositions are powerful tools in image coding, because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting which allows for efficient coding matched to the ..."
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Cited by 53 (4 self)
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Subband and wavelet decompositions are powerful tools in image coding, because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system. Vector quantization provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter and intraband correlation as well as of the more flexible partitions of higher dimensional vector spaces. Since 1988 a growing body of research has examined the use of vector quantization for subband/wavelet transform coefficients. We present a survey of these methods. 1 Introduction Image compression maps an original image into a bit stream suitable for communication over or storage in a digital medium. The number of bits required to represent the coded image should b...
On the asymptotic tightness of the Shannon lower bound
, 1997
"... New results are proved on the convergence of the Shannon lower bound (SLB) to the rate distortion function as the distortion decreases to zero. The key convergence result is proved using a fundamental property of informational divergence. As a corollary, it is shown that the SLB is asymptotically ti ..."
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Cited by 45 (15 self)
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New results are proved on the convergence of the Shannon lower bound (SLB) to the rate distortion function as the distortion decreases to zero. The key convergence result is proved using a fundamental property of informational divergence. As a corollary, it is shown that the SLB is asymptotically tight for normbased distortions, when the source vector has a finite differential entropy and a finite ffth moment for some ff ? 0, with respect to the given norm. Moreover, we derive a theorem of Linkov on the asymptotic tightness of the SLB for general difference distortion measures with more relaxed conditions on the source density. We also show that the SLB relative to a stationary source and single letter difference distortion is asymptotically tight under very weak assumptions on the source distribution. Key words: rate distortion theory, Shannon lower bound, difference distortion measures, stationary sources T. Linder is with the Coordinated Science Laboratory, University of Illinoi...
Transmit beamforming in multipleantenna systems with finite rate feedback: A VQbased approach
 IEEE Trans. Inform. Theory
, 2006
"... Abstract—This paper investigates quantization methods for feeding back the channel information through a lowrate feedback channel in the context of multipleinput singleoutput (MISO) systems. We propose a new quantizer design criterion for capacity maximization and develop the corresponding iterat ..."
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Cited by 36 (2 self)
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Abstract—This paper investigates quantization methods for feeding back the channel information through a lowrate feedback channel in the context of multipleinput singleoutput (MISO) systems. We propose a new quantizer design criterion for capacity maximization and develop the corresponding iterative vector quantization (VQ) design algorithm. The criterion is based on maximizing the meansquared weighted inner product (MSwIP) between the optimum and the quantized beamforming vector. The performance of systems with quantized beamforming is analyzed for the independent fading case. This requires finding the density of the squared inner product between the optimum and the quantized beamforming vector, which is obtained by considering a simple approximation of the quantization cell. The approximate density function is used to lowerbound the capacity loss due to quantization, the outage probability, and the bit error probability. The resulting expressions provide insight into the dependence of the performance of transmit beamforming MISO systems on the number of transmit antennas and feedback rate. Computer simulations support the analytical results and indicate that the lower bounds are quite tight. Index Terms—Bit error probability, channel capacity, channel state information, multiple antennas, transmit beamforming, outage probability, vector quantization (VQ). I.
Denoising by Sparse Approximation: Error Bounds Based on RateDistortion Theory
, 2006
"... If a signal x is known to have a sparse representation with respect to a frame, it can be estimated from a noisecorrupted observation y by finding the best sparse approximation to y. Removing noise in this manner depends on the frame efficiently representing the signal while it inefficiently repres ..."
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Cited by 30 (6 self)
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If a signal x is known to have a sparse representation with respect to a frame, it can be estimated from a noisecorrupted observation y by finding the best sparse approximation to y. Removing noise in this manner depends on the frame efficiently representing the signal while it inefficiently represents the noise. The meansquared error (MSE) of this denoising scheme and the probability that the estimate has the same sparsity pattern as the original signal are analyzed. First an MSE bound that depends on a new bound on approximating a Gaussian signal as a linear combination of elements of an overcomplete dictionary is given. Further analyses are for dictionaries generated randomly according to a sphericallysymmetric distribution and signals expressible with single dictionary elements. Easilycomputed approximations for the probability of selecting the correct dictionary element and the MSE are given. Asymptotic expressions reveal a critical input signaltonoise ratio for signal recovery.
Multipledescription vector quantization with lattice codebooks: Design and analysis
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—The problem of designing a multipledescription vector quantizer with lattice codebook 3 is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the latti ..."
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Cited by 27 (1 self)
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Abstract—The problem of designing a multipledescription vector quantizer with lattice codebook 3 is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices 2 and, =1 2 4 8 that make use of this labeling algorithm. The highrate squarederror distortions for this family ofdimensional vector quantizers are then analyzed for a memoryless source with probability density function (pdf) and differential entropy ( ). For any (0 1) and rate pair (),it is shown that the twochannel distortion 0 and the channel 1 (or channel 2) distortion satisfy
Asymmetric multiple description lattice vector quantizers
 IEEE Trans. Inf. Theory
, 2002
"... Abstract—We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to successively refinable. We present a solution to a labeling problem, which is an important part of the construction, a ..."
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Cited by 24 (2 self)
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Abstract—We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to successively refinable. We present a solution to a labeling problem, which is an important part of the construction, along with a general design procedure. The highrate asymptotic performance of the quantizer is also studied. We evaluate the ratedistortion performance of the quantizer and compare it to known informationtheoretic bounds. The highrate asymptotic analysis is compared to the performance of the quantizer. Index Terms—Cubic lattice, highrate quantization, lattice quantization, multiple descriptions, quantization, source coding, successive refinement, vector quantization. I.
Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis
, 2000
"... The problem of designing a multiple description vector quantizer with lattice codebook # is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A 2 a ..."
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Cited by 24 (9 self)
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The problem of designing a multiple description vector quantizer with lattice codebook # is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A 2 and Z i , i = 1, 2, 4, 8 that make use of this labeling algorithm. The highrate squarederror distortions for this family of vector quantizers are then analyzed for a memoryless source with probability density function p and di#erential entropy h(p) < #. For any a # (0, 1) and rate pair (R, R), it is shown that the twochannel distortion d 0 and the channel 1 (or channel 2) distortion d s satisfy lim R## d 0 2 2R(1+a) = 1 4 G(#)2 2h(p) and lim R## d s 2 2R(1a) = G(S L )2 2h(p) , where G(#) is the normalized second moment of a Voronoi cell of the lattice # and G(S L ) is the normalized second moment of a sphere in L dimensions. Index Terms: Source Coding, Quantization...
On Optimal EntropyConstrained Scalar Quantization
, 2000
"... Optimal scalar quantization subject to an entropyconstraint is studied. First the problem of nding analytically an optimal entropyconstrained scalar quantizer (ECSQ) is considered. For a wide class of dierence distortion measures including rth power distortions with r > 0, it is proved that if th ..."
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Cited by 19 (6 self)
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Optimal scalar quantization subject to an entropyconstraint is studied. First the problem of nding analytically an optimal entropyconstrained scalar quantizer (ECSQ) is considered. For a wide class of dierence distortion measures including rth power distortions with r > 0, it is proved that if the source is uniformly distributed over an interval, then for any entropy constraint R (in bits), an optimal quantizer has N = 2 R interval cells such that N 1 cells have equal length d and one cell has length c d. Based on this result, a parametric representation of the minimum achievable distortion D h (R) as a function of the entropy constraint R is obtained for a uniform source. Contrary to earlier expectations, the D h (R) curve turns out to be nonconvex in general. In particular, for the squared error distortion it is shown that D h (R) is a piecewise concave function. The structural properties of optimal ECSQs for more general source distributions are also investigated. In...