Lossy source coding

Berger, Toby; Gibson, J.D.

doi:10.1109/18.720552

Cited by 156 publications

(151 citation statements)

References 196 publications

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“…In [18] Shannon gave a nonconstructive asymptotic characterization of the expected rate-distortion curve of a random variable (Theorem 4 in Appendix A). References [1], [2] treat more general distortion measures and random variables in the Shannon framework.…”

Section: A Related Workmentioning

confidence: 99%

Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexity

Vereshchagin

Vitányi

2010

IEEE Trans. Inform. Theory

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Abstract-We examine the structure of families of distortion balls from the perspective of Kolmogorov complexity. Special attention is paid to the canonical rate-distortion function of a source word which returns the minimal Kolmogorov complexity of all distortion balls containing that word subject to a bound on their cardinality. This canonical rate-distortion function is related to the more standard algorithmic rate-distortion function for the given distortion measure. Examples are given of list distortion, Hamming distortion, and Euclidean distortion. The algorithmic rate-distortion function can behave differently from Shannon's rate-distortion function. To this end, we show that the canonical rate-distortion function can and does assume a wide class of shapes (unlike Shannon's); we relate low algorithmic mutual information to low Kolmogorov complexity (and consequently suggest that certain aspects of the mutual information formulation of Shannon's rate-distortion function behave differently than would an analogous formulation using algorithmic mutual information); we explore the notion that low Kolmogorov complexity distortion balls containing a given word capture the interesting properties of that word (which is hard to formalize in Shannon's theory) and this suggests an approach to denoising.

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Section: A Related Workmentioning

confidence: 99%

Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexity

Vereshchagin

Vitányi

2010

IEEE Trans. Inform. Theory

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“…Answering the question raised at the beginning of the paper concerning the lowest code length given a maximal coding error is equivalent to the calculation of the entropy of an error-control family (1). In this paper, we focus on methods that allow us to approximate this quantity.…”

Section: Motivationmentioning

confidence: 99%

“…Lossy source coding transforms possibly continuously-distributed information into a finite number of codewords [1,2]. Although this allows one to encode data efficiently, such an operation is irreversible, and once modified, information cannot be restored accurately.…”

Section: Introductionmentioning

confidence: 99%

Entropy Approximation in Lossy Source Coding Problem

Śmieja

Tabor

2015

Entropy

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In this paper, we investigate a lossy source coding problem, where an upper limit on the permitted distortion is defined for every dataset element. It can be seen as an alternative approach to rate distortion theory where a bound on the allowed average error is specified. In order to find the entropy, which gives a statistical length of source code compatible with a fixed distortion bound, a corresponding optimization problem has to be solved. First, we show how to simplify this general optimization by reducing the number of coding partitions, which are irrelevant for the entropy calculation. In our main result, we present a fast and feasible for implementation greedy algorithm, which allows one to approximate the entropy within an additive error term of log 2 e. The proof is based on the minimum entropy set cover problem, for which a similar bound was obtained.

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“…100-101], [7,Section II.E]. In this note, we investigate the degradation from optimal performance when the components are slightly mismatched.…”

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confidence: 99%

Sensitivity of Quadratic Gaussian Matching to Interference

Varshney

Mitter

2011

IEEE Commun. Lett.

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Abstract-It is well known that uncoded transmission of a memoryless Gaussian source over a memoryless additive white Gaussian noise channel results in optimal performance theoretically attainable. When there is additional interference in the channel, uncoded transmission is robust. It achieves the same sensitivity performance as optimal performance, measured using sensitivity results of Pinsker, Prelov, and Verdú.

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Lossy source coding

Cited by 156 publications

References 196 publications

Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexity

Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexity

Entropy Approximation in Lossy Source Coding Problem

Sensitivity of Quadratic Gaussian Matching to Interference

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