J. Ziv. Distortion-rate theory for individual sequences. IEEE Trans. Inform. Theory, IT-26(2):137--143, March 1980. 27  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sample will not be able to distinguish between two sources that are very close. A more detailed qualitative discussion of Theorem 3 will be given in Section 3, where the theorem is proven using the method of types for the direct part. While the problems of universal lossy source coding (e.g. [29, 19, 30, 21, 16, 3, 28]) and of noisy source coding (e.g. 2, 26, 25, 11, 18, 12] have been extensively studied, this work and, in particular, Theorem 3 is the first to address the combination of the two, namely, the problem of universal coding of noisy sources in the probabilistic setting . The merit of Theorem 3, ....

....universal coding of noisy sources in the probabilistic setting . The merit of Theorem 3, however, more than in its generalizing and merging the two problems, lies in its addressesing the approximation estimation The problem of finite rate coding of noisy individual sequences was considered in [30, 23]. tradeo# for the noisy source coding problem: Given a finite encoding rate for the noisy data, the statistical modeler will typically be faced with the problem of having to compromise between the tendency to take a rich family # of distributions in order to approximate the truth as closely as ....

J. Ziv. Distortion-rate theory for individual sequences. IEEE Trans. Inform. Theory, IT26 (2):137--143, March 1980.

....s 0 if for all i s and all y ; z 2 X such that y i Gammas = z i Gammas , D i (y ) D i (z s (R) denote the class of all source codes in (R) with a decoder of finite memory s. Note that, similarly to a finite memory decoder, one can define a finite state decoder (cf. [17]) While, admittedly, not every finite state encoder is a finite memory encoder, one can show, using the techniques of [5, 12] that finite memory machines perform asymptotically as well as finite state machines. Thus, the classes F s (R) are relevant for the modeling of a variety of coding ....

J. Ziv, "Distortion-Rate Theory for Individual Sequences," IEEE Trans. Inform. Theory, vol. IT-26, no. 2, pp. 137-143, March 1980.

....of Lempel and Ziv s algorithm for the compression of multi dimensional data arrays (shown in [14] to be universal in an individual picture setting) generated by MRF sources in an exponential sense. Section 4 is dedicated to the lossy case, where it is argued that by employing Ziv s lossy encoder [23] on the space lling curve used for the lossless case one is guaranteed to achieve the rate distortion function whenever the multi dimensional data is generated by a stationary and ergodic source. Section 5 contains some concluding remarks. 2 The Model and Preliminaries Let A be a nite alphabet ....

....compression schemes exist for the setting of the present paper, namely that where the multi dimensional data is the realization of an MRF. In particular, we shall argue that by scanning the data using, e.g. the Peano Hilbert curve, and then encoding the data via Ziv s universal lossy encoder [23], one is guaranteed to achieve the fundamental compression limit, namely, the ratedistortion function of the source. We assume that our multi dimensional data is generated by the stationary and ergodic (cf. 10, Ch. 14] or [11, Sec. 3.1] for a precise de nition, which is a natural extension of ....

[Article contains additional citation context not shown here]

J. Ziv, \Distortion-Rate Theory for Individual Sequences," IEEE Trans. Inform. Theory, vol. IT-26, no. 2, pp. 137-143, March 1980.

....National Science Foundation under Grant CCR 9202807. y This work was supported by NSF Grants NCR 9415491 and CCR 9201078, and in part by NATO Collaborative Grant CGR.950060. 1. INTRODUCTION Data compression based on exact pattern matching can be traced back to seminal papers of Lempel and Ziv [31, 32, 33], but recently there has been a resurgence of interest in this type of data compression. This might be a consequence of rapid growth in digital representation of multimedia (e.g. text, audio, image, video, etc. which are particularly amenable to pattern matching manipulations. It was known for a ....

....the lossy compression based on approximate pattern matching, we present our experimental results with pattern matching image compression that support the above claim. It must be said that early attempts on lossy compression based on pattern matching were rather unsuccessful. Already in 1980 Ziv [31] (cf. also [28] proposed an optimal lossy compression scheme at fixed rate level, while Ornstein and Shields [21] and independently Kieffer [14] gave a universal lossy compression for coding at fixed distortion level. Unfortunately, all of these schemes were prohibitively expensive from the ....

J. Ziv, Distortion-rate Theory for Individual Sequences, IEEE Trans. Information Theory, 26, 137-143 (1980).

.... the references therein, and the more recent work of Zhang and Wei [39] 40] Typically, these constructions either involve exhaustive searches over the space of all possible codebooks or are of exponential complexity at the encoder and therefore cannot be realistically implemented in practice (cf. [42][24] 23] 34] More practical algorithms have been recently proposed by Yang, Zhang and Berger [36] party expanding on the ideas of Muramatsu and Kanaya [23] where they suggest a new way for circumventing the exponential encoding complexity of earlier schemes. Motivated by the success of the ....

J. Ziv. Distortion-rate theory for individual sequences. IEEE Trans. Inform. Theory, 26(2):137-- 143, 1980.

....National Science Foundation under Grant CCR 9202807. y This work was supported by NSF Grants NCR 9415491 and CCR 9201078, and in part by NATO Collaborative Grant CGR.950060. 1. INTRODUCTION Data compression based on exact pattern matching can be traced back to seminal papers of Lempel and Ziv [31, 32, 33], but recently there has been a resurgence of interest in this type of data compression. This might be a consequence of rapid growth in digital representation of multimedia (e.g. text, audio, image, video, etc. which are particularly amenable to pattern matching manipulations. It was known for a ....

....which constitute a theoretical basis for the lossy compression, we present our experimental results with pattern matching image compression that support the above claim. It must be said that early attempts on lossy compression based on pattern matching were rather unsuccessful. Already in 1980 Ziv [31] (cf. also [28] proposed an optimal lossy compression scheme at fixed rate level, while Ornstein and Shields [21] and independently Kieffer [14] gave a universal lossy compression for coding at fixed distortion level. Unfortunately, all of these schemes were prohibitively expensive from the ....

J. Ziv, Distortion-rate Theory for Individual Sequences, IEEE Trans. Information Theory, 26, 137-143 (1980).

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J. Ziv. Distortion-rate theory for individual sequences. IEEE Trans. Inform. Theory, IT-26(2):137--143, March 1980. 27

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J. Ziv. Distortion-rate theory for individual sequences. IEEE Trans. Inform. Theory, 26(2):137-- 143, March 1980.

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J. Ziv. Distortion-rate theory for individual sequences. IEEE Trans. Inform. Theory, IT-26(2):137--143, March 1980. 30

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J. Ziv, "Distortion-rate theory for individual sequences," IEEE Trans. Inform. Theory, vol. 26, no. 2, pp. 137--143, 1980.

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