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87
The Design and Analysis of Efficient Lossless Data Compression Systems
, 1993
"... Our thesis is that high compression efficiency for text and images can be obtained by using sophisticated statistical compression techniques, and that greatly increased speed can be achieved at only a small cost in compression efficiency. Our emphasis is on elegant design and mathematical as well as ..."
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Cited by 49 (0 self)
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Our thesis is that high compression efficiency for text and images can be obtained by using sophisticated statistical compression techniques, and that greatly increased speed can be achieved at only a small cost in compression efficiency. Our emphasis is on elegant design and mathematical as well as empirical analysis. We analyze arithmetic coding as it is commonly implemented and show rigorously that almost no compression is lost in the implementation. We show that highefficiency lossless compression of both text and grayscale images can be obtained by using appropriate models in conjunction with arithmetic coding. We introduce a fourcomponent paradigm for lossless image compression and present two methods that give state of the art compression efficiency. In the text compression area, we give a small improvement on the preferred method in the literature. We show that we can often obtain significantly improved throughput at the cost of slightly reduced compression. The extra speed c...
Analysis of Arithmetic Coding for Data Compression
 INFORMATION PROCESSING AND MANAGEMENT
, 1992
"... Arithmetic coding, in conjunction with a suitable probabilistic model, can provide nearly optimal data compression. In this article we analyze the effect that the model and the particular implementation of arithmetic coding have on the code length obtained. Periodic scaling is often used in arithmet ..."
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Cited by 36 (6 self)
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Arithmetic coding, in conjunction with a suitable probabilistic model, can provide nearly optimal data compression. In this article we analyze the effect that the model and the particular implementation of arithmetic coding have on the code length obtained. Periodic scaling is often used in arithmetic coding implementations to reduce time and storage requirements; it also introduces a recency effect which can further affect compression. Our main contribution is introducing the concept of weighted entropy and using it to characterize in an elegant way the effect that periodic scaling has on the code length. We explain why and by how much scaling increases the code length for files with a homogeneous distribution of symbols, and we characterize the reduction in code length due to scaling for files exhibiting locality of reference. We also give a rigorous proof that the coding effects of rounding scaled weights, using integer arithmetic, and encoding endoffile are negligible.
Practical Implementations of Arithmetic Coding
 IN IMAGE AND TEXT
, 1992
"... We provide a tutorial on arithmetic coding, showing how it provides nearly optimal data compression and how it can be matched with almost any probabilistic model. We indicate the main disadvantage of arithmetic coding, its slowness, and give the basis of a fast, spaceefficient, approximate arithmet ..."
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Cited by 34 (6 self)
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We provide a tutorial on arithmetic coding, showing how it provides nearly optimal data compression and how it can be matched with almost any probabilistic model. We indicate the main disadvantage of arithmetic coding, its slowness, and give the basis of a fast, spaceefficient, approximate arithmetic coder with only minimal loss of compression efficiency. Our coder is based on the replacement of arithmetic by table lookups coupled with a new deterministic probability estimation scheme.
Soft decoding and synchronization of arithmetic codes: Application to image transmission over noisy channels
, 2003
"... ..."
Semantically Motivated Improvements for PPM Variants
 The Computer Journal
, 1997
"... This paper explains how to significantly improve the compression performance of any PPM variant ..."
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Cited by 25 (3 self)
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This paper explains how to significantly improve the compression performance of any PPM variant
On universal types
 PROC. ISIT 2004
, 2004
"... We define the universal type class of a sequence x n, in analogy to the notion used in the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same set of phrases in the incremental parsing of Ziv and Lempel (1978 ..."
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Cited by 22 (6 self)
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We define the universal type class of a sequence x n, in analogy to the notion used in the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same set of phrases in the incremental parsing of Ziv and Lempel (1978). We show that the empirical probability distributions of any finite order of two sequences of the same universal type converge, in the variational sense, as the sequence length increases. Consequently, the normalized logarithms of the probabilities assigned by any kth order probability assignment to two sequences of the same universal type, as well as the kth order empirical entropies of the sequences, converge for all k. We study the size of a universal type class, and show that its asymptotic behavior parallels that of the conventional counterpart, with the LZ78 code length playing the role of the empirical entropy. We also estimate the number of universal types for sequences of length n, and show that it is of the form exp((1+o(1))γ n/log n) for a well characterized constant γ. We describe algorithms for enumerating the sequences in a universal type class, and for drawing a sequence from the class with uniform probability. As an application, we consider the problem of universal simulation of individual sequences. A sequence drawn with uniform probability from the universal type class of x n is an optimal simulation of x n in a well defined mathematical sense.
Efficient Universal Lossless Data Compression Algorithms Based on a Greedy Sequential Grammar Transform  Part One: Without Context Models
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2000
"... A grammar transform is a transformation that converts any data sequence to be compressed into a grammar from which the original data sequence can be fully reconstructed. In a grammarbased code, a data sequence is first converted into a grammar by a grammar transform and then losslessly encoded. In ..."
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Cited by 21 (4 self)
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A grammar transform is a transformation that converts any data sequence to be compressed into a grammar from which the original data sequence can be fully reconstructed. In a grammarbased code, a data sequence is first converted into a grammar by a grammar transform and then losslessly encoded. In this paper, a greedy grammar transform is first presented; this grammar transform constructs sequentially a sequence of irreducible grammars from which the original data sequence can be recovered incrementally. Based on this grammar transform, three universal lossless data compression algorithms, a sequential algorithm, an improved sequential algorithm, and a hierarchical algorithm, are then developed. These algorithms combine the power of arithmetic coding with that of string matching. It is shown that these algorithms are all universal in the sense that they can achieve asymptotically the entropy rate of any stationary, ergodic source. Moreover, it is proved that their worst case redundancies among all individual sequences of length are upperbounded by �� � �� � �� � , where is a constant. Simulation results show that the proposed algorithms outperform the Unix Compress and Gzip algorithms, which are based on LZ78 and LZ77, respectively.
Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series
, 2006
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Is Huffman Coding Dead?
 Computing
, 1993
"... : In recent publications about data compression, arithmetic codes are often suggested as the state of the art, rather than the more popular Huffman codes. While it is true that Huffman codes are not optimal in all situations, we show that the advantage of arithmetic codes in compression performance ..."
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Cited by 17 (3 self)
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: In recent publications about data compression, arithmetic codes are often suggested as the state of the art, rather than the more popular Huffman codes. While it is true that Huffman codes are not optimal in all situations, we show that the advantage of arithmetic codes in compression performance is often negligible. Referring also to other criteria, we conclude that for many applications, Huffman codes should still remain a competitive choice. 1. Introduction It is paradoxical that, as the technology for storing and transmitting information has gotten cheaper and more effective, interest in data compression has increased. There are many explanations, but most conspicuous is that improvements in media have expanded our sense of what we wish to store. For example, CDRom technology allows us to store whole libraries instead of records describing individual items; but the requirements of storing full text easily exceeds the capabilities even of the optical format. Similarly, there is ...
Lossless compression of continuoustone images
 Proc. IEEE
, 2000
"... Abstract — In this paper, we survey some of the recent advances in lossless compression of continuoustone images. The modeling paradigms underlying the stateoftheart algorithms, and the principles guiding their design, are discussed in a unified manner. The algorithms are described and experiment ..."
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Cited by 17 (2 self)
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Abstract — In this paper, we survey some of the recent advances in lossless compression of continuoustone images. The modeling paradigms underlying the stateoftheart algorithms, and the principles guiding their design, are discussed in a unified manner. The algorithms are described and experimentally compared. I.