Arithmetic coding is a data compression technique that encodes data (the data string) by creating a code string which represents a fractional value on the number line between 0 and 1. The coding algorithm is symbolwise recursive; i.e., it operates upon and encodes (decodes) one data symbol per iteration or recursion. On each recursion, the algorithm successively partitions an interval

Over the last decade, arithmetic coding has emerged as an important compression tool. It is now the method of choice for adaptive coding on multisymbol alphabets because of its speed, low storage requirements, and effectiveness of compression. This article describes a new implementation of arithmetic coding that incorporates several improvements over a widely used earlier version by Witten, Neal, and Cleary, which has become a de facto standard. These improvements include fewer multiplicative operations, greatly extended range of alphabet sizes and symbol probabilities, and the use of low-precision arithmetic, permitting implementation by fast shift/add operations. We also describe a modular structure that separates the coding, modeling, and probability estimation components of a compression system. To motivate the improved coder, we consider the needs of a word-based text compression program. We report a range of experimental results using this and other models. Complete source code is available.

This paper surveys a variety of data compression methods spanning almost forty years of research, from the work of Shannon, Fano and Huffman in the late 40's to a technique developed in 1986. The aim of data compression is to reduce redundancy in stored or communicated data, thus increasing effective data density. Data compression has important application in the areas of file storage and distributed systems. Concepts from information theory, as they relate to the goals and evaluation of data compression methods, are discussed briefly. A framework for evaluation and comparison of methods is constructed and applied to the algorithms presented. Comparisons of both theoretical and empirical natures are reported and possibilities for future research are suggested. INTRODUCTION Data compression is often referred to as coding, where coding is a very general term encompassing any special representation of data which satisfies a given need. Information theory is defined to be the study of eff...

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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 high-efficiency lossless compression of both text and grayscale images can be obtained by using appropriate models in conjunction with arithmetic coding. We introduce a four-component 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...

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 end-of-file are negligible.

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, space-efficient, 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.

This paper explains how to significantly improve the compression performance of any PPM variant

The ability to predict the future based upon the past in finite-alphabet sequences has many applications, including communications, data security, pattern recognition, and natural language processing. By Shannon's theory and the breakthrough development of arithmetic coding, any sequence, a 1 a 2 \Delta \Delta \Delta a n , can be encoded in a number of bits that is essentially equal to the minimal information-lossless codelength, P i \Gamma log 2 p(a i ja 1 \Delta \Delta \Delta a i\Gamma1 ). The goal of universal on-line modeling, and therefore of universal data compression, is to deduce the model of the input sequence a 1 a 2 \Delta \Delta \Delta a n that can estimate each p(a i ja 1 \Delta \Delta \Delta a i\Gamma1 ) knowing only a 1 a 2 \Delta \Delta \Delta a i\Gamma1 so that the ex...

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