The state of the art in data compression is arithmetic coding, not the better-known Huffman method. Arithmetic coding gives greater compression, is faster for adaptive models, and clearly separates the model from the channel encoding.

/pdf/arithmetic-coding-for-data-compression-3eqc4smaaa.pdf

Arithmetic coding for data compression

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 of the number line between 0 and 1, and retains one of the partitions as the new interval. Thus, the algorithm successively deals with smaller intervals, and the code string, viewed as a magnitude, lies in each of the nested intervals. The data string is recovered by using magnitude comparisons on the code string to recreate how the encoder must have successively partitioned and retained each nested subinterval. Arithmetic coding differs considerably from the more familiar compression coding techniques, such as prefix (Huffman) codes. Also, it should not be confused with error control coding, whose object is to detect and correct errors in computer operations. This paper presents the key notions of arithmetic compression coding by means of simple examples.

An introduction to arithmetic coding

Approaches to the zero-frequency problem in adaptive text compression are discussed. This problem relates to the estimation of the likelihood of a novel event occurring. Although several methods have been used, their suitability has been on empirical evaluation rather than a well-founded model. The authors propose the application of a Poisson process model of novelty. Its ability to predict novel tokens is evaluated, and it consistently outperforms existing methods. It is applied to a practical statistical coding scheme, where a slight modification is required to avoid divergence. The result is a well-founded zero-frequency model that explains observed differences in the performance of existing methods, and offers a small improvement in the coding efficiency of text compression over the best method previously known. >

/pdf/the-zero-frequency-problem-estimating-the-probabilities-of-agqfv3785f.pdf

The zero-frequency problem: estimating the probabilities of novel events in adaptive text compression

An iterative descent algorithm based on a Lagrangian formulation for designing vector quantizers having minimum distortion subject to an entropy constraint is discussed. These entropy-constrained vector quantizers (ECVQs) can be used in tandem with variable-rate noiseless coding systems to provide locally optimal variable-rate block source coding with respect to a fidelity criterion. Experiments on sampled speech and on synthetic sources with memory indicate that for waveform coding at low rates (about 1 bit/sample) under the squared error distortion measure, about 1.6 dB improvement in the signal-to-noise ratio can be expected over the best scalar and lattice quantizers when block entropy-coded with block length 4. Even greater gains are made over other forms of entropy-coded vector quantizers. For pattern recognition, it is shown that the ECVQ algorithm is a generalization of the k-means and related algorithms for estimating cluster means, in that the ECVQ algorithm estimates the prior cluster probabilities as well. Experiments on multivariate Gaussian distributions show that for clustering problems involving classes with widely different priors, the ECVQ outperforms the k-means algorithm in both likelihood and probability of error. >

/pdf/entropy-constrained-vector-quantization-2djba6vhy4.pdf

Entropy-constrained vector quantization

This paper surveys a variety of data compression methods spanning almost 40 years of research, from the work of Shannon, Fano, and Huffman in the late 1940s 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.

Data compression

Algorithms are presented for encoding and decoding strings of characters as real binary fractions, using registers of fixed precision. The encoding is left to right and does not require blocking. The algorithms have storage requirements O(N) and computation time O(n \log_{2}N) for string length n and alphabet size N .

Arithmetic stream coding using fixed precision registers

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Arithmetic stream coding using fixed precision registers