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.

LOCO-I (LOw COmplexity LOssless COmpression for Images) is the algorithm at the core of the new ISO/ITU standard for lossless and near-lossless compression of continuous-tone images, JPEG-LS. It is conceived as a "low complexity projection" of the universal context modeling paradigm, matching its modeling unit to a simple coding unit. By combining simplicity with the compression potential of context models, the algorithm "enjoys the best of both worlds." It is based on a simple fixed context model, which approaches the capability of the more complex universal techniques for capturing high-order dependencies. The model is tuned for efficient performance in conjunction with an extended family of Golomb-type codes, which are adaptively chosen, and an embedded alphabet extension for coding of low-entropy image regions. LOCO-I attains compression ratios similar or superior to those obtained with state-of-the-art schemes based on arithmetic coding. Moreover, it is within a few percentage points of the best available compression ratios, at a much lower complexity level. We discuss the principles underlying the design of LOCO-I, and its standardization into JPEG-LS.

In an online decision problem, one makes a sequence of decisions without knowledge of the future. Tools from learning such as Weighted Majority and its many variants [13, 18, 4] demonstrate that online algorithms can perform nearly as well as the best single decision chosen in hindsight, even when there are exponentially many possible decisions. However, the naive application of these algorithms is inefficient for such large problems. For some problems with nice structure, specialized efficient solutions have been developed [10, 16, 17, 6, 3].

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...

Abstract. A new one-pass algorithm for constructing dynamic Huffman codes is introduced and analyzed. We also analyze the one-pass algorithm due to Failer, Gallager, and Knuth. In each algorithm, both the sender and the receiver maintain equivalent dynamically varying Huffman trees, and the coding is done in real time. We show that the number of bits used by the new algorithm to encode a message containing t letters is < t bits more than that used by the conventional two-pass Huffman scheme, independent of the alphabet size. This is best possible in the worst case, for any one-pass Huffman method. Tight upper and lower bounds are derived. Empirical tests show that the encodings produced by the new algorithm are shorter than those of the other one-pass algorithm and, except for long messages, are shorter than those of the two-pass method. The new algorithm is well suited for on-line encoding/decoding in data networks and for file compression.

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.

Data compression is widely used in data management to save storage space and network bandwidth. In this report, we outline the performance improvements that can be achieved by exploiting data compression in query processing. The novel idea is to leave data in compressed state as long as possible, and to only uncompress data when absolutely necessary. We will show that many query processing algorithms can manipulate compressed data just as well as decompressed data, and that processing compressed data can speed query processing by a factor much larger than the compression factor.

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.

We present a new method for lossless image compression that gives compression comparable to JPEG lossless mode with about five times the speed. Our method, called FELICS, is based on a novel use of two neighboring pixels for both prediction and error modeling. For coding we use single bits, adjusted binary codes, and Golomb or Rice codes. For the latter we present and analyze a provably good method for estimating the single coding parameter.

Three strongly sequential, lossless compression schemes, one with linearly growing per-letter computational complexity, and two with fixed per-letter complexity, are presented and analyzed for memoryless sources with abruptly changing statistics. The first method, which improves on Willems' weighting approach, asymptotically achieves a lower bound on the redundancy, and hence is optimal. The second scheme achieves redundancy of O (log N=N) when the transitions in the statistics are large, and O (log log N= log N) otherwise. The third approach always achieves redundancy of O i p log N=N j . Obviously, the two fixed complexity approaches can be easily combined to achieve the better redundancy between the two. Simulation results support the analytical bounds derived for all the coding schemes. Index Terms: Piecewise stationary memoryless source, universal coding, redundancy, minimum description length, ideal code length, sequential coding, strongly sequential coding, transition path, ...