We consider two problems in which machines with limited internal memory are used to compress and decompress data. In the first application, a powerful encoder transmits a coded file to a decoder that has severely constrained memory. A data structure that achieves minimum storage is presented, and alternative methods that sacrifice a small amount of storage to attain faster decoding are described. The second problem we address is that of encoding and decoding in limited memory. Methods for representing context models succinctly are described. These methods provide compression performance that is superior to state-of-the-art techniques, and competitive with newer approaches that use five times as much internal memory.

Context modeling has emerged as the most promising new approach to compressing text. While context-modeling algorithms provide very good compression, they suffer from the disadvantages of being quite slow and requiring large amounts of main memory in which to execute. We describe a context-model-based algorithm that runs significantly faster and uses less space than earlier context models. Although our algorithm does not achieve the compression performance of competing context models, it does provide a significant improvement over the widely-used Unix utility compress in terms of both use of memory and compression performance.

We discuss representations of prefix codes and the corresponding storage space and decoding time requirements. We assume that a dictionary of words to be encoded has been defined and that a prefix code appropriate to the dictionary has been constructed. The encoding operation becomes simple given these assumptions and given an appropriate parsing strategy, therefore we concentrate on decoding. The application which led us to this work constrains the use of internal memory during the decode operation. As a result, we seek a method of decoding which has a small memory requirement.

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.