Adaptive update algorithms for fixed dictionary lossless data compressors

Lossless data compressors strive to find a minimal size representation for a given source's output. Commonly used compression algorithms such as Lempel-Ziv, Huffman and arithmetic coding can be shown to achieve source entropy under ideal conditions. In practice however, the performance of these algorithms is limited by issues such as finite-memory in the coder and non-stationary source statistics. This paper presents results from our study of universal adaptive data compression algorithms for non-stationary sources with memory. We argue that by using a "clever" update algorithm, coupled with a compact data structure, a compressor can achieve a more compact data representation than that produced by a non-adaptive or weakly adaptive one. We present update heuristics that can be used. Further, an analytical framework for adaptive compressors is developed, along with an intuitive justification in the context of Kolmogorov complexity. Our study concentrates on dictionary style compressors such as the Lempel-Ziv algorithm and its avatars. However, the ideas contained herein can also be applied to source modeling processes that are used in arithmetic and Huffman type coders. The concepts presented are used in a new lossless compression algorithm for wide band audio.<<ETX>>