The aim of this note is to provide some reference facts for LZW---mostly from Thomas and Cover \cite{Cover:2006aa} and provide a reference for some metrics that can be derived from it. LZW is an algorithm to compute a Kolmogorov Complexity estimate derived from a limited programming language that only allows copy and insertion in strings (not Turing complete set). Despite its delightful simplic...

We explore the use of the LZW and LZSS data compression methods. These methods or some versions of them are very common in use of compressing different types of data. Even though on average LZSS gives better compression results, we determine the case in which the LZW perform best and when the compression efficiency gap between the LZW algorithm and its LZSS counterpart is the largest.

The goal of this research is twofold: (i) to analyze generalized digital search trees, and (ii) to derive the average proole (i.e., phrase length) of a generalization of the well known parsing algorithm due to Lempel and Ziv. In the generalized Lempel-Ziv parsing scheme, one partitions a sequence of symbols from a nite alphabet into phrases such that the new phrase is the longest substring seen...

The Lempel-Ziv parsing (LZ77) is a widely popular construction lying at the heart of many compression algorithms. These algorithms usually treat data as sequence bytes, i.e., blocks fixed length 8. Another common option to view bits. We investigate following natural question: what relationship between LZ77 parsings same interpreted fixed-length and bits (or other “elementary” letters)? In this ...

We explore the possibility of using multiple processors to improve the encoding and decoding times of Lempel–Ziv schemes. A new layout of the processors, based on a full binary tree, is suggested and it is shown how LZSS and LZW can be adapted to take advantage of such parallel architectures. The layout is then generalized to higher order trees. Experimental results show an improvement in compr...

This paper considers the problem of data compression for dependent quantum systems. It is the second in a series under the same title which began with [6] and continues with [12]. As in [6], we are interested in Lempel–Ziv encoding for quantum Gibbs ensembles. Here, we consider the canonical ideal lattice Boseand Fermi-ensembles. We prove that as in the case of the grand canonical ensemble, the...