Combining a note by Rissanen and an idea of enumerative coding we obtain a new implementation of the Ziv-Lempel incremental parsing algorithm for coding and decoding discrete data sequences. Index Terms -Ziv-Lempel algorithm, enumerative coding.

Indexing text collections to support pattern matching queries is a fundamental problem in computer science. New challenges keep arising as databases grow, and for repetitive collections, compressed indexes become relevant. To successfully exploit the regularities of repetitive collections different approaches have been proposed. Some of these are Compressed Suffix Array, Lempel-Ziv, and Grammar...

The aim of this study is to show that the measures derived from Electrocardiogram (ECG) signals many a time perform better than the same measures obtained from heart rate (HR) signals. A comparison was made to investigate how far the nonlinear symbolic dynamics approach helps to characterize the nonlinear properties of ECG signals and HR signals, and thereby discriminate between normal and cong...

This paper expands upon existing and introduces new formulations of Bennett's logical depth. In previously published work by Jordon Moser, notions finite-state-depth pushdown-depth were examined compared. These based on finite-state transducers information lossless pushdown compressors respectively. Unfortunately a full separation between the two was not established. formulation restricting how...

The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but they all demand prohibitive amounts of input data. In this paper we consider real-valued time series and construct conditional distribution estimates that make...

Random sequences attain the highest entropy rate. The estimation of entropy rate for an ergodic source can be done using the Lempel Ziv complexity measure yet, the exact entropy rate value is only reached in the infinite limit. We prove that typical random sequences of finite length fall short of the maximum Lempel-Ziv complexity, contrary to common belief. We discuss that, for a finite length,...

A compression algorithm takes a finite structure of a class K as input and produces a finite structure of a different class K’ as output. Given a property P on the class K defined in a logicL, we study the definability of property P on the class K’. We consider two compression schemas on unary ordered structures (words), compression by runlength encoding and the classical Lempel-Ziv. First-orde...

In the implementation of lossless compression, the traditional Lempel-Ziv dictionary algorithm produces good compression performance, but at a relatively slow processing speed for use in real-time applications. This paper highlights a technique to speed up the overall compression process through introduction of a prediction pre-processor stage. A variety of predictors are applied to two variati...

In this paper, a natural extension of the Lempel-Ziv complexity for several finitetime sequences, defined on finite size alphabets is proposed. Some results on the defined joint Lempel-Ziv complexity are given, as well as properties in connection with the Lempel-Ziv complexity of the individual sequences. Also, some links with Shannon entropies are exhibited and, by analogy, some derived quanti...