Journal ArticleDOI
Compression of individual sequences via variable-rate coding
Jacob Ziv,A. Lempel +1 more
TLDR
The proposed concept of compressibility is shown to play a role analogous to that of entropy in classical information theory where one deals with probabilistic ensembles of sequences rather than with individual sequences.Abstract:
Compressibility of individual sequences by the class of generalized finite-state information-lossless encoders is investigated. These encoders can operate in a variable-rate mode as well as a fixed-rate one, and they allow for any finite-state scheme of variable-length-to-variable-length coding. For every individual infinite sequence x a quantity \rho(x) is defined, called the compressibility of x , which is shown to be the asymptotically attainable lower bound on the compression ratio that can be achieved for x by any finite-state encoder. This is demonstrated by means of a constructive coding theorem and its converse that, apart from their asymptotic significance, also provide useful performance criteria for finite and practical data-compression tasks. The proposed concept of compressibility is also shown to play a role analogous to that of entropy in classical information theory where one deals with probabilistic ensembles of sequences rather than with individual sequences. While the definition of \rho(x) allows a different machine for each different sequence to be compressed, the constructive coding theorem leads to a universal algorithm that is asymptotically optimal for all sequences.read more
Citations
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Book ChapterDOI
A Lempel-Ziv text index on secondary storage
Diego Arroyuelo,Gonzalo Navarro +1 more
TL;DR: A new index for full-text searching on secondary storage, based on the Lempel-Ziv compression algorithm and requiring 8uHk +o(u log σ) bits of space, where Hk denotes the k-th order empirical entropy of T, for any k = o(logσ u).
Proceedings ArticleDOI
Bit-parallel approach to approximate string matching in compressed texts
TL;DR: This work addresses the problem of approximate string matching on compressed text with an algorithm that exploits bit-parallelism and is competitive to the algorithm proposed by J. Kida et al. (1999) that captures various dictionary-based compression methods.
Journal ArticleDOI
Performance Evaluation of LZ-Based Location Prediction Algorithms in Cellular Networks
TL;DR: This letter compares three LZ based prediction algorithms, separates the algorithms into two independent phases (tree updating and probability calculation), includes Active LeZi in the study, and evaluates hit rate and resource consumption, including processing time.
Journal ArticleDOI
On the optimal asymptotic performance of universal ordering and of discrimination of individual sequences
TL;DR: Data compression is applied to derive a universal algorithm that solves the problem of ordering strings of a fixed length over a discrete alphabet according to decreasing probabilities of having been emitted by an unknown finite-state source with an optimal asymptotic performance.
Book ChapterDOI
ESP-index: a compressed index based on edit-sensitive parsing
TL;DR: A compressed self-index based the edit-sensitive parsing (ESP) that supports locating P and displaying substring of S, which can be represented as a DAG G.
References
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Book
Information Theory and Reliable Communication
TL;DR: This chapter discusses Coding for Discrete Sources, Techniques for Coding and Decoding, and Source Coding with a Fidelity Criterion.
Journal ArticleDOI
A universal algorithm for sequential data compression
Jacob Ziv,A. Lempel +1 more
TL;DR: The compression ratio achieved by the proposed universal code uniformly approaches the lower bounds on the compression ratios attainable by block-to-variable codes and variable- to-block codes designed to match a completely specified source.
Journal ArticleDOI
On the Complexity of Finite Sequences
A. Lempel,Jacob Ziv +1 more
TL;DR: A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented, related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated.
Journal ArticleDOI
Coding theorems for individual sequences
TL;DR: The finite-state complexity of a sequence plays a role similar to that of entropy in classical information theory (which deals with probabilistic ensembles of sequences rather than an individual sequence).
Journal ArticleDOI
On Information Lossless Automata of Finite Order
TL;DR: The application of the tests to finite deterministic automata is discussed and a method of constructing a decoder for a given finite automaton that is information lossless of finite order, is described.