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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Journal ArticleDOI
Diagnosis of Alzheimer's disease from EEG signals: where are we standing?
TL;DR: Several state-of-the-art pre-processing techniques based on blind source separation and other non-linear filtering paradigms based on electroencephalograms for diagnosing Alzheimers disease based on EEG are outlined.
Journal ArticleDOI
The string B-tree: a new data structure for string search in external memory and its applications
Paolo Ferragina,Roberto Grossi +1 more
TL;DR: This work introduces a new text-indexing data structure, the String B-Tree, that can be seen as a link between some traditional external-memory and string-matching data structures that is made more effective by adding extra pointers to speed up search and update operations.
Online Learning: Theory, Algorithms, and Applications
TL;DR: This dissertation describes a novel framework for the design and analysis of online learning algorithms and proposes a new perspective on regret bounds which is based on the notion of duality in convex optimization.
Journal ArticleDOI
Interpretation of the Lempel-Ziv Complexity Measure in the Context of Biomedical Signal Analysis
TL;DR: An investigation aimed at gaining a better understanding of the LZ complexity itself and its interpretability as a biomedical signal analysis technique indicates that LZ is particularly useful as a scalar metric to estimate the bandwidth of random processes and the harmonic variability in quasi-periodic signals.
Patent
High speed data compression and decompression apparatus and method
TL;DR: In this paper, a data compressor compresses an input stream of data character signals by storing in a string table strings encountered in the input stream, where each string comprises a prefix string and an extension character where the extension character is the last character in the string and the prefix string comprises all but the extension characters.
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.