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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Proceedings ArticleDOI
At the roots of dictionary compression: string attractors
Dominik Kempa,Nicola Prezza +1 more
TL;DR: In this paper, it was shown that the problem of finding a small set of positions capturing all distinct text substrings is NP-hard for k ≥ 3. But the problem is APX-complete for constant k, and give strong inapproximability results.
Data mining and compression : where to apply it and what are the effects?
TL;DR: In this article, the authors investigate the effects of selecting features, learning, and making predictions from data that has been compressed using lossy transformations, and propose a specialised feature selection approach that considers predictive performance alongside compressibility, measured by compressing them individually or in a single concatenated stream.
Journal ArticleDOI
Cloud-based adaptive compression and secure management services for 3D healthcare data
Arcangelo Castiglione,Raffaele Pizzolante,Alfredo De Santis,Bruno Carpentieri,Aniello Castiglione,Francesco Palmieri +5 more
TL;DR: This work proposes an engine for lossless dynamic and adaptive compression of 3D medical images, which also allows the embedding of security watermarks within them and defines the architecture of a SaaS Cloud system, which is based on the aforementioned engine.
Journal ArticleDOI
Optimal sequential probability assignment for individual sequences
TL;DR: A deterministic performance bound is derived for the class of finite-state schemes and other related families, analogous to the classical (probabilistic) minimum description length (MDL) bound, which holds for "most" sequences, similarly to the probabilistic setting, where the bound holds for 'most' sources in a class.
Patent
High speed lossless data compression system
TL;DR: In this paper, a data compression process and system that identifies the data type of an input data stream and then selects in response to the identified data type at least one data compression method from a set of data compression methods that provides an optimal compression ratio for that particular data type, thus maximizing the compression ratio of that data stream.
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.