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
Block-oriented compression techniques for large statistical databases
TL;DR: The authors explore the compression of large statistical databases and propose techniques for organizing the compressed data such that standard database operations such as retrievals, inserts, deletes and modifications are supported.
Book ChapterDOI
Designing smart environments: a paradigm based on learning and prediction
Sajal K. Das,Diane J. Cook +1 more
TL;DR: The proposed paradigm optimizes such goal functions of smart environments as minimizing maintenance cost, manual interactions and energy utilization and applies the proposed paradigm to the inhabitant’s location and activity tracking and prediction, and automated decision-making capability.
Journal ArticleDOI
Double-dictionary matching pursuit for fault extent evaluation of rolling bearing based on the Lempel-Ziv complexity
TL;DR: Wang et al. as discussed by the authors proposed a double-dictionary matching pursuit (DDMP) for fault extent evaluation of rolling bearing based on the Lempel-Ziv complexity (LZC) index.
Journal ArticleDOI
Simple universal lossy data compression schemes derived from the Lempel-Ziv algorithm
En-hui Yang,John C. Kieffer +1 more
TL;DR: Two universal lossy data compression schemes, one with fixed rate and the other with fixed distortion, are presented, based on the well-known Lempel-Ziv algorithm, both of which are universal in the sense that for any stationary, ergodic source or for any individual sequence, the sample distortion performance is given almost surely by the distortion rate function.
Journal ArticleDOI
Distortion-rate theory for individual sequences
TL;DR: The coding theorem demonstrates the existence of {\em universal} encoders which are asymptotically optimal for every infinite sequence over a given finite alphabet.
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.