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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Patent
Efficient Ziv-Lempel LZI data compression system using variable code fields
TL;DR: In this article, an improved Ziv-Lempel LZ1 process that uses a history buffer to save the most recent source string symbols for use in encoding the source symbols as "match-length" and "match offset" tokens was proposed.
Patent
Method and apparatus for the compression and decompression of data using lempel-ziv based techniques
TL;DR: In this article, a fixed-length codeword from a variable number of data symbols is constructed from the length and starting point of the longest substring in the first half of a buffer that matches a substring from the second half of the buffer.
Proceedings ArticleDOI
One-Lead ECG-based Personal Identification Using Ziv-Merhav Cross Parsing
TL;DR: A new % NEW DAV non-fiducial ECG biometric identification method based on data compression techniques, namely the Ziv-Merhav cross parsing algorithm for symbol sequences (strings), which achieves 100% subject recognition rate despite the existence of differentiated stress states.
Journal ArticleDOI
Low-algorithmic-complexity entropy-deceiving graphs
TL;DR: This work explains how integer sequences with properties such as Borel normality are not independent of the way in which an object, such as a graph, can be described or observed, and introduces recursive and nonrecursive graphs and graph constructions based on these integer sequences.
Journal ArticleDOI
The interactions between ergodic theory and information theory
TL;DR: A brief history of this interaction between information theory and entropy, together with a more detailed look at three areas of connection, namely, recurrence theory, blowing-up bounds, and direct sample-path methods.
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.