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
Method and means for character string pattern matching for compression and the like using minimal cycles per character
Joe-Ming Cheng,Yancy Cheng +1 more
TL;DR: In this article, a method and means for ascertaining maximal length pattern matches of K characters per cycle between character strings in a reduced amount of time using a pipeline like concurrent dataflow model in which a recursive exhaustive greedy comparison matching between the strings in consistent direction yields a parsing of the longest matches.
Journal ArticleDOI
Fixed Data Base Version Of The Lempel-Ziv Data Compression Algorithm
A.D. Wyner,Jacob Ziv +1 more
TL;DR: It is demonstrated that a variant of the Lempel-Ziv data compression algorithm where the database is held fixed and is reused to encode successive strings of incoming input symbols is optimal, provided that the source is stationary and satisfies certain conditions.
Journal ArticleDOI
Universal linear least squares prediction: upper and lower bounds
TL;DR: It is shown that a prediction algorithm demonstrated whose accumulated squared prediction error is asymptotically as small as the best fixed linear predictor for that sequence, taken from the class of all linear predictors of a given order p, is optimal in a min-max sense.
Patent
Method and Apparatus for Processing Financial Information at Hardware Speeds Using FPGA Devices
TL;DR: In this article, a method and apparatus use hardware logic deployed on a reconfigurable logic device to process a stream of financial information at hardware speeds, which can be configured to perform data reduction operations on the financial information stream.
Journal ArticleDOI
On the privacy afforded by adaptive text compression
Ian H. Witten,John G. Cleary +1 more
TL;DR: This paper introduces the modern approach to text compression and describes a highly effective adaptive method, with particular emphasis on its potential for protecting messages from eavesdroppers.
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.