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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Universal schemes for prediction, gambling and portfolio selection'
TL;DR: In this article, a universal portfolio selection scheme for a stationary ergodic market with unknown distribution was proposed. But it is not necessary to have the infinite past and hence of the distribution of the market were known to begin with.
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A survey on data compression techniques: From the perspective of data quality, coding schemes, data type and applications
TL;DR: Insight is gained to various open issues and research directions to explore the promising areas for future developments in data compression techniques and its applications.
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A tree-structured adaptive network for function approximation in high-dimensional spaces
TL;DR: The author proposes a technique based on the idea that for most of the data, only a few dimensions of the input may be necessary to compute the desired output function, and it can be used to reduce the number of required measurements in situations where there is a cost associated with sensing.
The design and analysis of efficient lossless data compression systems
TL;DR: It is shown that high-efficiency lossless compression of both text and grayscale images can be obtained by using appropriate models in conjunction with arithmetic coding, and that greatly increased speed can be achieved at only a small cost in compression efficiency.
Journal ArticleDOI
Interval and recency rank source coding: Two on-line adaptive variable-length schemes
TL;DR: Both schemes can do much better than Huffman coding when successive selections of each message type cluster much more than in the independent case.
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.