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
On the universality of the LZ-based decoding algorithm
Amos Lapidoth,Jacob Ziv +1 more
TL;DR: Ziv's (1985) decoding algorithm is studied, and it is demonstrated that while it was originally proposed as a universal decoder for the family of finite- state channels with deterministic (but unknown) transitions, it is in fact universal for the broader class of all finite-state channels.
Journal ArticleDOI
Claude E. Shannon: a retrospective on his life, work, and impact
TL;DR: The process under which the impact of Shannon's work evolved from the creation of a beautiful and challenging theory to the establishment of the central principles guiding digital communication technology is considered.
Proceedings ArticleDOI
DNA sequence compression using the Burrows-Wheeler Transform
TL;DR: Off-line dictionary oriented approaches to DNA sequence compression, based on the Burrows-Wheeler Transform, are investigated, which proposes off-line methods to compress DNA sequences that exploit the different repetition structures inherent in such sequences.
Universal lossless data compression algorithms
TL;DR: This paper focuses on compression of video or picture data, a field in which data of vast sizes are processed and the amount of information stored in databases grows fast, while their contents often exhibit much redundancy.
Patent
Compression and decompression methods on two-dimensional image data
TL;DR: In this paper, a data compression apparatus includes a dictionary buffer for holding data of the immediately preceding line of successively inputted two-dimensional image data, a buffer for extracting a plurality of continuous data strings from the inputted data of a current line to store them as a partial data string to be compressed, a scanning comparison section for detecting whether or not the same data string as the part of the compressed data string exists in the data stored in the dictionary buffer, and a code generator by which in the case where the presence of the same string is detected by the scanning comparison
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.