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
Universal Randomized Guessing With Application to Asynchronous Decentralized Brute–Force Attacks
Neri Merhav,Asaf Cohen +1 more
TL;DR: This work designs efficient algorithms in order to sample from the universal distributions, resulting in strategies which do not depend on the source distribution, are efficient to implement, and can be used asynchronously by multiple agents.
Journal ArticleDOI
Universal lossless data compression with side information by using a conditional MPM grammar transform
TL;DR: A universal lossless data compression algorithm with side information is developed, which can achieve asymptotically the conditional entropy rate of any stationary, ergodic source pair and is the first in the coming family of conditional grammar-based codes, whose expected high efficiency is due to the efficiency of the corresponding unconditional codes.
Journal ArticleDOI
Asymptotic properties on codeword lengths of an optimal FV code for general sources
Hiroki Koga,Hirosuke Yamamoto +1 more
TL;DR: This correspondence is concerned with asymptotic properties on the codeword length of a fixed-to-variable length code (FV code) for a general source {X/sup n/}/sub n=1//sup /spl infin// with a finite or countably infinite alphabet.
Journal ArticleDOI
Average profile of the Lempel-Ziv parsing scheme for a Markovian source
TL;DR: It is proved that appropriately normalized phrase length in all three models tends to the standard normal distribution, which leads to bounds on the average redundancy of the Lempel—Ziv code.
Journal ArticleDOI
A compressed self-index using a Ziv---Lempel dictionary
TL;DR: A new compressed self-index able to locate the occurrences of P in O((m + occ)log u) time, where occ is the number of occurrences and the fundamental improvement over previous LZ78 based indexes is the reduction of the search time dependency on m from O( m2) to O(m).
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.