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Arithmetic coding as a non-linear dynamical system

✍ Scribed by Nithin Nagaraj; Prabhakar G. Vaidya; Kishor G. Bhat

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
285 KB
Volume
14
Category
Article
ISSN
1007-5704

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✦ Synopsis

In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, nonlinear dynamical system known as Generalized Luro Β¨th Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.

πŸ“œ SIMILAR VOLUMES

A GENERALIZED LOCAL LINEARIZATION PRINCI
A GENERALIZED LOCAL LINEARIZATION PRINCIPLE FOR NON-LINEAR DYNAMICAL SYSTEMS
✍ D. ROY; L.S. RAMACHANDRA πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 470 KB

Tangent spaces in non-linear dynamical systems are state dependent. Hence, it is generally not possible to exactly represent a non-linear dynamical system by a linear one over "nite segments of the evolving trajectories in the phase space. It is known from the well-known theorem of Hartman and Grobm