Arithmetic coding as a non-linear dynamical system |
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| Authors: | Nithin Nagaraj Prabhakar G Vaidya Kishor G Bhat |
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| Institution: | 1. Institute of Energy and Climate Research (IEK-2), Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany;2. Institute of Materials Science and Engineering (WKK), TU Kaiserslautern, D-67653 Kaiserslautern, Germany;1. Department of Physics and Mathematics, Anhui University of Science and Technology, Huainan, 232001, PR China;2. Department of Physics, Yunnan University, Kunming, 650091, PR China;1. School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK;2. Thales Underwater Systems Ltd, Dolphin House, Ashurst Drive, Cheadle Heath, Stockport SK3 0XB, UK |
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| Abstract: | 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, non-linear dynamical system known as Generalized Luröth 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. |
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