NDLI: Relations Between Redundancy Patterns of the Shannon Code and Wave Diffraction Patterns of Partially Disordered Media

Content Provider	IEEE Xplore Digital Library
Author	Merhav, N.
Copyright Year	1963
Abstract	The average redundancy of the Shannon code, Rn, as a function of the block length n, is known to exhibit two very different types of behavior, depending on the rationality or irrationality of certain parameters of the source: It either converges to 1/2 as n grows without bound, or it may have a nonvanishing, oscillatory, (quasi-) periodic pattern around the value 1/2 for all large n. In this paper, we make an attempt to shed some insight into this erratic behavior of Rn, by drawing an analogy with the realm of physics of wave propagation, in particular, the elementary theory of scattering and diffraction. It turns out that there are two types of behavior of wave diffraction patterns formed by crystals, which are correspondingly analogous to the two types of patterns of Rn. When the crystal is perfect, the diffraction intensity spectrum exhibits very sharp peaks, a.k.a. Bragg peaks, at wavelengths of full constructive interference. These wavelengths correspond to the frequencies of the harmonic waves of the oscillatory mode of Rn . On the other hand, when the crystal is imperfect and there is a considerable degree of disorder in its structure, the Bragg peaks disappear, and the behavior of this mode is analogous to the one where Rn is convergent.
Sponsorship	IEEE Information Theory Society
Starting Page	3402
Ending Page	3406
Page Count	5
File Size	1366200
File Format	PDF
ISSN	00189448
Volume Number	58
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Redundancy Crystals Fourier series Analytical models Coherence Data compression Shannon code Bragg peaks diffraction disorder Hendricks-Teller model lossless source coding redundancy scattering
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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