NDLI: Shannon ’ s Formula and Hartley ’ s Rule : A Mathematical Coincidence ?

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Shannon ’ s Formula and Hartley ’ s Rule : A Mathematical Coincidence ?

Content Provider	Semantic Scholar
Author	Rioul, Olivier Magossi, José Carlos
Copyright Year	2014
Abstract	Shannon’s formula C = 2 log(1+P/N) is the emblematic expression for the information capacity of a communication channel. Hartley’s name is often associated to it, owing to Hartley’s rule: counting the highest possible number of distinguishable values for a given amplitude A and precision ±∆ yields a similar expression C′ = log(1+A/∆). In the information theory community, the following “historical” statements are generally well accepted: (1) Hartley did put forth his rule twenty years before Shannon; (2) Shannon’s formula as a fundamental tradeoff between transmission rate, bandwidth, and signal-to-noise ratio came out unexpected in 1948; (3) Hartley’s rule is an imprecise relation while Shannon’s formula is exact; (4) Hartley’s expression is not an appropriate formula for the capacity of a communication channel. We show that all these four statements are questionable, if not wrong.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://www.see.asso.fr/bitcache/2dc4b6c75635c1d4df681bae3f93dd54accce2e8?disposition=attachment&op=download&vid=34223
Alternate Webpage(s)	http://djafari.free.fr/MaxEnt2014/papers/30_paper.pdf
Alternate Webpage(s)	https://www.see.asso.fr/en/printpdf/11326/landing
Alternate Webpage(s)	http://perso.telecom-paristech.fr/~rioul/publis/201409rioulmagossi-conf.pdf
Alternate Webpage(s)	https://perso.telecom-paristech.fr/rioul/publis/201409rioulmagossi-conf.pdf
Language	English
Access Restriction	Open
Subject Keyword	Channel (communications) Channel capacity Communications Media Hartley (unit) Hartley Guinea Pig Information theory Mathematics Shannon (unit) Signal-to-noise ratio Whittaker–Shannon interpolation formula
Content Type	Text
Resource Type	Article

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