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Shannon's formula and Hartley's rule: A mathematical coincidence?

Abstract : Shannon’s formula C=1/2log(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 transmis- sion 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.
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Submitted on : Friday, September 13, 2019 - 4:23:04 PM
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Olivier Rioul, José Carlos Magossi. Shannon's formula and Hartley's rule: A mathematical coincidence?. 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), Sep 2014, Amboise, France. pp.105-112. ⟨hal-02286941⟩



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