No input symbol should occur more frequently than 1-1/e

2012/01/31 by Gowtham Kumar, Kumar, Gowtham, Alexandros Manolakos +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.1201.6425

arxiv created 2012/01/31 · arxiv updated 2012/02/01

Abstract

Consider any discrete memoryless channel (DMC) with arbitrarily but finite input and output alphabets X, Y respectively. Then, for any capacity achieving input distribution all symbols occur less frequently than 1-1/e. That is, max_{x ∈ X} P^*(x) < 1-(1)/(e) \noindent where P^*(x) is a capacity achieving input distribution. Also, we provide sufficient conditions for which a discrete distribution can be a capacity achieving input distribution for some DMC channel. Lastly, we show that there is no similar restriction on the capacity achieving output distribution.

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