No input symbol should occur more frequently than 1-1/e
Information Theory
2012-02-01 v1 math.IT
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, \[ \max\limits_{x \in \mathcal{X}} P^*(x) < 1-\frac{1}{e} \] \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.
Keywords
Cite
@article{arxiv.1201.6425,
title = {No input symbol should occur more frequently than 1-1/e},
author = {Gowtham Kumar and Alexandros Manolakos},
journal= {arXiv preprint arXiv:1201.6425},
year = {2012}
}