Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: No input symbol should occur more frequently than 1-1/e   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.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph