Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithmic Computability and Approximability of Capacity-Achieving
  Input Distributions   The capacity of a channel can usually be characterized as a maximization of
certain entropic quantities. From a practical point of view it is of primary
interest to not only compute the capacity value, but also to find the
corresponding optimizer, i.e., the capacity-achieving input distribution. This
paper addresses the general question of whether or not it is possible to find
algorithms that can compute the optimal input distribution depending on the
channel. For this purpose, the concept of Turing machines is used which
provides the fundamental performance limits of digital computers and therewith
fully specifies tasks are algorithmically feasible in principle. It is shown
for discrete memoryless channels that it is impossible to algorithmically
compute the capacity-achieving input distribution, where the channel is given
as an input to the algorithm (or Turing machine). Finally, it is further shown
that it is even impossible to algorithmically approximate these input
distributions.

36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin