Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the binary adder channel with complete feedback, with an application
  to quantitative group testing   We determine the exact value of the optimal symmetric rate point $(r, r)$ in
the Dueck zero-error capacity region of the binary adder channel with complete
feedback. We proved that the average zero-error capacity $r = h(1/2-\delta)
\approx 0.78974$, where $h(\cdot)$ is the binary entropy function and $\delta =
1/(2\log_2(2+\sqrt3))$. Our motivation is a problem in quantitative group
testing. Given a set of $n$ elements two of which are defective, the
quantitative group testing problem asks for the identification of these two
defectives through a series of tests. Each test gives the number of defectives
contained in the tested subset, and the outcomes of previous tests are assumed
known at the time of designing the current test. We establish that the minimum
number of tests is asymptotic to $(\log_2 n) / r$ as $n \to \infty$.

17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat