Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Broadcasting on trees near criticality   We revisit the problem of broadcasting on $d$-ary trees: starting from a
Bernoulli$(1/2)$ random variable $X_0$ at a root vertex, each vertex forwards
its value across binary symmetric channels $\mathrm{BSC}_\delta$ to $d$
descendants. The goal is to reconstruct $X_0$ given the vector $X_{L_h}$ of
values of all variables at depth $h$. It is well known that reconstruction
(better than a random guess) is possible as $h\to \infty$ if and only if
$\delta < \delta_c(d)$. In this paper, we study the behavior of the mutual
information and the probability of error when $\delta$ is slightly subcritical.
The innovation of our work is application of the recently introduced
"less-noisy" channel comparison techniques. For example, we are able to derive
the positive part of the phase transition (reconstructability when
$\delta<\delta_c$) using purely information-theoretic ideas. This is in
contrast with previous derivations, which explicitly analyze distribution of
the Hamming weight of $X_{L_h}$ (a so-called Kesten-Stigum bound).

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The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph