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- W3025993335 abstract "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 $hto infty$ 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)." @default.
- W3025993335 created "2020-05-21" @default.
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- W3025993335 date "2020-05-15" @default.
- W3025993335 modified "2023-10-02" @default.
- W3025993335 title "Broadcasting on trees near criticality" @default.
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- W3025993335 doi "https://doi.org/10.48550/arxiv.2005.07801" @default.
- W3025993335 hasPublicationYear "2020" @default.
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