  It is known that the Kesten-Stigum reconstruction bound is tight for roughly
symmetric binary channels. In this paper, we will adopt a refined analysis of
moment recursion on a weighted version of the magnetization, which is engaged
in Sly [2011] to handle the symmetric Potts model, and establish the critical
condition of the asymmetric Ising model to make Kesten-Stigum bound the
reconstruction threshold on regular $d$-ary trees.
