  The noisy broadcast model was first studied in [Gallager, TranInf'88] where
an $n$-character input is distributed among $n$ processors, so that each
processor receives one input bit. Computation proceeds in rounds, where in each
round each processor broadcasts a single character, and each reception is
corrupted independently at random with some probability $p$. [Gallager,
TranInf'88] gave an algorithm for all processors to learn the input in
$O(\log\log n)$ rounds with high probability. Later, a matching lower bound of
$\Omega(\log\log n)$ was given in [Goyal, Kindler, Saks; SICOMP'08].
  We study a relaxed version of this model where each reception is erased and
replaced with a `?' independently with probability $p$. In this relaxed model,
we break past the lower bound of [Goyal, Kindler, Saks; SICOMP'08] and obtain
an $O(\log^* n)$-round algorithm for all processors to learn the input with
high probability. We also show an $O(1)$-round algorithm for the same problem
when the alphabet size is $\Omega(\mathrm{poly}(n))$.
