  In this paper, we study the problem of relaying a single bit of information
across a series of binary symmetric channels, and the associated trade-off
between the number of hops $m$, the transmission time $n$, and the error
probability. We introduce a simple, efficient, and deterministic protocol that
attains positive information velocity (i.e., a non-vanishing ratio
$\frac{m}{n}$ and small error probability) and is significantly simpler than
existing protocols that do so. In addition, we characterize the optimal
low-noise and high-noise scaling laws of the information velocity, and we adapt
our 1-bit protocol to transmit $k$ bits over $m$ hops with $O(m+k)$
transmission time.
