Simple Coding Techniques for Many-Hop Relaying

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
$\mathcal {O}(m+k)$
transmission time.