  In the noisy channel model from coding theory, we wish to detect errors
introduced during transmission by optimizing various parameters of the code.
Bennett, Dudek, and LaForge framed a variation of this problem in the language
of alternating paths in edge-colored complete bipartite graphs in 2016. Here,
we extend this problem to the random graph $\mathbb{G}(n,p)$. We seek the
alternating connectivity, $\kappa_{r,\ell}(G)$, which is the maximum $t$ such
that there is an $r$-edge-coloring of $G$ such that any pair of vertices is
connected by $t$ internally disjoint and alternating (i.e. no consecutive edges
of the same color) paths of length $\ell$. We have three main results about how
this parameter behaves in $\mathbb{G}(n,p)$ that basically cover all ranges of
$p$: one for paths of length two, one for the dense case, and one for the
sparse case. For paths of length two, we found that $\kappa_{r,\ell}(G)$ is
essentially the codegree of a pair of vertices. For the dense case when $p$ is
constant, we were able to achieve the natural upper bounds of minimum degree
(minus some intersection) or the total number of disjoint paths between a pair
of vertices. For the sparse case, we were able to find colorings that achieved
the natural obstructions of minimum degree or (in a slightly less precise
result) the total number of paths of a certain length in a graph. We broke up
this sparse case into ranges of $p$ corresponding to when $\mathbb{G}(n,p)$ has
diameter $k$ or $k+1$. We close with some remarks about a similar parameter and
a generalization to pseudorandom graphs.
