Existence of bounded local encoding delays for cyclic multicast networks

Let $e$ be an edge in the flow-acyclic part of a cyclic multicast network, let $P(e)$ be the set of its predecessor edges, and let $T(e)$ be the set of sinks whose matrices are updated when $e$ is processed. Let $D$ denote the unit-delay operator, and choose nonnegative integer delays $i_e(p)\in\mathbb{Z}_0^+$ for $p\in P(e)$ in the local encoding equations

$$v_e(x)=\sum_{p\in P(e)}D^{i_e(p)}\tau(p,e)v_p(x).$$

In the unit-link-delay case, these become

$$v_e(x)=\sum_{p\in P(e)}D^{i_e(p)+1}v_p(x).$$

Bounded-delay existence conjecture. There exists a finite value $I$, depending on the graph and in particular on $T(e)$, such that one can choose delays satisfying $i_e(p)<I$ for every $p\in P(e)$ so that the resulting encoding equations satisfy the full-rank condition for all updated matrices $M_t$, with $t\in T(e)$. This is intended to provide the finite-delay choice required by the centralized binary multicast network-coding algorithm for cyclic networks; the supplied text does not establish whether the assertion is proved or remains open.