Minimum Worst-Case-Erasure QOS Routing

In communication networks where (1) some nodes are capable of correcting up to a maximum number of erasure, and (2) the nodes are connected by the q-ary symmetric erasure channels parametrized by their bit erasure ratios (BER); it is often possible to find the path with minimum (zero) worst possible erasure. We introduce (1) the BER and worst-case erasure (WCE) metrics and (2) an algebra equipped with a total ordering that allows us to compute and compare the path lengths from its edges' lengths, and ultimately measure edge QoS. We use these metrics with a generalized Dijkstra's algorithm to compute the minimum WCE path