  Coverage is one of the main quality of service of a wirelessnetwork.
$k$-coverage, that is to be covered simultaneously by $k$network nodes, is
synonym of reliability and numerous applicationssuch as multiple site MIMO
features, or handovers. We introduce here anew algorithm for computing the
$k$-coverage of a wirelessnetwork. Our method is based on the observation that
$k$-coverage canbe interpreted as $k$ layers of $1$-coverage, or simply
coverage. Weuse simplicial homology to compute the network's topology and
areduction algorithm to indentify the layers of $1$-coverage. Weprovide figures
and simulation results to illustrate our algorithm.
