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