Optimal slotted random access in coded wireless packet networks

We consider the problem of jointly optimizing random access and subgraph selection in coded wireless packet networks. As opposed to the corresponding scheduling approach, the problem cannot be formulated as a convex optimization problem and is thus difficult to solve. We propose a special adaptation of the branch and bound method which allows for computing the optimal strategy for small and medium networks. The key tool for efficiency is a random access specific convex relaxation bound. We compare these results to both optimal and suboptimal joint medium access and subgraph selection techniques, to conclude that there is room for further improvement of suboptimal yet practical random access schemes.