Evaluation of Inference Algorithms for Distributed Channel Allocation in Wireless Networks

Resource allocation in wireless networks, i.e., assigning time and frequency slots over specific terminals under spatio-temporal constraints, is a fundamental and challenging problem. Belief Propagation/message passing (inference) algorithms have been proposed for constraint satisfaction problems (CSP), since they are inherently amenable to distributed implementation. This work compares two message passing algorithms for time and frequency allocation, satisfying signal-to-interference-and-noise-ratio, half-duplex-radio operation and routing constraints. The first method periodically checks whether the constraints are satisfied locally and restarts specific messages, when the local constraints (encoded in corresponding factors) are not satisfied. The second method stochastically perturbs Belief Propagation, using Gibbs sampling. The methods are evaluated, based on how often they fail to converge to a valid (i.e., constraint-satisfying) allocation, coined as outage probability. Numerical results demonstrate that, as the maximum number of iterations increase, both methods decrease the outage probability. However, the restarting method offers faster convergence to a valid CSP solution. Future work will focus on next generation 5/6G wireless networks.