Capacity of large hybrid erasure networks with random node distribution

The Gupta–Kumar’s nearest-neighbor multihop routing with/without infrastructure support achieves the optimal capacity scaling in a large erasure network in which n wireless nodes and m relay stations are regularly placed. In this paper, a capacity scaling law is completely characterized for an infrastructure-supported erasure network where n wireless nodes are randomly distributed, which is a more feasible scenario. We use two fundamental path-loss attenuation models (i.e., exponential and polynomial power-laws) to suitably model an erasure probability. To show our achievability result, the multihop routing via percolation highway is used and the corresponding lower bounds on the total capacity scaling are derived. Cut-set upper bounds on the capacity scaling are also derived. Our result indicates that, under the random erasure network model with infrastructure support, the achievable scheme based on the percolation highway routing is order-optimal within a polylogarithmic factor of n for all values of m.