Network Resources Optimization for Random Linear Network Coding

In a multisource multicast network using random linear network coding, only the lower bounds on the decoding probability, the probability that all receivers can decode all source processes, have been known. We obtained new topology-independent and topology-dependent upper bounds on the decoding probability by using a simple counting argument. These upper bounds and the best known lower bound on the decoding probability are used to optimize the finite field size governing the use of network resources by exploiting a trade-off between computational complexity and the decoding probability.