OPTIMAL SELECTION OF REED-SOLOMON CODE RATE AND THE NUMBER OF FREQUENCY SLOTS IN ASYNCHRONOUS FHSS-MA NETWORKS

Abstract

In this paper we consider the performance of Reed-Solomon codes in asynchronous FHSS-MA networks. When q denotes the number of frequency slots available to the network and r denotes the rate of the Reed-Solomon code, we obtain optimal (q, r) pairs that achieve a given performance criteria with minimum bandwidth expansion (q/r) for a given number of active users. We show that the optimal code rate rapidly converges to a constant value and the optimum number of slots increase approximately linearly as the number of active users increase. This suggests that one should fix the code rate and increase the number of slots to accommodate the increasing number of users in the network under a given performance criteria with minimum bandwidth expansion.