Optimal selection of Reed-Solomon code rate and the number of frequency slots in asynchronous FHSS-MA networks

The performance of Reed-Solomon codes in an asynchronous frequency-hop spread-spectrum multiple-spectrum (FHSS-MA) network is discussed. When q denotes the number of frequency slots available to the network and r denotes the rate of the Reed-Solomon code, optimal (q,r) pairs that meet a given performance criterion with minimum bandwidth expansion (q/r) for a given number of active users are obtained. It is shown that the optimal code rate rapidly converges to a constant value and the optimum number of slots increases approximately linearly as the number of active users increases. 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 criterion with minimum bandwidth expansion