OPTIMUM SELECTION OF REED-SOLOMON AND BOSE-CHAUDHURI-HOCQUENGHEM CODES FOR FREQUENCY-HOPPED MULTIPLE ACCESS-SPREAD SPECTRUM COMMUNICATION-SYSTEMS

In this paper, we consider the trade-off between coding gain, processi ng gain, and M-ary orthogonal modulation gain in multiple-access frequ ency-hopped spread-spectrum systems. M-ary FSK modulation and non cohe rent demodulation which employ forward-error-control coding are used. The effect of thermal noise is ignored, and channel errors are due to other-user interference. The total bandwidth expansion due to modulati on, coding, and spread-spectrum is fixed. Two coding schemes are analy sed: Reed-Solomon (RS) codes over GF(M(m)) and BCH(n,k,e) with binary FSK. The performance measure is the maximum number of users which can communicate with a probability of error below a given value. For RS co des we find the optimum modulation alphabet M(opt) as a function of RS codeword length N. The maximum number of users is obtained for variou s bandwidth expansion and bit-error-rate objectives. Both the asynchro nous and the synchronous hopping cases are considered. Our results agr ee with previous results [1,2] when bandwidth expansion due to M-ary o rthogonal modulation is ignored. However, we show the merit of simulta neously optimizing modulation and coding. For BCH codes we show that p erformance improves with increasing the word length n, and that for a given n, the optimum code is chosen such that the product k e is maxim ised. Finally, we present a comparison of the two coding schemes for t he multiple-access channel.