. The RS codes by themselves were particularly ineffective, as evidenced by Table 2.19. This poor performance could in part be attributed to the use of a hard decision decoder. However, it has been shown that for a given sig- nalling scheme and jamming environment, there is a unique code rate which optimizes the system performance [23]. So far, we have only considered a single (n, k) RS code (rate k/n) over GF(2°) for each block length n = 2° - 1. To investigate the significance of optimizing the RS code rate for FH/MFSK systems in worst case jamming, we will examine the values of Mopt and Eb/N, required to achieve P = 10-5 for the class of (255, k) RS codes with optimum diversity used over a 16-ary channel. Recall from Table 2.19 that the (255, 191) code over this channel required Mopt ~ 5 or 6 depending on whether the jamming was noise or multitone. It is certainly plausible that a lower rate n = 255 RS code might have sufficient redundancy to provide better system performance with less or no diversity. In general, the performance is specified by (2.153) and (2.170): for the case of interest (i.e., M = 16, K = 4, Q = 8, L = 1/2 n = 255), with y defined by (2.164) and Table 2.7, these equations reduce to noise multitone Non-Coherent Frequency-Hopped Systems where noise (2.176) Mopt; multitone The RS code rate is k/n over GF(2°); however, the entire FH/MFSK system including the RS outer code and the optimum diversity has an overall code (2.177) nmopt over GF(2*). Recall that R was defined in Section 2.3.2 (e.g., see (2.133)) as the system code rate in information bits per M-ary channel use: r is the same parameter expressed in M-ary information symbols per channel use, SO that r VI 1. Therefore, Eb/N, a r-1 for both kinds of jamming, and the optimum RS code rate that minimizes the required E/ is the one that maximizes the over- all system code rate. Berlekamp's table of RS character error rates Po for a given block length n and P with hard decision decoding was limited to redundancies n - k that were powers of 2 