s afforded by combining an RS outer code, a binary convo- lutional inner code, and optimum diversity. As in Section 2.3.2.3 when we considered the same systems with diversity, because the inner code operates on binary data, the RS outer code sees a binary rather than an M-ary super channel. Analytically, this requires that we use (2.171) with M = 2 and L = Q, which reduces it to (2.156). As before, we will use the Odenwalder (7,1) convolutional inner code for the K = 1 FH/MFSK system, and the Trumpis (7,1) and (7,1) codes for K = 2 and K = 3, respectively. The inner code Pb translates into a required EIN and Mopt through (2.163-2.164) and (2.173), with G() specified by (2.146), (2.148), or (2.149) depending on the particular inner code, and R' = k x inner code rate. (2.175) These systems are compared in Table 2.21 for an overall Pb = 10-5 in worst case noise and tone jamming. In all cases, Mopt ~ 1 SO that the concatenated RS/binary convolutional coding structure is capable of coping with the jam- ming without the need for additional coding redundancy through diversity; this is underscored by the similarity between the results in Tables 2.15 and 2.21. In fact, the addition of optimum diversity only provides an improve- ment of .2 dB in the sense that the best system in Table 2.21 (the (1023,959) RS outer code with the (7,1) Trumpis convolutional inner code over a 4-ary channel) requires EIN = 8.11 dB to achieve the benchmark bit error rate of 10-5 in worst case non-adaptive jamming, whereas Eb/N, = 8.31 dB for the best system in Table 2.15. Still, this particular coding scheme provides the best performance of all implementations considered SO far. Lest these results be taken out of context without regard for the associ- ated design constraints, we should note that there are realistic scenarios which reduce the EbIN1 requirement for a given . For example, band mul- titone jamming is only possible if the M-ary bands are distinct; that is, the MFSK tones on a given hop occupy M adjacent FH slots as shown in Figure 2