of p. If for each of the four possible cases in Table 4.1, Part 1, the worst value of p that maximizes D is chosen, then the resulting values of the cutoff rates as a function of EJN1 are shown in Figure 1.8. Also shown here is the additive white Gaussian noise channel reference. For each case the worst case value of p is given in Figure 1.9. To obtain the bit error bounds from standard error rate curves such as those shown in Figure 1.7 when there are worst case pulse jammers consider the constraint length K = 7, rate R = 1/2 convolutional code shown in Figure 1.7 for the additive white Gaussian noise channel with soft decision decod- ing. Suppose we wanted the bit error bound for this code with a hard deci- sion decoder operating with no jammer state information and where the jammer is a worst case pulse jammer for this coded DS/BPSK system. At 10-5 bit error probability, the K = 7, R = 1/2 convolutional code shown in Figure 1.7 requires Eb/No = 4.5 dB (1.95) or since there is a rate of R = 1/2 code, it requires E/No = 1.5 dB. (1.96) (O) Reference soft decision with P = I (1) Jammer state information, soft decision (2) Jammer state information, hard decision (3) No jammer state information, soft decision (4) No jammer state information, hard decision Es/Nj (dB) Figure 1.8. R0 for DS/BPSK examples. -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 O 2 4 (3) 6 8 10 12 14 16 Es/N, (dB) Figure 1.9. Worst case p for DS/BPSK examples. Standard Codes and Cutoff Rates From Figure 1.8 this choice of E/No gives the cutoff rate R0 = 0.7 (1.97) on the reference cutoff rate corresponding to the additive white Gaussian noise channel with soft decision decoding. This gives the value of R required to achieve 10-5 bit error probabilities regardless of the channel. For this choice of R0, the worst case pulse jamming channel with hard decision and no jamming state information requires (see curve labelled (4)) E/NJ = 8.0 dB (1.98) Eb/N J = 11.0 dB. (1.99) Uncoded (O) Reference Eb/NJ (dB) Figure 1.10. Worst pulse jamming: K = 7, R = 1/2 code. Co