E-SHIFT-KEYING The impact of pulse jamming can be neutralized with coding techniques where the use of coding not only provides the usual coding gain but also forces the worst pulse jammer to be the constant power jammer. Thus, for Basic Concepts and System Models example, at 10-6 bit error probability, the total coding gain against the worst pulse jammer is 40 dB as a result of pulse jammer neutralization plus the usual coding gain. This is a significant gain compared to the coding gain achieved in the usual additive white Gaussian noise channel. Reducing the data rate or expanding the signal bandwidth is usually asso- ciated with coding since some form of redundancy is required. For spread- spectrum signals it is not necessary to reduce the data rate or increase the signal bandwidth in order to use coding techniques. To illustrate this consider a sim- ple constraint length K = 2, rate R=1bits = per coded symbol convolutional code. For each data bit the encoder generates two coded bits. Let {dn} be the data bit sequence as before. For the k-th transmission time interval, the two coded bits are ak = (ak1, ak2) (3.46) where ak1=dk dk=dk-1. Suppose that Tb is the data bit time. Then each coded bit must be trans- mitted in Ts = Tb/2 seconds. Here Ts is the time of each coded symbol. Defining k = integer (3.47) shown in Figure 3.9 is the uncoded waveform d(t), coded waveform a(t), and PN waveform c(t) for N = 6. With ordinary BPSK modulation, the coded waveform will have twice the bandwidth of the uncoded waveform. However, when we multiply the PN waveform with the coded and uncoded waveform, we obtain c(t)d(t) and c(t)a(t) shown in Figure 3.10. At this point, the resulting spread-spectrum signals have the same bandwidth. Also shown here is the convolutional code diagram when {1, - 1} binary symbols are con- verted to {1,0} binary symbols. To illulstrate the impact of coding, consider the simplest of all coding tech- niques, the repeat code. This is a code of rate R = 1/m bits per coded sym- bol for some integer m. Fo