With no interleaver-deinterleaver pair the optimum decision rule is to form the sum (3.54) and make the bit decision d in accordance with (3.32). The bit error prob- ability is, thus, Ph==Pr{r>0ld=-1} (3.55) This bit error probability is identical to that of the uncoded DS/BPSK sys- tem (see (3.42)). Thus, without interleaving and deinterleaving, there is no difference between the uncoded and simple repeat-coded systems. In general, coding techniques are ineffective without interleaving and deinterleaving. Burst error correcting codes [10] may be effective against some pulse jammers, but would be useless against others. For robust system designs, interleavers and deinterleavers must be used with coding techniques SO that the effect of the pulse jammer is independent among coded symbol transmissions. This is also true for other types of coded spread-spectrum sys- tems and jammers. For the remainder of this work, ideal interleaving and deinterleaving is assumed where the impact of jamming is independent among transmitted coded symbols. (See Appendix 3A for more details.) 3.5.2 Unknown Channel State With ideal interleaving and deinterleaving the channel outputs are as given in (3.49) where again Z, Z,...,Zm , and N1,N2...., Nm are all independent random variables. The decoder takes makes a decision à = 1 or a = -1. With pulse jamming there is the possibility that the decoder may have additional information about the values Z, Z,..., that might aid the decision rule. This might be possible with channel mea- Basic Concepts and System Models surements. Here, however, assume the decoder has no knowledge of Z, Z, Zm and consider two standard decision rules. 3.5.2.1 Soft Decision Decoder The soft decision decoder computes (3.56) and makes the decision in accordance with (3.32). The bit error probability Unknown Jammer State Soft Decision .0005 .0001 Eb/N, (dB) Figure 3.12. Repeat code m = 5 with unknown jammer state/soft decision. Coded Direct-Sequence Spread Binary Phase-Shift-Keying is given by Pb = -1} = Pr m Zini > mE