8.8 Performance Illustration

Let us consider an example of a PCCC turbo code with g _FF ( D) = 1 + D ⁴ and g _FB ( D) =1 + D + D ² + D ³ + D ⁴. The first encoder is terminated, while the second encoder is not. We set N _b = 330, so that N _c = 998. We use BPSK modulation. The interleaver between the encoders is pseudo-random and changes from codeword to codeword. The channel is an AWGN channel so that , where n _k are iid complex Gaussian, zero mean and . We evaluate the performance in terms of bit error rate (BER) versus signal-to-noise ratio (SNR). The SNR is expressed as E _b/ N ₀ (in decibels ^[2]), with E _b = E _s/( R log ₂ ?), where R denotes the code rate. The resulting performance is shown in Fig. 8.22. As the iterations proceed, the BER drops by several orders of magnitude. We discern three SNR regions for the turbo code: below 0 dB, the BER is fairly high. Then, above 0 dB the BER suddenly drops. The SNR value at which the BER suddenly drops is known as the pinch-off point (0 dB in our case). Above 0 dB the turbo code enters the so-called waterfall region, where the BER drops...