 process. Usually, after a given number of iterations, one observes that the two decoders converge to a stable final decision for d. In practice, depending on the nature of the soft-decision decoder, scaling or clipping operations may be applied to the extrinsic information in order to ensure convergence within a small number of iterations. It is shown in the literature that the Max-Log-MAP decoding algorithm can make a good trade-off between performance and complexity with the added advantage of not requiring any knowledge of the noise level (see Figure 9-43). A stop criterion facilitates the convergence of the iterative decoding process and helps reduce the average power consumption of the decoder by reducing the average number of iterations required to decode a block, without compromising performance [85,86,91]. For practical applications the turbo code parameters are very often required to be adapted to those of the application. The systematic bits are always present at the output of the turbo encoder; however, depending on the desired code rate, the parity bits from the two constituent encoders may be punctured prior to transmission (see Figure 9-41). The puncturing mechanism involves deleting some of the 9.12 Channel coding and modulation Target BER=10-3 Target BER=10-5 Frame Size (Bits) FIGURE 9-42 Minimum Eb/No to achieve a target BER using the UMTS turbo coder (R = 1/3) with BPSK modulation over an AWGN channel [89] parity bits prior to transmission. As an example, if the minimum code rate of a turbo coder is 1/5, a code rate of 1/3 can be generated by deleting the second parity output of each encoder. Note that the puncturing pattern for each code rate must be known by the decoder for correct interpretation of the received bits. It is shown that for the smaller input frame sizes fewer iterations are required and the performance of the turbo coder improves with increasing the frame size. This is due to an increase in interleaver gain as the input frame size becomes larger. Figure 9-42 shows the minimum E