Turbo Decoding and Detection for Wireless Applications

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Table 1 Standard Turbo Encoder and Decoder Parameters Used results in this section are for half-rate codes, where half the parity bits generated by each of the two component RSC codes are punctured. However, for comparison, we also include some results for turbo codes where all the parity bits from both component encoders are transmitted, leading to a one-third rate code. At the decoder two SISO component decoders are used in parallel, as shown in Fig. 2. In most of our simulations we use the Log-MAP decoder, but the effect of using other component decoders is investigated in Section II-E3. Usually eight component decoder iterations are used, but in the next section we also consider the effect of different number of iterations. 1) Effect of Number of Iterations Used: Fig. 7 shows the performance of a turbo decoder using the MAP algorithm Hanzo et al.: Turbo Decoding and Detection for Wireless Applications versus the number of decoding iterations which were used. For comparison, the uncoded BER and the BER obtained using convolutional coding with a standard (2,1,3) nonrecursive convolutional code are also shown. Like the component codes in the turbo encoder, the convolutional encoder uses the optimum octal generator polynomials of seven and five. It can be seen that the performance of the turbo code after one iteration is roughly similar to that of the convolutional code at low SNRs, but improves more rapidly than that of the convolutional coding as the SNR is increased. As the number of iterations used by the turbo decoder increases, the turbo decoder’s performance gradually improves, although the improvements become marginal for more than eight iterations. 2) Effect of Puncturing: In our investigations we have used two RSC component encoders, and this is the arrangement most commonly used for turbo codes having code rates below R ¼ 2=3. Typically, in order to give a halfrate code, half the parity bits from each component encoder are punctured. This was the arrangement used in their original paper by Berrou et al. on turbo codes [4]. However, it is of course possible to omit the puncturing and transmit all the parity information from both component encoders, which gives a one-third rate code. The performance of such a code, compared to the corresponding half-rate code, is shown in Fig. 8, which provides an Eb=N0 gain of about 0.6 dB at a BER of 10 4 . 3) Effect of Component Decoder: Fig. 9 shows a comparison between turbo decoders using the parameters Fig. 7. Turbo coding BER performance using different numbers of iterations of MAP algorithm. Other parameters as in Table 1. Vol. 95, No. 6, June 2007 | Proceedings of the IEEE 1189
Hanzo et al.: Turbo Decoding and Detection for Wireless Applications Fig. 8. BER performance comparison between one-third and half-rate turbo codes using parameters of Table 1. described above. In this figure, the BLog MAP (exact)[ curve refers to a decoder which calculates the correction term fcðxÞ in (28) of Section II-D exactly, i.e., using fcðxÞ ¼lnð1 þ e x Þ (29) rather than using a look-up table as described in [19]. The Log MAP curve refers to a decoder which does use a lookup table with eight values of fcðxÞ stored and hence introduces an approximation to the calculation of the LLRs. It can be seen that, as expected, the MAP and the Log-MAP (exact) algorithms give identical performances. Fig. 9. BER performance comparison between different component decoders for a random interleaver with L ¼ 1000. Other parameters as in Table 1. 1190 Proceedings of the IEEE |Vol.95,No.6,June2007
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Turbo Decoding and Detection for Wireless Applications

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