on the influence of the extrinsic information scaling coefficient on the performance of single and double binary turbo codes

This paper presents a study on the influence of the extrinsic information scaling coefficient value (eic) on the bit and frame error rate (BER/FER), for single and double binary turbo codes (S/DBTC) decoded with maximum a posteriori (MAP) and maximum logarithmic MAP (MaxLogMAP) component algorithms. Firstly, we estimate the distance spectrum of the code with the so-called error impulse method (EIM), and we analyze its dependence as well as the dependence of the asymptotic FER on eic. Secondly, we estimate the actual FER using Monte Carlo simulations with eic as a parameter. The comparison of the FER(eic) curves obtained by the two methods allows us, on the one hand, to assess the quality of the decoding algorithms, and on the other hand, to estimate the very low BER/FER performance of TCs, where the Monte Carlo method is practically unusable. The results presented also provide a practical guide for the appreciation of the optimal value of the scaling factor, eic. We may notice that also the MAP algorithm performance could be improved using eic<1.