On The Iterative Decoding Analysis For Turbo Codes

Turbo codes have been widely studied, and the analysis of the performance theory and iterative decoding mechanism of Turbo codes have been a hot research topic as soon as it was proposed. The existing methods for the theoretical analysis of the Turbo code performance are mainly analyzing the Turbo decoding as deterministic or stochastic processes. These methods mainly focus on the characteristics and variation of parameters in the whole decoding process, such as the mean variance of the Extrinsic Information, the variation of the output SNR, and so on. In this paper, we analyze the behavior and performance of Turbo iterative decoding based on the LLR and Extrinsic Information.Based on the LogMAP algorithm, a large number of simulations are conducted in this paper which show that the probability distribution of LLR can be characterized by the mixed Gauss model. In the meantime, when modeling the LLR of different bits wih the same code length, we observe that the reliability of different bits may not be the same and the value of LLR for different bit positions is still different under noise free condition, which illustrates that the sensitive bits are determined by the code structure of the Turbo code instead of the SNR. Then sorting problems of sensitive bits when check sequence is interleaving and when check sequence is not interleaving are analyzed based on LogMAP algorithm through simulation caculation. The results show that when the check sequence is not interleaving the sensitivity of system bits is basically reduced from the last bit to the forward, and when the check sequence is interleaving the sensitivity sorting is disrupted and present a certain regularity based on the nature of OPP interleaver. Besides, sensitivity sorting of system bits of the original Turbo codes is more chaotic, while its LLR value is greater compared with non-interleaved. By simulation, the paper also finds out that after the convergence of the iterative decoding, two results of LLR will occur as the number of iterations increase:LLR stable onto a fixed-point, or fluctuate periodically(asymptotically stable,limit cycles), and further simulation show that the situation of asymptotically stable has little effect on the overall bit error rate.In this paper, we derive the iterative decode algorithm from the perspective of ergodicity and Maximum A Posteriori decoding, and give the iterative formula for external information, and study shows that the iterative computation of External Information so complicated that it is hard to get its analytical solution. Besides, we analyze the Extrinsic Information in two kinds of extreme SNR situation, which finds that when the SNR is large the extrinsic information is mainly determined by the weight spectrum, while when the noise is particularly large, the iterative decoding mechanism doesn’t have much effect on the extrinsic information and LLR lost most of its associations with the weight spectrum. At the same time, this paper also gives the reliability formula when this code length is longer, and compare it to the LogMAP algorithm, which find that when the code length is longer, the results got by these two algorithm are consistent.