Efficient polynomial regression algorithm for LTE turbo decoding

In this paper, an efficient turbo decoding technique is proposed based on the polynomial regression method. The most known Logarithmic Maximum A Posteriori (Log-MAP) algorithms for turbo decoding in the Third Generation Partnership Project Long Term Evolution (3GPP LTE) is tested against most recent approaches in this area. The main reason for this work is to find the most suitable turbo decoding algorithm where the logarithmic-domain correction function is replaced with an approximation function with less complexity and close performance to the Log-MAP algorithm. One of the recent approaches replaces the logarithmic term in the Jacobian logarithmic function based on Taylor series. In the proposed approach, the approximation of the logarithmic function is performed by the polynomial regression procedure. The results show that the Taylor series algorithm achieved a satisfying bit error rate (BER) performance when compared to the Log-MAP with much less complexity and a gain of 0.38 dB when compared to the Max-Log-MAP algorithm. Moreover, the proposed efficient polynomial regression method results show that after a certain polynomial degree value the BER performance can be better than that of the Log-MAP algorithm with a 0.01 dB difference and decreased complexity as well. Also, the proposed algorithm shows an improvement of 0.07 dB compared to the recent Taylor series algorithm. A polynomial degree n = 4 is chosen according to the BER performance, processing time and the complexity of additions and multiplications procedures.