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A Linear Approximation of Logarithm Based on Least Squares and Interpolation Function for BICM-ID Embedded Turbo Codes

Jianping Li, Jian Wang, Tingting Han


We propose a novel method to simply Logarithmic Maximum a posteriori (Log-MAP) algorithm BICM-ID embedded turbo codes in this paper. Firstly, we exploit a linear wise-function to approximate the logarithmic correction in the Jacobian logarithmic function based on the Least Squares and Interpolation Function, which avoids complicated logarithm look-up table operations in Log-MAP algorithm. Secondly, we utilize points estimation to replace the approximately lines in some ranges which have less influence on decoding performance. Simulation results show that the novel algorithm can offer almost equivalent performance to the optimal algorithm i.e. Log-MAP algorithm. In addition, compared with the improved MAX-Log-MAP algorithm proposed by S. Talakoub et al, the proposed algorithm can reduce about 40% of computational complexity, meanwhile it achieves about 0.1db performance gains.


BICM-ID; Interpolation Function; Least Squares; Linear approximation; Log-MAP.

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