Approximation of Log-Likelihood Ratio for Wireless Channels Based on Taylor Series

A new approach for the approximation of the channel log-likelihood ratio (LLR) for wireless channels based on Taylor series is proposed. The approximation is applied to the uncorrelated flat Rayleigh fading channel with unknown channel side information at the receiver. It is shown that the proposed approximation greatly simplifies the calculation of channel LLRs, and yet provides results almost identical to those based on the exact calculation of channel LLRs. The results are obtained in the context of iterative decoding of low-density parity-check (LDPC) codes and include threshold calculations and error rate performance of finite-length codes. Compared to the existing approximations, the proposed method is either significantly less complex, or considerably more accurate.