  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 state 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 bit-interleaved
coded modulation (BICM) schemes with 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.
