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A new approach for the approximation of the channel log-likelihood ratio(LLR) for wireless channels based on Taylor series is proposed. Theapproximation is applied to the uncorrelated flat Rayleigh fading channel withunknown channel state information at the receiver. It is shown that theproposed approximation greatly simplifies the calculation of channel LLRs, andyet provides results almost identical to those based on the exact calculationof channel LLRs. The results are obtained in the context of bit-interleavedcoded modulation (BICM) schemes with low-density parity-check (LDPC) codes, andinclude threshold calculations and error rate performance of finite-lengthcodes. Compared to the existing approximations, the proposed method is eithersignificantly less complex, or considerably more accurate.

LLR Approximation for Wireless Channels Based on Taylor Series and Its Application to BICM with LDPC Codes