Calculation and error bound of Min‐approximated bitwise log‐likelihood ratios of generalised M ‐ary PAM

In modern digital communication systems, a high‐order modulation and advanced channel coding are often jointly used to increase the spectral efficiency and coding gain. In this work, the authors investigate a computationally efficient method for evaluating the bitwise log‐likelihood ratios of generalised M ‐ary pulse amplitude modulation (PAM) signals with the Min approximation. The proposed scheme is simple and can be applied to demodulate the M ‐ary PAM having an arbitrary symbol spacing and a bit stream mapping. The computational complexity and upper bounds of the approximation error are also provided for a better understanding of the proposed scheme.