Max-Log-MAP Soft Demapper with Logarithmic Complexity for $M$-PAM Signals

A max-log-MAP soft demapping algorithm with logarithmic complexity is proposed for M-PAM signals. Its algorithm complexity is only Θ(logM) for M-PAM signals, in contrast to Θ(MlogM) as achieved by the conventional max-log-MAP algorithm using exhaustive search. The algorithm applies to both Gray-coded and natural-coded signals. The max-log-MAP algorithm with logarithmic complexity may be straightforwardly extended to rectangular QAM signals when the rectangular QAM signal can be decomposed into two independent PAM signals.