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Low complexity max-log-MAP demapper for M-PAM signals with nonuniform constellations

Constellation shaping is beneficial for approaching the Shannon capacity limit. However, the nonuniform signal caused by constellation shaping could increase the complexity of the signal demodulation. The reflective symmetry of the uniform PAM constellation can be exploited to reduce the demapping complexity. However, nonuniform PAM signals lose this symmetry because of the distribution of constellation points, which increase the amount of demapping calculation. A low complexity max-log-MAP demapping algorithm is proposed for demodulating nonuniform M-PAM signals in this paper. We divide decision boundaries into two parts: ordinary ones and special ones. We find the symmetry of the received symbols and derive the analytic expressions for all boundaries. Based on this, the complexity of the proposed algorithm is lower than other similar works, and the proposed algorithm can be further simplified with acceptable performance loss.