Low-complexity probabilistically shaped coded modulation based on multi-stage distribution matching for coherent transmission

What we believe to be a novel multiplication-free multi-stage distribution-matching (MSDM) algorithm based on bit-level probabilistic shaping (PS) is proposed and experimentally validated. Unlike classical probabilistic shaping methods such as constant composition distribution matching (CCDM), which require bit-to-symbol class arithmetic coding, the proposed MSDM scheme achieves target probabilistic distributions by decomposing symbol probability into bit probabilities. By doing so, in contrast to conventional distribution matchers where extensive multiplication operations are needed, only simple bit-level logical operations are required, while excellent signal shaping performance is preserved. Experimental results indicate that, when compared to the uniform distribution signal under the same net bit rate, the MSDM-based PS-16QAM signal at 1.6 bits/dimension achieves an optical signal-to-noise ratio gain of 1.28 dB. Meanwhile, the proposed scheme exhibits significantly lower complexity than the conventional CCDM while maintaining comparable performance. This proposed method also alleviates the error propagation effect in the inverse DM process compared to CCDM.