Multi-Dimensional Distribution Matching With Bit-Level Shaping for Probabilistically Shaped High Order Modulation Formats

In this paper, multi-dimensional distribution matching (MDDM) based on bit-level shaping is proposed to implement probabilistic shaping (PS) for high order modulation formats. MDDM is optimized across multiple dimensions including polarizations and different time slots to achieve better performance. The implementation complexity of PS can also be reduced by optimizing the multiple bit-level distribution matchers (DMs) for generating multi-dimensional symbols. To further reduce the complexity, degenerate MDDM is also proposed with almost the same performance as MDDM. In simulations of an additive white Gaussian noise (AWGN) channel, for probabilistically shaped 256-ary quadrature amplitude modulation (256QAM) at a shaping rate of 2.2 bits/amplitude with a block length of 80, four-dimensional distribution matching (4D-DM) and degenerate 4D-DM provide normalized generalized mutual information (NGMI) gains of 0.047 and 0.046 over constant composition distribution matching (CCDM), respectively. The performance of 4D-DM and degenerate 4D-DM is also evaluated by experiments. Compared to CCDM, degenerate 4D-DM achieves a NGMI gain of 0.055.