Nonlinearity Tolerance of Hierarchical Distribution Matching in Optical Fiber Communication

This letter reports the nonlinearity tolerance properties of hier-archical distribution matching (HiDM), which is a distribution matcher of reasonable complexity for probabilistic amplitude shaping (PAS) in non-linear fiber-optic transmission. Recent studies have demonstrated that PAS exhibits unique nonlinearity tolerance, which varies depending on channel conditions. This tolerance is influenced by the choice of distribution matcher, as analyzed using statistical moments. In this work, we explore the nonlinearity tolerance of HiDM through moment-based analysis and numerical simulations. The results show that the dependence on blocklength in nonlinearity tolerance of HiDM is significantly smaller than in one of enumerative sphere shaping, a common DM. In addition, the property in HiDM is almost independent on the number of layers.