Multi-Level Decomposition Enumerative Sphere Shaping Scheme for Short Blocklengths

Benefiting from its shaping gain and flexible information rates, probabilistic shaping (PS) is on track to become a popular coded modulation standard in optical communication systems. Though producing amplitude sequences with a fixed em-pirical distribution, constant composition distribution matching (CCDM) suffers from high rate losses for small block lengths. In this paper, a multi-level decomposition enumerative sphere shaping (MDESS) scheme is proposed to implement PS for the application in the short blocklengths regime, which is a practical solution of enumerative sphere shaping (ESS) methodology and could always ensure the ultimate energy efficiency of the output sequences. Compared with traditional ESS, MDESS makes full use of low-energy sequences and small-amplitude sequences. We demonstrate the superiority of MDESS through a 28 Gbaud PS simulation system, which successfully reduces the rate loss and improves the optical signal-to-noise ratio (OSNR) gain without increasing the complexity.