Block-length aware enumerative sphere shaping for probabilistic shaping optical transmission system

Due to its large transmission capacity and low complexity, probabilistic shaping (PS) technology has been attracting increasing attention. The commonly used constant composition distribution matching (CCDM) in PS technology, which generates amplitude sequences with a fixed empirical distribution, exhibits higher rate loss for short block lengths. In this paper, we present a block-length aware enumerative sphere shaping (BA-ESS) designed to implement probability shaping within high-order modulation formats, which can transition between static (BA-ESS-S) and dynamic (BA-ESS-D) modes based on the block length. When dealing with short block lengths, it will be switched to the static mode. On the contrary, for longer block lengths, the algorithm will be transitioned to dynamic mode, which is a real-time coding method that effectively reduces storage complexity. We validate the transmission performance of this scheme through a 28 GBaud PS-64QAM simulation system and an 8 GBaud PS-64QAM transmission experiment. Through the analysis of simulation results, it can be observed that BA-ESS achieves handsome gains over ESS and optimum ESS (OESS). When all three schemes reach the NGMI threshold, for a block length of 40, BA-ESS provides OSNR gains of 0.88 dB and 0.34 dB compared to ESS and OESS, respectively. Additionally, experimental results indicate that for a block length of 20, the BA-ESS scheme offers an OSNR gain of 0.97 dB relative to ESS.