Nonlinearity aware bisection-based sphere shaping for optical digital subcarrier multiplexing systems

In this paper, a nonlinearity-tolerant sphere shaping is proposed based on the parallel bisection structure. Compared to enumerative sphere shaping (ESS), the bisection-based sphere shaping (BS-SS) can achieve a lower average energy and rate loss at the same blocklength by selecting all preferential sequences. The nonlinearity-tolerant BS-SS (BS-SS-NLI) can mitigate the fiber nonlinearity by reducing the energy variation, which is demonstrated in the simulations with probabilistically shaped, single channel, dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) for a multi-span long-haul transmission over 2500 km of standard single-mode fiber (SSMF) applying digital subcarrier multiplexing (SCM), comparing with recent literature kurtosis-limited ESS (K-ESS) and list-encoding constant composition distribution matching (L-CCDM). The BS-SS-NLI can provide 0.25 dB effective signal-to-noise ratio (SNR) gain over ESS and 0.39 dB gain over L-CCDM. The achievable information rate (AIR) can be improved ∼0.1 bits/4D-symbol by BS-SS-NLI over ESS.