Information rates of probabilistically shaped coded modulation for a multi-span fiber-optic communication system with 64QAM

This paper studies probabilistic shaping in a multi-span wavelength-division multiplexing optical fiber system with 64-ary quadrature amplitude modulation (QAM) input. In split-step fiber simulations and via an enhanced Gaussian noise model, three figures of merit are investigated, which are signal-to-noise ratio (SNR), achievable information rate (AIR) for capacity-achieving forward error correction (FEC) with bit-metric decoding, and the information rate achieved with low-density parity-check (LDPC) FEC. For the considered system parameters and different shaped input distributions, shaping is found to decrease the SNR by 0.3 dB yet simultaneously increases the AIR by up to 0.4 bit per 4D-symbol. The information rates of LDPC-coded modulation with shaped 64QAM input are improved by up to 0.74 bit per 4D-symbol, which is larger than the shaping gain when considering AIRs. This increase is attributed to the reduced coding gap of the higher-rate code that is used for decoding the nonuniform QAM input.