Huffman-Coded Sphere Shaping for Extended Reach Single-Span Links

Huffman-coded sphere shaping (HCSS) is an algorithm for finite-length probabilistic constellation shaping, which provides nearly optimal energy efficiency at low implementation complexity. In this paper, we experimentally study the nonlinear performance of HCSS employing dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) in an extended-reach single-span link comprising 200 km of standard single-mode fiber (SSMF). We investigate the effects of shaping sequence length, dimensionality of symbol mapping, and shaping rate. We determine that the naïve approach of Maxwell-Boltzmann distribution matching-which is optimal in the additive white Gaussian noise channel-provides a maximum achievable information rate (AIR) gain of 0.18 bits/4D-symbol with respect to uniform signaling at optimum launch power in the infinite length regime. Conversely, HCSS can achieve a gain of 0.37 bits/4D-symbol over uniform signaling using amplitude sequence length of 32, which may be implemented without multiplications, using integer comparison and addition operations only. Coded system performance, with a net data rate of approximately 425 Gb/s for both shaped and uniform inputs, is also analyzed