Nonlinearity Tolerant LUT-Based Probabilistic Shaping for Extended-Reach Single-Span Links

We propose Huffman-coded sphere shaping (HCSS) as a method for probabilistic constellation shaping which provides improved tolerance to fiber nonlinearities in single-span links. An implementation of this algorithm based on look-up-tables (LUTs) allows for low-complexity, multiplier-free shaping. The advantage of short-length shaping for mitigating fiber nonlinear impairments is experimentally demonstrated for a system employing dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) at 56 GBd and operating over 210 km of standard single-mode fiber (SSMF). A gain in achievable information rate (AIR) of 0.4 bits/4D-symbol compared with uniform signaling is measured, corresponding to a 100% improvement in shaping gain compared with ideal Maxwell-Boltzmann (MB) shaping. The combinatorial mapping and demapping algorithms can be implemented with integer addition and comparison operations only, utilizing an LUT with 100 kbit size.