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

Abstract

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 extendedreach single-span link comprising 200 km of standard singlemode 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/4Dsymbol 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.

Kurtosis-limited Sphere Shaping for Nonlinear Interference Noise Reduction in Optical Channels

“…2.10]. For the mapping of amplitudes to QAM symbols, the 4D mapping strategy illustrated in [33,Fig. 3(c)] is used.…”

“…More precisely, a shaped amplitude sequence of length N is mapped to a 4D symbol sequence of length N/4, or equivalently, four consecutive shaped amplitudes are mapped to four concurrent quadratures. Note that in the SP case, this corresponds to the 2D mapping strategy of [33,Fig. 3(b)].…”

List-encoding CCDM: A Nonlinearity-tolerant Shaper Aided by Energy Dispersion Index

“…The top and bottom branches show the generation of shaped pulse amplitude modulation (PAM) symbols for in-phase and quadrature dimensions of QAM symbols, respectively. This PAS structure corresponds to the so-called "1D symbol mapping strategy" [27,Fig. 3(a)].…”

Exponentially-Weighted Energy Dispersion Index for the Nonlinear Interference Analysis of Finite-Blocklength Shaping

“…Therefore, a straightforward approach would be to simply employ short blocklengths [10], [11]. The NLI mitigation is intuitively explained by the fact that using short blocklengths avoids multiple consecutive occurrences of high-energy symbols, and thus, induces less NLI [12], [13].…”