Constellation Shaping for Fiber-Optic Channels With QAM and High Spectral Efficiency

Abstract

In this letter, the fiber-optic communication channel with a quadrature amplitude modulation (QAM) input constellation is treated. Using probabilistic shaping, we show that high-order QAM constellations can achieve and slightly exceed the lower bound on the channel capacity, set by ring constellations. We then propose a mapping function for turbocoded bit-interleaved coded modulation based on optimization of the mutual information between the channel input and output. Using this mapping, spectral efficiency as high as 6.5 bits/s/Hz/polarization is achieved on a simulated single channel long-haul fiber-optical link excluding the pilot overhead, used for synchronization, and taking into account frequency and phase mismatch impairments, as well as laser phase noise and analog-to-digital conversion quantization impairments. The simulations suggest that major improvements can be expected in the achievable rates of optical networks with high-order QAM.

Digital signal processing for fiber nonlinearities [Invited]

“…The simplicity of the rate matcher, together with its transparency to the FEC makes it attractive for optical fiber communications. An iterative approach to probabilistic shaping was taken in [62], where the PMF was not restricted to the MB family. The PMF was optimized by a modified Blahut-Arimoto algorithm, and it was shown that probabilistic shaping outperforms the geometric shaping scheme from [52].…”

Probabilistic shaping and non-binary codes

“…This concerns areas where current technologies operate close to fundamental limits. For example, different methods have been experimented in optical communications [26], [27]. Hence, because there are already efficient VLSI implementations of contemporary coding schemes that have been proven to asymptotically achieve capacity with constant complexity per information unit [17], [21]- [23], it is then natural to combine them with efficient shaping methods.…”

A Shaping Algorithm for Mitigating Inter-Channel Nonlinear Phase-Noise in Nonlinear Fiber Systems

“…Most existing proposals for constellation shaping for fiber-optic communication systems amount to using known techniques such as trellis shaping [4], shell mapping [5] and probabilistic shaping [6]- [8]. The gains resulting from ring-shaped constellation were O. Geller, M. Feder, and M. Shtaif are with with the School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel (emails: omrigell@post.tau.ac.il, meir@eng.tau.ac.il, shtaif@tauex.tau.ac.il).…”