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We investigate a digital back-propagation simplification method to enable computationally-efficient digital nonlinearity compensation for a coherently-detected 112 Gb/s polarization multiplexed quadrature phase shifted keying transmission over a 1,600 km link (20x80km) with no inline compensation. Through numerical simulation, we report up to 80% reduction in required back-propagation steps to perform nonlinear compensation, in comparison to the standard back-propagation algorithm. This method takes into account the correlation between adjacent symbols at a given instant using a weighted-average approach, and optimization of the position of nonlinear compensator stage to enable practical digital back-propagation.

We demonstrate 400 Gbit/s frequency-division-multiplexed and polarization-division-multiplexed 256 QAM-OFDM transmission over 720 km with a spectral efficiency of 14 bit/s/Hz by using high-resolution frequency domain equalization (FDE) and digital back-propagation (DBP) methods. A detailed analytical evaluation of the 256 QAM-OFDM transmission is also provided, which clarifies the influence of quantization error in the digital coherent receiver on the waveform distortion compensation with DBP.

We demonstrate a marked performance improvement in a 512 QAM transmission by employing frequency-domain equalization (FDE) instead of an FIR filter. FDE enables us to compensate for distortions due to hardware imperfections in the transmitter with higher precision, which successfully reduced the power penalty by 4 dB in a 54 Gbit/s (3 Gsymbol/s)-160 km transmission. FDE also allows the transmission distance to be extended up to 240 km.

We demonstrate substantial performance improvements in 256 QAM transmission in terms of both data rate and distance that we realized by using a digital back-propagation (DBP) method. 160 Gbit/s-160 km and 64 Gbit/s-560 km transmissions were successfully achieved with a polarization-multiplexed 256 QAM signal, in which the symbol rate and transmission distance were greatly increased by compensating for the interplay between dispersion and nonlinearity, which is responsible for the transmission impairment especially for a higher symbol rate and longer distance.

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We demonstrate 400 Gbit/s PDM-256 QAM-OFDM transmission with 14 bit/s/Hz spectral efficiency by employing an improved FDE technique that extended the transmission distance to 720 km and achieved an SE-distance product of 10,080 km⋅bit/s/Hz.