Probabilistic shaping for optical coherent transmission

• Description

  Adaptive spectral efficiency can be achieved either by modifying the size (and shape) of the transmitted alphabet (the constellation in the case of optical transmission) or by using non-uniform distribution for the occurrence probability of the symbols of a given constellation. This technique is known as probabilistic shaping [1]. In optical communication, it is employed to limit the occurrence of high-power symbols in order to reduce nonlinear effects and increase the SNR for all other symbols. Probabilistic shaping can be performed using modified FEC codes [2-3] or using constellation shaping [4]. An advantage of probabilistic shaping is that the same DSP unit can be used to equalize the signal at different spectral efficiency.

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• Typical Results

  In this example we illustrate the use of probabilistic shaping with square or circular QAM constellations. Constellation shaping is used to map the bits to be encoded into constellation symbols (see Figure 1) following a specific occurrence probability of these symbols. The constellation shaping is implemented as follows: the probability-shaped constellation is represented as an overlap of sub-constellations. For instance the bits can be mapped in C8QAM, C16QAM and C32QAM constellations using different weights. For instance weights of [0 0 1] is a pure 32QAM constellation (5bits/symbol) while weights of [1 1 1] means that C8QAM, C16QAM and C32QAM are used in the same proportion to map bits and therefore that the occurrence of central symbols is higher as they are present in all constellations. In this specific case the resulting spectral efficiency is 4.33 bits/symbol (Figure 2).
  
  Probabilistic shaping is also performed on circular (Figure 3) or square (Figure 4) 16QAM. In the reported square 16QAM case (weights of [1 1 1]), the SE is reduced from 4 to 3bits/symbol improving the system performance (BER is reduced from 1e-3 to 1e-4 at 28dB OSNR).

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• Further Information

  Keywords: Coherent, QAM, probabilistic shaping, coded modulation
  
  Similar demonstrations are available in VPItransmissionMaker Optical Systems and on the VPIphotonics Forum.
  
  [1] B.P. Smith and F. R. Kschischang, 'A pragmatic coded modulation scheme for high-spectral-efficiency fiber-optic communications', J. Lightw. Technol. 30(13), pp. 2047-2053, Jul. 2012.
  [2] M.P. Yankov et al., 'Constellation shaping for fiber-optic channels with QAM and high spectral efficiency.', Photonics Technology Letters, IEEE 26.23 (2014): 2407-2410.
  [3] T. Fehenberger et al. 'LDPC coded modulation with probabilistic shaping for optical fiber systems.' Optical Fiber Communication Conference. Optical Society of America, 2015.
  [4] L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, 'Coded modulation for fiber-optic networks', IEEE Signal Process. Mag., vol. 31, no. 2, pp. 93-103, Mar. 2014

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