Constellation shaping -Geometric versus Probabilistic

In this article we are going to have an overview of differences between?Probabilistic constellation shaping and Geometric constellation shaping and their overview :-

As we are aware?The?constellation diagram?is a graphic representation of the In phase and quadrature components?of the digital symbols received over a period of time. This can be done in two possible ways geometric constellation shaping and probabilistic constellation shaping. Constellation shaping is a technique in optical communications to enhance system performance .It can be done in two possible ways - Geometric or Probabilistic .

Geometric constellation shaping modifies the geometric location of the constellation points in Euclidean space to approach Gaussian distribution while keeping the same probabilities for all constellation points. The main advantage of Geometric constellation shaping is that we can design the constellation for improved tolerance to both linear and non-linear impairments which can increase system gain .This is usually used in coherent receivers .

Now comes PCS aka Probabilistic constellation shaping .Why did we have to think about this while we already had Geometric constellation shaping in place .The answer is for Data center Interconnect (DCI) while we use quadrature amplitude modulation we wanted to achieve better OSNR and this was only possible via PCS .It is well-known fact that for an additive white Gaussian noise (AWGN) channel, the mutual information of a quadrature amplitude modulation (QAM) modulation can be maximized when the QAM constellation follows Maxwell–Boltzmann (M-B) family of distributions .So in PCS we use distribution matcher alongwith FEC.DM maps uniformly distributed input bits into the shaped amplitudes.

So in summary PCS is more useful for DCI applications with improved OSNR where we require large bandwidths using QAM modulation .