16-QAM probabilistic constellation shaping by adaptively modifying the distribution of transmitted symbols based on errors at the receiver

We simulate and experimentally demonstrate a feedback-based probabilistic constellation shaping (FB-PCS) of a 10 Gbaud 16-ary quadrature amplitude modulation (16-QAM) signal. Our approach is to adaptively modify the distribution of transmitted symbols based on errors at the receiver, and assumptions about the channel model are not required. Specifically, the error feedback enables solving an optimization problem to find the distribution that maximizes the mutual information between the input and output of the channel without knowledge of the channel itself. A known training sequence with uniform distribution is transmitted, and the errors at each constellation point are counted at the receiver. This information is relayed to the transmitter, which then updates the data constellation with a new probability distribution such that constellation points with more errors are used less frequently. We examine four different system scenarios in simulation and one scenario in experiment. In simulation, we find that FB-PCS (a) reduces the number of errors when compared to uniform shaping for the four scenarios, and (b) reduces symbol error rate (SER) by approximately an order of magnitude or has similar SER compared to conventional Maxwell–Boltzmann (M–B) shaping. Moreover, we demonstrate that FB-PCS can lead to an SER reduction of ∼50%.