Joint Precoding and Probabilistic Constellation Shaping using Arithmetic Distribution Matching

The problem of joint shaping and precoding is studied in this paper. We introduce statistical dependencies among consecutive symbols to shape the constellation while minimizing the total transmit power when the signal goes through the precoding filter. We propose a stationary Markovian model for optimizing the transition probability of transmit symbols to avoid high-energy sequences when convolved with the precoding filter. A new algorithm based on arithmetic coding is proposed to generate a shaped sequence of symbols with the given Markov model transition probabilities.