Probabilistic Shaping via Non-Binary Codes

Shaping refers to engineering methods that adapt the signal distribution to a communication channel for increased efficiency. Recently, shaping methods have regained interest especially in optical communications where current technologies operate close the fundamental limits of the linear fiber channel model. Probabilistic amplitude shaping (PAS) has been proposed in [1] as a rather simple and efficient way to shape binarylabeled QAM constellations. In this paper, we show how this method can be generalized to non-binary alphabets. Information data is assumed to be shaped via look-up-tables and modern coding schemes to be used. We first present a scheme based on time sharing over prime fields. Second we design p2 circular constellations which are a natural modulation scheme for nonbinary PAS.