Finite-Precision Methods for Energy-Based Direct Arithmetic Coding in Probabilistic Shaping

We introduce finite-precision encoding and decoding methods for energy-based direct arithmetic coding (AC), a newly coined technique that enables fixed-to-fixed invertible distribution matching (DM) in probabilistic amplitude shaping (PAS) systems and approaching the sphere shaping gain. Moreover, we introduce novel methods for determining calibration guarantees to account for computational precision loss due to the finite-precision nature of encoding and decoding, and present methods of finite-precision approximation for estimating key energy-based quantities. As we shall present, our methods enable efficient implementations with a negligible degradation due to the finite-precision computations, thus readily establishing a pragmatic approach to energy-efficient communication from a practical standpoint.