Introducing RSESS: An Open Source Enumerative Sphere Shaping Implementation Coded in Rust

Abstract

In this work, we present an open source implementation of the enumerative sphere shaping (ESS) algorithm used for probabilistic constellation shaping (PCS). PCS aims at closing the shaping gap caused by using uniformly distributed modulation symbols in channels for which information theory shows non-uniformly distributed signaling to be optimal. ESS is one such PCS algorithm that sets itself apart as it operates on a trellis representation of a subset of the possible symbol sequences. ESS leads to an empirical distribution of the symbols that closely approximates the optimal distribution for the additive white Gaussian noise (AWGN) channel. We provide an open source implementation of this algorithm in the compiled language Rust, as well as Python bindings with which our Rust code can be called in a regular Python script. We also compare simulation results on the AWGN channel using our implementation with previous works on this topic.