# Partial Enumerative Sphere Shaping

## TL;DR

This paper introduces partial enumerative sphere shaping (P-ESS) within the PAS framework, achieving near-capacity performance with reduced complexity by shaping only part of the amplitude bits in ASK modulation.

## Contribution

The paper proposes P-ESS, a novel method for probabilistic amplitude shaping that simplifies implementation while maintaining high efficiency, based on approximations to the Maxwell-Boltzmann distribution.

## Key findings

- Shaping 2 amplitude bits nearly matches the performance of shaping 3 bits.
- Achieves 1.3 dB power efficiency gain over uniform signaling.
- Reduces storage and computational complexity by factors of 6 and 3.

## Abstract

The dependency between the Gaussianity of the input distribution for the additive white Gaussian noise (AWGN) channel and the gap-to-capacity is discussed. We show that a set of particular approximations to the Maxwell-Boltzmann (MB) distribution virtually closes most of the shaping gap. We relate these symbol-level distributions to bit-level distributions, and demonstrate that they correspond to keeping some of the amplitude bit-levels uniform and independent of the others. Then we propose partial enumerative sphere shaping (P-ESS) to realize such distributions in the probabilistic amplitude shaping (PAS) framework. Simulations over the AWGN channel exhibit that shaping 2 amplitude bits of 16-ASK have almost the same performance as shaping 3 bits, which is 1.3 dB more power-efficient than uniform signaling at a rate of 3 bit/symbol. In this way, required storage and computational complexity of shaping are reduced by factors of 6 and 3, respectively.