Document Type

Article

Publication Date

2026

DOI

10.3390/electronics15184229

Publication Title

Electronics

Volume

15

Issue

18

Pages

4229 (13 pp.)

Abstract

Distribution matching (DM) transforms a stream of equally likely bits into digital symbols that correspond to a specific digital modulation scheme with probabilities of occurrence following a specified statistical distribution. This technique is referred to as probabilistic constellation shaping (PCS), and using the Maxwell–Boltzmann (MB) distribution improves spectral and energy efficiency of digital modulation schemes by enabling more frequent transmissions of lower energy digital symbols. The background behind PCS is presented in the paper and the two main DM methods widely used in practice are discussed, outlining scenarios in which one DM method may be preferable over the other. For illustration, a 64-QAM digital constellation is considered as a case study for which the two DM scenarios presented are simulated and compared in terms the average signal power, entropy, and rate loss.

Rights

© 2026 by the authors. 

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) License.

Data Availability

Article states: "The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author."

Original Publication Citation

Popescu, D. C., & Kowaki, C. (2026). On distribution matching for probabilistic constellation shaping. Electronics, 15(18), Article 4229. https://doi.org/10.3390/electronics15184229

ORCID

0000-0002-2102-8139 (Popescu), 0009-0009-0083-5079 (Kowaki)

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