Geometric shaping: Low-density coding of Gaussian-like constellations

Joseph J. Boutros, Uri Erez, Johannes Van Wonterghem, Gil I. Shamir, Gilles Zémor

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Constellation shaping is necessary to approach channel capacity for information rates above 1 bit/dim. Probabilistic shaping shows a small gap to capacity, however a complex distribution matcher is required to modify the source distribution. Spherical shaping of lattice constellations also reduces the gap to capacity, but practical Voronoi shaping is feasible in small dimensions only. In this paper, our codebook is a real geometrically nonuniform Gaussian-like constellation. We prove that this discrete codebook achieves channel capacity when the number of points goes to infinity. Then we build a special mapping to interface between non-binary low-density codes and the codebook, allowing the code alphabet size to be equal to the square root of the codebook size. Excellent performance is shown with fast-encoding and practical iterative probabilistic decoding, e.g. 0.7 dB gap to capacity at 6 bits/s/Hz with a code defined over the ring Z/8Z.

Original languageEnglish
Title of host publication2018 IEEE Information Theory Workshop, ITW 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781538635995
StatePublished - 15 Jan 2019
Event2018 IEEE Information Theory Workshop, ITW 2018 - Guangzhou, China
Duration: 25 Nov 201829 Nov 2018

Publication series

Name2018 IEEE Information Theory Workshop, ITW 2018


Conference2018 IEEE Information Theory Workshop, ITW 2018


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