Figure: An enumerative shaping trellis.
The enumerative shaping project started long ago in 1991 as an internal trainee-project done by Jos J. Wuijts at Eindhoven University of Technology (TU/e). The project was continued as a master-graduation project by Jos and was finished early 1993. The research resulted in a conference paper “Pragmatic Approach to Shaped Coded Modulation”, that was presented at the 1st IEEE Symposium on Communications and Vehicular Technology in the Benelux, in Delft, October 1993. Research in this area slowed down in TU/e since we found out in 1993 that it was overlapping with the shaping approach of Laroia, Farvardin and Tretter, that was published in the IEEE Transactions on Information Theory paper “On Optimal Shaping of Multidimensional Constellations” in 1994.
Old Results and Publications
J.J. Wuijts, “De constructie van een energiebegrensde kanaalcode met behulp van enumeratieve technieken.”, Stageverslag, 14 Oct. 1991.
J.J. Wuijts, “Shaping and coding bij n-dimensionale Puls Amplitude Modulatie”, Afstudeerverslag, 21 Feb. 1993.
F.M.J. Willems and J.J. Wuijts, “A Pragmatic Approach to Shaped Coded Modulation”, in Proceedings of the IEEE 1st Symposium on Communications and Vehicular Technology in the Benelux, Delft, The Netherlands, pp. 4.3.1 - 4.3.6, October 27-28, 1993.
Shaping for Wireless Communication (IMPULS)
Our shaping research came back to life again in 2016 when Yunus Can Gültekin (PhD student in the IMPULS project) investigated the performance of enumerative shaping for 802.11 systems. After visiting TU Munich, we realized that shaping gain for shorter block lengths could not be realized with “constant composition distribution matching”, a brilliant idea of Georg Böcherer (TUM) that was successfully applied in fiber-optical communication, where block lengths are typically quite large. However the enumerative approach gave significant gains also for short block lengths. This resulted in a PIMRC paper.
F.M.J. Willems, “Enumerative Source Coding and Shaping”, Invited Talk at the 2018 Munich Doctoral Seminar on Communications (MSC), Munich, Germany, 20 July 2018.
Y.C. Gültekin, F.M.J. Willems, W.J. van Houtum and S. Serbetli, “Approximate Enumerative Sphere Shaping”, in Proceedings of the 2018 IEEE International Symposium on Information Theory (ISIT), Vail, CO, Jun. 2018, pp. 676-680.
Y.C. Gültekin, W.J. van Houtum and F.M.J. Willems, “On Constellation Shaping for Short Block Lengths”, in Proceedings of the 2018 Symposium on Information Theory and Signal Processing in the Benelux (SITB), Enschede, the Netherlands, Jun. 2018, pp. 86-96.
Y.C. Gültekin, W.J. van Houtum, S. Serbetli and F.M.J. Willems, “Constellation Shaping for IEEE 802.11”, in Proceedings of the IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), Montreal, QC, Oct. 2017, pp. 1-7.
F.M.J. Willems, “Information Theory and its Application to Optical Communication”, Talk at Signal Processing in Photonic Communications: Advanced Photonics, New Orleans, USA, 25 Jul. 2017.
Y.C. Gültekin, “Comparison of Enumerative and Probabilistic Shaping for Short Blocks”, Poster Presentation at the 2017 European School of Information Theory, Madrid, Spain, 11 May 2017.