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1. Shaped TCM with List Decoding that Exceeds the RCU Bound by Optimizing a Union Bound on FER

   https://doi.org/10.1109/GLOBECOM48099.2022.10000695  

   Song, Dan ; Areces, Felipe ; Wang, Linfang ; Wesel, Richard ( December 2022 , GLOBECOM 2022 - 2022 IEEE Global Communications Conference)

   This paper derives a union bound on the frame error rate (FER) of a probabilistic amplitude shaping (PAS) system which uses a CRC-aided, rate −k/k+1 , systematic, recursive trellis-coded modulation (TCM). A tail-biting convolutional code (TBCC) provides the feed-forward error correction (FEC) code for the TCM. The system is referred as CRC-TCM-PAS [1]. In order to derive the union bound, we first prove that the concatenation of a CRC and a rate −k/k+1 convolutional code is equivalent to a new convolutional code. Then, we give the generating function of the new convolutional code using Biglieri's product-state-diagram approach. A union bound can be calculated using the generating function. Simulation results show that the derived union bound is tight in the high signal-to-noise ratio (SNR) regime and can be used to design the convolutional and CRC codes. Simulation results also show that the optimized CRC-TCM-PAS system exceeds the random coding union (RCU) bound and outperforms the PAS systems with various FEC codes studied in [2] for the same number of input bits and the same transmission rate. 

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2. An improved lower bound for Folkman's theorem: AN IMPROVED LOWER BOUND FOR FOLKMAN'S THEOREM

   https://doi.org/10.1112/blms.12058  

   Balogh, József ; Eberhard, Sean ; Narayanan, Bhargav ; Treglown, Andrew ; Wagner, Adam Zsolt ( August 2017 , Bulletin of the London Mathematical Society)
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   https://doi.org/10.1088/0031-8949/90/5/054014  

   Kellerbauer, Alban ; Cerchiari, Giovanni ; Jordan, Elena ; Walter, C. Wesley ( April 2015 , Physica Scripta)
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   https://doi.org/10.1063/5.0018346  

   Liu, Gaoxiang ; Ciborowski, Sandra M. ; Graham, Jacob D. ; Buytendyk, Allyson M. ; Bowen, Kit H. ( July 2020 , The Journal of Chemical Physics)
5. Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks

   https://doi.org/10.1103/PhysRevB.96.075161  

   Liu, Chun-Xiao ; Sau, Jay D. ; Stanescu, Tudor D. ; Das Sarma, S. ( August 2017 , Physical Review B)