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1. Block-Level Interference Exploitation Precoding without Symbol-by-Symbol Optimization

   https://doi.org/10.1109/WCNC55385.2023.10118875  

   Li, Ang; Shen, Chao; Liao, Xuewen; Masouros, Christos; Swindlehurst, A. Lee (March 2023, Proc. 2023 IEEE Wireless Communications and Networking Conference (WCNC))

   Symbol-level precoding (SLP) based on the concept of constructive interference (CI) is shown to be superior to traditional block-level precoding (BLP), however at the cost of a symbol-by-symbol optimization during the precoding design. In this paper, we propose a CI-based block-level precoding (CI-BLP) scheme for the downlink transmission of a multi-user multiple-input single-output (MU-MISO) communication system, where we design a constant precoding matrix to a block of symbol slots to exploit CI for each symbol slot simultaneously. A single optimization problem is formulated to maximize the minimum CI effect over the entire block, thus reducing the computational cost of traditional SLP as the optimization problem only needs to be solved once per block. By leveraging the Karush-Kuhn-Tucker (KKT) conditions and the dual problem formulation, the original optimization problem is finally shown to be equivalent to a quadratic programming (QP) over a simplex. Numerical results validate our derivations and exhibit superior performance for the proposed CI-BLP scheme over traditional BLP and SLP methods, thanks to the relaxed block-level power constraint. 

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2. Symbol functions for symmetric frameworks

   https://doi.org/10.1016/j.jmaa.2020.124895  

   Kastis, Eleftherios; Kitson, Derek; McCarthy, John E. (May 2021, Journal of Mathematical Analysis and Applications)
3. Symbol Separation in Double Occurrence Words

   https://doi.org/10.1142/S0129054120500343  

   Jonoska, Nataša; Saito, Masahico; Kim, Hwee; Mostowski, Brad (November 2020, International Journal of Foundations of Computer Science)

   null (Ed.)

   A double occurrence word (DOW) is a word in which every symbol appears exactly twice. We define the symbol separation of a DOW [Formula: see text] to be the number of letters between the two copies of a symbol, and the separation of [Formula: see text] to be the sum of separations over all symbols in [Formula: see text]. We then analyze relationship among size, reducibility and separation of DOWs. Specifically, we provide tight bounds of separations of DOWs with a given size and characterize the words that attain those bounds. We show that all separation numbers within the bounds can be realized. We present recursive formulas for counting the numbers of DOWs with a given separation under various restrictions, such as the number of irreducible factors. These formulas can be obtained by inductive construction of all DOWs with the given separation. 

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4. Techniques for symbol grounding with SATNet

   Topan, S.; Si, X (December 2021, NeurIPS)
5. Developing symbol sense for the minus sign

   Lamb, L. L.; Bishop, J. P.; Philipp, R. A.; Schappelle, B. P.; Whitacre, I.; & Lewis, M. (January 2012, Mathematics teaching in the middle school)

   Three meanings of the minus sign are shared. 

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