2025 yaer, volume 29, issue 2 (PDF)

Podkolzin A.S. Introduction to Logical Processes. Representation of Problems in the Solver

The article describes the interface of the mathematical problem solver; tells about the logical system "Iskra"; describes the logical language used in the solver; tells how the logical formalization of problems is carried out.

Keywords: mathematical problem solver, logical processes, logical language, logical formalization of problems.

Yudakov D.A. Geometric shaping of the QAM constellation on the transmitter side in a wireless channel with a fixed decoding algorithm.

The paper explores the optimization of constellation geometry to improve throughput in wireless communication systems. It presents an approach where constellations can be unevenly distributed to enhance transmission efficiency. The optimization is performed on the base station side, and its effectiveness is validated through numerical experiments using LDPC coding, OFDM modulation, and MIMO technologies.

Keywords: Wireless, Constellation diagram, Geometric Shaping, Mutual Information.

Cui Zh., Romanov D.S. The Growing Lower Bound for the Shannon Function of the Detection Test Set Cardinality with Respect to Single Stuck-at Faults at the Outputs of Gates in Formulas over Bases Close to the Standard One

Lower bounds asymptotically equal to the number of variables are established for Shannon functions of the cardinality of single fault detection test set with respect to stuck-at faults at outputs of gates in Boolean formulas over bases \[\{x\mathbin{\&}y,\,x\vee y,\,\bar x\}\], \[\{x\mathbin{\&}y,\,\bar x\}\], \[\{x\vee y,\,\bar x\}\], \[\{x\mathbin{\&}{\bar y},\,\bar x\}\], \[\{x\vee {\bar y},\,\bar x\}\].

Keywords: fault detection test set, stuck-at faults, Boolean formula