A hybrid satellite–terrestrial relay network is a simple and flexible solution that can be used to improve the performance of land mobile satellite systems, where the communication links between satellite and mobile terrestrial users can be unstable due to the multipath effect, obstacles, as well as the additional atmospheric losses. Motivated by these facts, in this paper, we analyze a system where the satellite–terrestrial links undergo shadowed Rice fading, and, following this, terrestrial relay applies the selection relaying protocol and forwards the information to the final destination using the communication link subjected to Nakagami-m fading. For the considered relaying protocol, we derive the exact closed-form expressions for the outage probability, outage capacity, and ergodic capacity, presented in polynomial–exponential form for the integer-valued fading parameters. The presented numerical results illustrate the usefulness of the selection relaying for various propagation scenarios and system geometry parameters. The obtained analytical results are corroborated by an independent simulation method, based on the originally developed fading simulator.

In this paper, we introduce a novel gradient descent bit-flipping algorithm with a finite state machine (GDBF-wSM) for iterative decoding of low-density parity-check (LDPC) codes. The algorithm utilizes a finite state machine to update variable node potentials—for each variable node, the corresponding finite state machine adjusts the update value based on whether the node was a candidate for flipping in previous iterations. We also present a learnable framework that can optimize decoder parameters using a database of uncorrectable error patterns. The performance of the proposed algorithm is illustrated for various regular LDPC codes, both in a binary symmetric channel (BSC) and the channel with additive white Gaussian noise (AWGN). The numerical results indicate a performance improvement when comparing our algorithm to previously proposed GDBF-based approaches.

Bit-flipping (BF) is a very simple algorithm for decoding linear block codes. For the BF to achieve high performances of belief-propagation (BP) algorithms, which are far more complex, we apply several optimizations using the genetic algorithm (GA), to optimize the parameters of our decoder. Adaptive diversity gradient descent bit-flipping with momentum (AD-GDBFwM) algorithm is designed as a cascade of multiple decoders with different parameters, which are optimized with GA. In this paper we consider AD-GDBFwM decoding of mediumdensity parity-check (MDPC) codes. We measure the decoding performance and compare it with the results of various types of decoders, including BP and neural BP.