The main challenge for hardware implementation of non-binary LDPC decoding is the high computational complexity and large memory requirement. To address this challenge, five new low complexity LDPC decoding algorithms are proposed in this paper. The proposed algorithms are developed specifically towards the low complexity, yet effective, decoding of the NB LDPC codes. The proposed decoding algorithms update, iteratively, the hard decision received vector to search for the valid codeword in the vector space of Galois field ${(GF)}$ . The selection criterion for least reliable symbol positions is based on the information from the failed checks and the reliability information from the Galois field structure as well as from the received channel soft information. To choose the correct value for the candidate symbol, two methods are used. The first method is based on the prediction of the error symbol from the set of Galois field symbols which maximize an objective function. In the second method, individual bits are flipped based on the reliability information obtained from the channel. Algorithms 1 and 2 flip a single symbol per iteration whilst the other three algorithms 3, 4 and 5 flip multiple symbols in each iteration. The proposed voting based Algorithms 1, 2 and 5 first short list the unreliable positions using a majority voting scheme and then choose the candidate symbol value from the set of the symbols in ${GF(q)}$ while not violating the field order ${q}$ . These methods simplify the decoding complexity in terms of computation and memory. Results and analysis of these algorithms show an appealing tradeoff between computational complexity and bit error rate performance for NB LDPC codes.

Secure and reliable information flow is one of the main challenges in social IoT and mobile networks. Information flow and data integrity is still an open research problem. In this paper, we develop new methods of constructing systematic and regular Low-Density Parity-Check Matrices (LDPCM), inspired by the structure of the Sarrus method and geometric designs. Furthermore, these codes have cyclic structure and therefore, are less complex in computation and also require less memory in hardware implementation. Besides, an optimal method of post-processing for deleting girths four is presented. Numerical results show that the codes constructed by these methods perform well over the additive white Gaussian noise (AWGN) channel when decoded with the sum-product LDPC iterative algorithms. The proposed methods can be very efficient in terms of reducing memory consumption and improving the convergence speed of the decoder particularly in IoT and mobile networks.

A compact fork‐shaped MIMO antenna system with a 2 × 2 arrangement with four elements is presented. The MIMO elements are arranged orthogonally to achieve a small overall size of 36 × 28 mm² and a wide bandwidth for 5G mm‐wave applications. MIMO elements are positioned 4 mm from each corner of the substrate to achieve compact size and minimize coupling. To improve the isolation of the proposed MIMO system, a metamaterial slab is inserted in the middle of the substrate and between radiating elements of the MIMO antenna system, which improves isolation by 10 dB within the whole operating band and achieves maximum isolation of 65 dB at 34.5 GHz. The proposed MIMO system operates in the Ka‐band frequency range of 22–50 GHz with isolation greater than 30 dB and efficiency above 80% across the entire frequency spectrum for 5G communication. Additionally, the performance parameters of MIMO are examined, including diversity gain (DG) and envelope correlation coefficient (ECC), and it is found that they meet the required standards of DG approximately equal to 10 and ECC < 0.05. The proposed MIMO system has been fabricated and tested. The measured results are consistent with the design of the simulated structure using the CST Microwave Studio (CSTMWS) simulator.