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Secret key extraction is a crucial issue in physical layer security and a less complex and, at the same time, a more robust scheme for the next generation of 5G and beyond. Unlike previous works on this topic, in which Orthogonal Frequency Division Multiplexing (OFDM) sub-channels were considered to be independent, the effect of correlation between sub-channels on the secret key rate is addressed in this paper. As an assumption, a realistic model for dependency among sub-channels is considered. Benchmarked by simulation, the result shows that the key exchange rate may decline by up to 72% due to the correlation of sub-channels. A new approach for efficient key extraction is used in this study. To do this, a Singular Value Decomposition based (SVD-based) pre-coding is utilized to alleviate the subchannels correlation and the channel noise. The low computational complexity of our proposed approach makes it a promising candidate for developing secure and high-speed networks. Results obtained through simulation indicate that applying pre-coding on the measured correlated data resulted in a minimum gain of 9 dB. In addition, the result also depicts the advantage of SVD versus other pre-coding techniques, namely PCA, DCT, and WT.

The bandwidth minimization problem can be used in data storage and VLSI design issues and saving large hypertext media, etc. The Matrix Bandwidth Minimization Problem involves finding matrix rows and columns permutation so that non-zero elements of the matrix A are located in a band that is as close as possible to the original diameter to minimize the amount of {max{|i−j|:aij≠.}. The Bandwidth Minimization Problem for Graphs (BMPG) is a complicated problem; hence the deterministic algorithms are not appropriate to solve these kinds of problems. The purpose of this research is to reduce the required computations through the use of heuristic algorithms and evolutionary algorithms, so that instead of using purely mathematical methods to find answers, we can turn the problem into an optimization problem through the use of collective intelligence and evolutionary algorithms and the concepts in this field. In the present paper, the use of meta-heuristic algorithm, Imperialist competitive algorithm is proposed in order to solve minimization problem. In this paper, the performance of presented algorithm with random samples has been evaluated compared with the results of genetic algorithms. The results of tests show that the Imperialist competitive algorithm can be considered as an efficient method to solve the bandwidth minimization problem for graphs.