On the Diversity of Network-Coded Cooperation With Decode-and-Forward Relay Selection

Internet of Things (IoT) plays a significant role in facilitating our work and making ease the life of human, for the reason that it can connect a lot of embedded devices to deal with many complicated and difficult tasks. However, security of IoT is more concern because every device is connected through internet network, and eavesdroppers are ready to steal or even uncover our private data. Therefore, in this paper, we propose joint single relay and jammer selection (JSRJS) to enhance the physical layer security (PLS) of IoT. Moreover, outage probability (OP) and intercept probability (IP) as well as the system tradeoff performance (STP) for JSRJS under Nakagami-m fading channel are analyzed, and OP、IP as well as STP of JSRJS are all compared with that of the pure single relay selection (SRS), respectively. Simulation results show that the OP of JSRJS is the same as that of SRS, while the IP of JSRJS is always better than that of SRS. In addition, the STP for JSRJS is also more perfect than that of SRS. Besides, as the number of relay nodes increases, the STP of these two approaches both improve notably.

Cooperative cognitive radio (CCR) is a novel paradigm for improving both radio spectrum efficiency and communication quality. However, for the CCR networks with energy harvesting, how to achieve specific relay selection is still an open issue. In this paper, we consider a CCR network with energy harvesting in which multiple secondary transmitters are able to harvest energy from the received signals to serve their own receivers and primary transmitters. Furthermore, we propose two relay selection schemes, i.e., single relay selection and multiple relay selection, by considering harvested energy and analyze the outage probability for both schemes over Nakagami-m fading channels. Simulation results validate our analysis on outage performance and compare the effects of the number of selected relays, energy harvesting ratio and transmission phase division ratios on two schemes in terms of outage probability. different parameters.

Cooperative communication is regarded as a key technology in wireless networks, including cognitive radio networks (CRNs), which increases the diversity order of the signal to combat the unfavorable effects of the fading channels, by allowing distributed terminals to collaborate through sophisticated signal processing. Underlay CRNs have strict interference constraints towards the secondary users (SUs) active in the frequency band of the primary users (PUs), which limits their transmit power and their coverage area. Relay selection offers a potential solution to the challenges faced by underlay networks, by selecting either single best relay or a subset of potential relay set under different design requirements and assumptions. The best relay selection schemes proposed in the literature for amplify-and-forward (AF) based underlay cognitive relay networks have been very well studied in terms of outage probability (OP) and bit error rate (BER), which is deficient in multiple relay selection schemes. The novelty of this work is to study the outage behavior of multiple relay selection in the underlay CRN and derive the closed-form expressions for the OP and BER through cumulative distribution function (CDF) of the SNR received at the destination. The effectiveness of relay subset selection is shown through simulation results.

In this paper, we consider amplify-and-forward (AnF) cooperative systems under correlated fading environments. We first present a brief overview of existing works on the effect of channel correlations on the system performance. We then focus on our main contribution which is analyzing the outage probability of a multi-AnF-relay system with the best relay selection (BRS) scheme under a condition that two channels of each relay, source-relay and relay-destination channels, are correlated. Using lower and upper bounds on the end-to-end received signal-to-noise ratio (SNR) at the destination, we derive corresponding upper and lower bounds on the system outage probability. We prove that the system can achieve a diversity order (DO) equal to the number of relays. In addition, and importantly, we show that the considered correlation form has a constructive effect on the system performance. In other words, the larger the correlation coefficient, the better system performance. Our analytic results are corroborated by extensive Monte-Carlo simulations.

Relay selection (RS) and power control are two essential parts in cooperative cognitive relay network. RS is equal to power control in the condition that a relay cooperates with its full power or doesn't cooperate at all. So the optimal signal-to noise ratio (SNR) value is described as a 0-1 nonlinear programming integer problem (NLIP). In this paper, a multiple relay selection (MRS) scheme based on artificial bee colony algorithm (ABC) is proposed that can fully obtain optimal SNR value. Simulations show the performance of MRS scheme by ABC algorithm is better than that of exhaustive search, single RS scheme and other sub optimal MRS schemes.

The Joint Relay Selection and Power Allocation (JRSPA) for Amplify-and-Forward (AF) relaying (JRSPA-AF) combines Power Allocation (PA) and Relay Selection (RS) very well in Two-Way Relaying (TWR) system. In order to explore the system performance of JRSPA-AF protocol, the outage probability and Diversity-Multiplexing Trade-off (DMT) of JRSPA-AF protocol are analysed. One upper bound, two lower bounds and approximate expressions of outage probability along with the DMT are derived. Based on this, the idea of JRSPA is introduced into Decode-and-Forward (DF) relaying TWR system, and the JRSPA-DF protocol is proposed. Moreover, the exact expressions of outage probability and DMT for JRSPA-DF are derived. Simulations are developed to validate the analytical results, the results show that the approximation outage probability of JRSPA-AF can be used well to evaluate system outage probability over the entire transmission SNR region, and the analysis results of outage probability of JRSPA-DF are consistent with its simulation results. In addition, the simulation results indicate that JRSPA-DF can achieve lower outage probability than JRSPA-AF and other protocols.

In this research, the combination of the relay selection and network coding is used to measure the performance in LOS and NLOS condition over cooperative communication. The research aims are to select the best relay as assisted relay as well as to improve performance system. The research method used four nodes, two nodes as source and destination and two nodes as relays. The single relay selection is used to select best relay of several relays. Measurements are conducted by altering the positions of the relays to achieve optimal outcomes. The findings indicate that the relay with the lowest Bit Error Rate (BER) and the shortest distance is chosen. The study's outcomes, when measuring throughput, reveal that network coding throughput is 21.8% higher than that without network coding in Non-Line of Sight (NLOS) conditions. In Line of Sight (LOS) conditions, the throughput is increased by 23%.

This paper analyzes the unified performance of partial relay selection protocol for multiple relay assisted free space optical (FSO) network over exponentiated weibull (EW) links. The unification has been done for heterodyne and intensity modulation/direct (IM/DD) detection techniques. We have considered a decode and forward (DF) based network consisting of multiple finite sized two way relays (TWR) between two distant terminals. In partial relay selection protocol, two TWRs are chosen in order to create the bidirectional communication path between the two terminals. The considered protocol compresses the requirement of channel state information (CSI). More specifically, we derive the unified expressions for probability density function (PDF) and cumulative distribution function (CDF) of instantaneous signal to noise ratio (SNR) over EW turbulent FSO link along with pointing error and path loss. We then utilize the unified statistics in obtaining the outage probability expression for the considered network. It is shown by analytical and simulation results that the relay selection protocol based on partial CSI completely outperforms the single relay selection protocol for both detection techniques.

Maximum distance separable (MDS) codes are those codes whose minimum distance attains the Singleton bound for a given length and given dimension. It is a well-known fact that the only binary linear block codes that are MDS are the simple parity codes and the repetition codes. Known MDS codes (the Reed-Solomon codes, for instance) are defined over larger alphabets. This approach requires that (i) the encoding and decoding procedures are performed as operations over a finite field and (ii) an update in a single information bit (e.g. in storage applications) requires an update in the redundancy symbols and usually affects a number of bits in each redundancy symbol. Thus, the optimal redundancy is achieved at the expense of additional complexity in the encoding/decoding procedures as well as in the number of redundancy bits affected by an update in the information. We construct MDS codes that have the following two properties: (i) the redundancy bits are computed by simple XOR operations; and (ii) an update in an information bit affects a minimal number of redundancy bits. >

The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses the covering radius of the dual code.

This paper investigates the impact of relay selection (RS) on the performance of cooperative non-orthogonal multiple access (NOMA), where relays are capable of working in either full-duplex (FD) or half-duplex (HD) mode. A number of relays (i.e., K relays) are uniformly distributed within the disc. A pair of RS schemes are considered insightfully: 1) single-stage RS (SRS) scheme; and 2) two-stage RS (TRS) scheme. In order to characterize the performance of these two RS schemes, new closed-form expressions for both exact and asymptotic outage probabilities are derived. Based on analytical results, the diversity orders achieved by the pair of RS schemes for FD/HD cooperative NOMA are obtained. Our analytical results reveal that: 1) the FD-based RS schemes obtain a zero diversity order, which is due to the influence of loop interference at the relay; and 2) the HD-based RS schemes are capable of achieving a diversity order of K , which is equal to the number of relays. Finally, simulation results demonstrate that: 1) the FD-based RS schemes have better outage performance than HD-based RS schemes in the low signal-to-noise ratio (SNR) region; 2) as the number of relays increases, the pair of RS schemes considered are capable of achieving the lower outage probability; and 3) the outage behaviors of FD/HD-based NOMA SRS/TRS schemes are superior to that of random RS and orthogonal multiple access based RS schemes.

In this study, the performance of wirelessly powered relay‐aided non‐orthogonal multiple access networks is investigated in terms of outage probability. Specifically, two relay selection strategies, i.e. two‐stage relay selection (TRS) and maximum energy harvesting relay selection (MEHS), and two energy harvesting scenarios, i.e. time switching (TS) and power splitting (PS) are considered. In each setup, outage probabilities' analytical expressions and their asymptotics are derived. Monte‐Carlo simulations are also carried out to verify the correctness of the analysis. The results show that regardless of relay selection and energy harvesting strategies, increasing transmit power can improve the proposed system performance. However, TRS can achieve a full diversity order, while MEHS has a unit diversity order. Besides, the results recommend parameter selections of PS and TS coefficients for optimal performance in term of outage probability.

<p style='text-indent:20px;'>The weight distribution of the cosets of maximum distance separable (MDS) codes is considered. In 1990, P.G. Bonneau proposed a relation to obtain the full weight distribution of a coset of an MDS code with minimum distance <inline-formula><tex-math id="M1">\begin{document}$ d $\end{document}</tex-math></inline-formula> using the known numbers of vectors of weights <inline-formula><tex-math id="M2">\begin{document}$ \le d-2 $\end{document}</tex-math></inline-formula> in this coset. In this paper, the Bonneau formula is transformed into a more structured and convenient form. The new version of the formula allows to consider effectively cosets of distinct weights <inline-formula><tex-math id="M3">\begin{document}$ W $\end{document}</tex-math></inline-formula>. (The weight <inline-formula><tex-math id="M4">\begin{document}$ W $\end{document}</tex-math></inline-formula> of a coset is the smallest Hamming weight of any vector in the coset.) For each of the considered <inline-formula><tex-math id="M5">\begin{document}$ W $\end{document}</tex-math></inline-formula> or regions of <inline-formula><tex-math id="M6">\begin{document}$ W $\end{document}</tex-math></inline-formula>, special relations more simple than the general ones are obtained. For the MDS code cosets of weight <inline-formula><tex-math id="M7">\begin{document}$ W = 1 $\end{document}</tex-math></inline-formula> and weight <inline-formula><tex-math id="M8">\begin{document}$ W = d-1 $\end{document}</tex-math></inline-formula> we obtain formulas of the weight distributions depending only on the code parameters. This proves that all the cosets of weight <inline-formula><tex-math id="M9">\begin{document}$ W = 1 $\end{document}</tex-math></inline-formula> (as well as <inline-formula><tex-math id="M10">\begin{document}$ W = d-1 $\end{document}</tex-math></inline-formula>) have the same weight distribution. The cosets of weight <inline-formula><tex-math id="M11">\begin{document}$ W = 2 $\end{document}</tex-math></inline-formula> or <inline-formula><tex-math id="M12">\begin{document}$ W = d-2 $\end{document}</tex-math></inline-formula> may have different weight distributions; in this case, we proved that the distributions are symmetrical in some sense. The weight distributions of the cosets of MDS codes corresponding to arcs in the projective plane <inline-formula><tex-math id="M13">\begin{document}$ \mathrm{PG}(2,q) $\end{document}</tex-math></inline-formula> are also considered. For MDS codes of covering radius <inline-formula><tex-math id="M14">\begin{document}$ R = d-1 $\end{document}</tex-math></inline-formula> we obtain the number of the weight <inline-formula><tex-math id="M15">\begin{document}$ W = d-1 $\end{document}</tex-math></inline-formula> cosets and their weight distribution that gives rise to a certain classification of the so-called deep holes. We show that any MDS code of covering radius <inline-formula><tex-math id="M16">\begin{document}$ R = d-1 $\end{document}</tex-math></inline-formula> is an almost perfect multiple covering of the farthest-off points (deep holes); moreover, it corresponds to an optimal multiple saturating set in the projective space <inline-formula><tex-math id="M17">\begin{document}$ \mathrm{PG}(N,q) $\end{document}</tex-math></inline-formula>.</p>

The algebraic setting for threshold secret sharing scheme can vary, dependent on the application. This algebraic setting can limit the number of participants of an ideal secret sharing scheme. Thus it is important to know for which thresholds one could utilize an ideal threshold sharing schemeand for which thresholds one would have to use non-ideal schemes. The implication is that more than one share may have to be dealt to some or all parties. Karnin, Greene and Hellman constructed several bounds concerning the maximal number of participants in threshold sharing scheme. There has been a number of researchers who have noted the relationship between k-arcs in projective spaces and ideal linear threshold secret schemes, as well as between MDS codes and ideal linear threshold secret sharing schemes. Further, researchers have constructed optimal bounds concerning the size of k-arcs in projective spaces, MDS codes, etc. for various finite fields. Unfortunately, the application of these results on the Karnin, Greene and Hellamn bounds has not been widely disseminated. Our contribution in this paper is revisiting and updating the Karnin, Greene, and Hellman bounds, providing optimal bounds on the number of participants in ideal linear threshold secret sharing schemes for various finite fields, and constructing these bounds using the same tools that Karnin, Greene, and Hellman introduced in their seminal paper. We provide optimal bounds for the maximal number of players for a tout of nideal linear threshold scheme when t= 3, for all possible finite fields. We also provide bounds for infinitely many tand infinitely many fields and a unifying relationship between this problem and the MDS (maximum distance separable) codes that shows that any improvement on bounds for ideal linear threshold secret sharing scheme will impact bounds on MDS codes, for which there is a number of conjectured (but open) problems.

In this paper, we propose a new multiple relay selection scheme with the availability of outdated channel state information (CSI) for decode and forward (DaF) relay systems, namely the $N$ plus normalized threshold opportunistic relay selection ($N$+NT-ORS). In particular, we first opportunistically select $N$ best relays out of all relays in the decoding subset with respect to CSI. Then the ratios of the instantaneous signal-to-noise ratios (SNRs) on the rest of the relays to that of the $N$-th highest instantaneous SNR are tested against a normalized threshold $\mu$$\in$$[0,1]$ and only those relays passing this test are selected. Through the derivation of the moment generation function (MGF) of SNR, together with the relationship between MGF and outage probability, we obtain a closed-form expression for the outage probability. In addition to analyzing the asymptotic diversity order for $N$+NTS-ORS, we also outline a distributed $N$+NT-ORS selection protocol without the need of global CSI at each relay. Numerical results confirm the correctness of the derivation and show how $N$+NT-ORS outperforms its existing counterparts.