# An Overview of Key Technologies in Physical Layer Security
## 2 Background
### Concept and Evolution of PLS
\(B\) denotes the bits received by [PERSON], and the outcome observed by [PERSON] is denoted by \(E\). In order to ensure that the communication channel is secure,  
Figure 5: [PERSON] information content. it is significant to maximize the achievable mutual information by optimizing the input distribution \(p_{(A)}\) such that [35]  
\[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]0  
Therefore the difference between the capacities of [PERSON] and [PERSON]'s channels gives the secrecy rate of the PLS system model given in Figure 4 by  
\[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]1  
The notion of secrecy capacity plays a central role in PLS. It is a metric that defines the rate at which the transmitted signal reaches the legitimate receiver without any form of invasion from the eavesdropper. To define perfect secrecy, we consider [PERSON]'s wiretap channel model shown in \[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]2 In this model, [PERSON] intends to transmit confidential information, \(A\), to an authentic receiver, [PERSON], under a condition that an eavesdropper exists, [PERSON]. \(A\) is encoded into \(X^{n}\), which represents the information vector of length \(n\). The received information vectors for [PERSON] and [PERSON] are given by \(B^{n}\) and \(E^{n}\), respectively. Consequently, the source information entropy together with the amount of uncertainty of the message received by [PERSON] are given by \(H(A)\) and \(H(A|E^{n})\), respectively. [PERSON] showed that legitimate parties could achieve information-theoretically secure communication in a wireless communication environment by using the same random secret key, which is unknown to the eavesdropper. This is known as perfect secrecy, and it is given by Equation (10) in terms of the entropy. Transforming Equation (10) into Equation (11) shows that the eavesdropper is not able to receive any of the transmitted information content. \[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]3  
\[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]4  
The theorem also proves that perfect secrecy could be guaranteed if \(H(K)\geq H(A)\), where \(K\) is the random variable modeling the key. This means that the key should be equal to or longer than the confidential message [36]. However, perfect secrecy was proven to be impractical because the key management may be cumbersome for specific networks, such as ad hoc networks, which do not operate under fixed infrastructures [37]. To expand [PERSON]'s information-theoretic secrecy theorem, [PERSON] proposed the concept of weak secrecy. Weak secrecy is defined by the [PERSON]'s wiretap channel model shown in \[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]5  
\[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]6 [PERSON]’s wiretap channel. In this model, the encoder operates on blocks of \(k\) source bits \(A^{k}=(A^{1},A^{2},\ldots,A^{k})\) and produces an encoded sequence \(X^{n}=(X^{1},X^{2},\ldots,X^{n})\) of length \(n\). The transmission rate, which is the proportion of information sent in each codeword, is given by Equation (12). The equivocation rate, defined as a measure of confusion at the eavesdropper, is employed to investigate the weak secrecy of transmitted information. The said rate is given by Equation (13). \[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]7  
\[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]8  
where \(k\) is the total number of source bits in the code, and \(n\) is the code length. A scheme is considered to have weak secrecy in the event that  
\[C=Blog_{2}(1+\texttt{SNR}) \tag{1}\]9  
Unlike the Shannon perfect secrecy metric, this metric proved that it is possible to obtain secrecy in a practical scenario [38]. Figure 8 illustrates the relationship between the transmission rate and equivocation. It shows the region of achievable pairs as \((R,\Delta)\)[26]. The highest rate capable of achieving complete equivocation \(H_{s}\) (i.e., confusion at the eavesdropper) is the secrecy capacity \(C_{s}\) of the channel.