a fixed scalar $\vartheta$, we represent by $p(\vartheta)$ the conditional probability of a transmission failure given that the jamming interference power is set to $\vartheta$. In particular, (\[eq:ldef\]) implies $$\begin{aligned}
\mathbb{P}[l(t)=1|v(t)=\vartheta] & =\mathbb{P}[r(t)\leq p(\vartheta)|v(t)=\vartheta]\\
 & =\mathbb{P}[r(t)\leq p(\vartheta)]=p(\vartheta).\end{aligned}$$ Observe that, if $v(t)$ is large so that $p(v(t))$ is close to $1$, then it becomes more likely that $r(t)\leq p(v(t))$, and hence by (\[eq:ldef\]), a transmission failure is likely to occur. Note also that transmission failures at different times are *conditionally independent* given the interference powers at those times. Namely, for every $t_{1}<t_{2}<\cdots<t_{k}$, $k\in\mathbb{N}$, $$\begin{aligned}
 & \mathbb{P}[l(t_{1})=1,\ldots,l(t_{k})=1|v(t_{1})=\vartheta_{1},\ldots,v(t_{k})=\vartheta_{k}]\\
 & \quad=\prod_{i=1}^{k}\mathbb{P}[l(t_{i})=1|v(t_{i})=\vartheta_{i}]=\prod_{i=1}^{k}p(\vartheta_{i}).\end{aligned}$$

The characterization in (\[eq:ldef\]) enables us to describe security properties of different wireless channel models by utilizing different $p$ functions. For instance, to describe the additive white Gaussian noise channel with quadrature amplitude modulation scheme considered in [@IFACli2016sinr], $p$ can be selected as $$\begin{aligned}
p(\vartheta)=2Q\Big(\sqrt{c\frac{\xi}{\vartheta+\sigma}}\Big),\label{eq:p_from_reference-1}\end{aligned}$$ where $Q(y)\triangleq\frac{1}{\sqrt{2\pi}}\int_{y}^{\infty}e^{-\frac{s^{2}}{2}}\mathrm{d}s$, $\xi\in(0,\infty)$ and $\sigma\in(0,\infty)$ are constants associated respectively with the transmission power and the power of the channel noise, and $c\in(0,\infty)$ is a constant associated with the parameters of the communication protocol. Notice that the term $\frac{\xi}{\vartheta+\sigma}$ in (\[eq:p\_from\_reference-1\]) corresponds to Signal-to-Interference-plus-Noise-Ratio (SINR), indicating the quality of a wireless channel [@shi2017signal]. Even if there is no attack 