On the Estimation of Joint Mutual Information for Physical Layer Security

In a two node communication environment, the number of key bits (IK) per observation of the reciprocal channel can be computed using the mutual information between the forward and reverse estimated channels. The mutual information can not be computed in closed form, if the probability density function (pdf) of the channel is unknown. This work studies the computation of IK for an arbitrary channel distribution using four approaches namely, Gaussian approximation, Numerical computation, Histogram based approximation, and Gaussian mixtures based approximation. Gaussian approximation is the most sub-optimal method, whereas numerical computational is the most rigorous technique when underlying pdf is unknown. Results indicate that Gaussian mixture based approximation is less computationally expensive as compared to other three techniques, and gives results fairly close to the numerical computation.