We consider a discrete memoryless broadcast channel consists of two users and a sender. The sender has two independent confidential messages for each user. We extend the work of Liu et al. on broadcast channels with two confidential messages with wea
k secrecy criterion to strong secrecy. Our results are based on an extension of the techniques developed by Hou and Kramer on bounding Kullback-Leibler divergence in context of textit{resolvability} and textit{effective secrecy}.
Various wireless sensor network applications involve the computation of a pre-defined function of the measurements without the need for reconstructing each individual sensor reading. Widely-considered examples of such functions include the arithmetic
mean and the maximum value. Standard approaches to the computation problem separate computation from communication: quantized sensor readings are transmitted interference-free to a fusion center that reconstructs each sensor reading and subsequently computes the sought function value. Such separation-based computation schemes are generally highly inefficient as a complete reconstruction of individual sensor readings is not necessary for the fusion center to compute a function of them. In particular, if the mathematical structure of the wireless channel is suitably matched (in some sense) to the function, then channel collisions induced by concurrent transmissions of different nodes can be beneficially exploited for computation purposes. Therefore, in this paper a practically relevant analog computation scheme is proposed that allows for an efficient estimate of linear and nonlinear functions over the wireless multiple-access channel. After analyzing the asymptotic properties of the estimation error, numerical simulations are presented to show the potential for huge performance gains when compared with time-division multiple-access based computation schemes.
