Analysis of Secrecy in Multi-User Wireless Networ

We consider an Ergodic Fading Broadcast Channel with one Legitimate receiver and one Eavesdropper (BCoLoE) having arbitrary fading statistics, where the instantaneous Channel State Information (CSI) are known only at the receivers (CSIR). The secrecy capacity of this channel is characterized within 11 bits irrespective of fading statistics and Signal-to-Noise Ratios (SNRs). This is achieved by deriving a new upper bound to the secrecy capacity of the channel and two new lower bounds. The upper bound is derived by approximating Complementary Cumulative Distribution Functions (CCDFs) of the two links by corresponding staircase functions. The smaller lower bound, although looser, has a form which can be analytically compared with the upper bound and facilitates the approximate secrecy capacity characterization. It is proved that, the so called Binary Expansion Signaling with Reverse Stripping (BES-RS) scheme can achieve a secrecy rate larger than both these lower bounds with the help of numerical computation for several BCoLoEs with practical fading statistics.;We further characterize the secrecy capacity of a class of 2-user binary fading interference channel (BFIC) and 2-user layered fading interference channel (LFIC), under the same assumptions as for the wiretap channel. The secrecy capacity region for a very weak BFIC turns out to be quadrangular while for LFIC it is polygonal. We explicitly characterize the corner points in both the cases. The converse in either case is proved by dividing the set of upper bounds into two carefully chosen regions depending on the values of o - the weighting factor of the weighted sum bounds. In case of LFIC each of the regions are also shown to be piece-wise linear. The achievability on the other hand is proved by using capacity optimal code for a layered erasure wiretap channel at both the transmitters and treating interference as erasure while decoding the signals at the receivers. In addition, the achievability of the layered case also involves proper assignment of the layers to the two transmitters based on some constraints. We also prove the secrecy capacity of strong BFIC and LFIC as zero.