Parallel BCC with one common and two confidential messages and imperfect CSIT

We consider a broadcast communication system over parallel sub-channels where the transmitter sends three messages: a common message to two users, and two confidential messages to each user which need to be kept secret from the other user. We assume partial channel state information at the transmitter (CSIT), stemming from noisy channel estimation. The first contribution of this paper is the characterization of the secrecy capacity region boundary as the solution of weighted sum-rate problems, with suitable weights. Partial CSIT is addressed by adding a margin to the estimated channel gains. The second paper contribution is the solution of this problem in an almost closed-form, where only two single real parameters must be optimized, e.g., through dichotomic searches. On the one hand, the considered problem generalizes existing literature where only two out of the three messages are transmitted. On the other hand, the solution finds also practical applications into the resource allocation of orthogonal frequency division multiplexing (OFDM) systems with both secrecy and fairness constraints.