Compound wire-tap channels

The compound wire-tap channel is studied, which is based on the classical wire-tap channel with the channel from the source to the destination and the channel from the source to the wire-tapper taking a number of states, respectively. This channel can also be viewed as the wire-tap channel with mul-tiple destinations and multiple wire-tappers, i.e., multicast with multiple wire-tappers. The source wishes to transmit information to all destinations and wants to keep the information secret from all wire-tappers. For the discrete memoryless compound wire-tap channel, lower and upper bounds on the secrecy capacity are derived and are shown to match for the degraded channel. The parallel Gaussian compound wire-tap channel is further studied, for which the secrecy capacity and the characterization of an optimal power allocation are obtained. The secrecy degree of freedom (s.d.o.f.) is also derived, which connects the secure communication rate in the high SNR regime to secure networking coding for deterministic networks. Finally, the multi-antenna (i.e., MIMO) compound wire-tap channel is studied. The secrecy capacity is established for the degraded MIMO compound wire-tap channel and an achievable s.d.o.f. is given for the general MIMO compound wire-tap channel.