Strong secrecy capacity of compound wiretap channels is studied. The knownlower bounds for the secrecy capacity of compound finite-state memorylesschannels under discrete alphabets are extended to arbitrary uncertainty setsand continuous alphabets under the strong secrecy criterion. The conditionsunder which these bounds are tight are given. Under the saddle-point condition,the compound secrecy capacity is shown to be equal to that of the worst-casechannel. Based on this, the compound Gaussian MIMO wiretap channel is studiedunder the spectral norm constraint and without the degradedness assumption.First, it is assumed that only the eavesdropper channel is unknown, but isknown to have a bounded spectral norm (maximum channel gain). The compoundsecrecy capacity is established in a closed form and the optimal signaling isidentified: the compound capacity equals the worst-case channel capacity thusestablishing the saddle-point property; the optimal signaling is Gaussian andon the eigenvectors of the legitimate channel and the worst-case eavesdropperis isotropic. The eigenmode power allocation somewhat resembles the standardwater-filling but is not identical to it. More general uncertainty sets areconsidered and the existence of a maximum element is shown to be sufficient fora saddle-point to exist, so that signaling on the worst-case channel achievesthe compound capacity of the whole class of channels. The case ofrank-constrained eavesdropper is considered and the respective compound secrecycapacity is established. Subsequently, the case of additive uncertainty in thelegitimate channel, in addition to the unknown eavesdropper channel, isstudied. Its compound secrecy capacity and the optimal signaling areestablished in a closed-form as well, revealing the same saddle-point property.
展开▼
