Worst-case power-constrained noise for binary-input channels

Additive noise channels with binary-valued inputs and real-valued outputs are considered. The maximum error probability and the minimum channel capacity achieved by any power-constrained noise distribution are obtained. A general framework which applies to a variety of performance measures shows that the least-favorable noise distribution is, in general, a mixture of two lattice probability mass functions. The framework holds for m-ary input constellations on finite-dimensional lattices.