Capacity of the Gaussian Erasure Channel

This paper finds the capacity of linear time-invariant additive Gaussian noise channels observed through a memoryless erasure channel. This problem requires obtaining the asymptotic spectral distribution of a submatrix of a nonnegative definite Toeplitz matrix obtained by retaining each column/row independently and with identical probability. We show that the optimum normalized power spectral density is the waterfilling solution for reduced signal-to-noise ratio.