A comparison of skewed and orthogonal lattices in Gaussian wiretap channels

We consider lattice coset-coded transmissions over a wiretap channel with additive white Gaussian noise (AWGN). Examining a function that can be interpreted as either the legitimate receiver´s error probability or the eavesdropper´s correct decision probability, we rigorously show that, albeit offering simple bit labeling, orthogonal nested lattices are suboptimal for coset coding in terms of both the legitimate receiver´s and the eavesdropper´s probabilities.