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We consider lattice coset-coded transmissions over a wiretap channel withadditive white Gaussian noise (AWGN). Examining a function that can beinterpreted as either the legitimate receiver's error probability or theeavesdropper's correct decision probability, we rigorously show that, albeitoffering simple bit labeling, orthogonal nested lattices are suboptimal forcoset coding in terms of both the legitimate receiver's and the eavesdropper'sprobabilities.

A Comparison of Skewed and Orthogonal Lattices in Gaussian Wiretap Channels