Spherical codes for the Gaussian wiretap channel with continuous input alphabets

We address the problem of designing codes for transmission over a Gaussian wiretap channel when the source is continuously-valued. We show that spherical codes based on flat tori can provide a natural constructive method to design codes for secrecy. In particular, their geometrical properties allow to fine tune the code for prescribed levels of reliability and secrecy, while providing a basis for efficient encoding and decoding. We present a suitable parametrization for these codes which enables legitimate users to communicate under a small distortion, while forcing the eavesdropper to operate at large distortions.