On Analytical and Geometric Lattice Design Criteria for Wiretap Coset Codes

This paper considers physical layer security and the design of secure coset codes for wiretap channels, where information is not to be leaked to an eavesdropper having a degraded channel. The eavesdropper’s bounds for correct decoding probability and information are first revisited, and a new variant of the information bound is derived. The new bound is valid for a general channel with any fading and Gaussian noise. From these bounds, it is explicit that both the information and probability are upper bounded by the average flatness factor, i.e., the expected theta function of the faded lattice related to the eavesdropper. Taking the minimization of the average flatness factor as a design criterion, simple geometric heuristics to minimize it in the Gaussian and Rayleigh fast fading channels are motivated. It is concluded that in the Gaussian channel, the security boils down to the sphere packing density of the eavesdropper’s lattice, whereas in the Rayleigh fading channel a full-diversity well-rounded lattice with a dense sphere packing will provide the best secrecy. The proposed criteria are backed up by extensive numerical experiments.