Lattice codes for wiretap fading channels - Ong, Soon Sheng (2014)
This thesis is dedicated to the design of wiretap codes for fading channels, that is, codes that promise both reliability and confidentiality for wireless channels. By upper bounding the eavesdropper's probability of correctly decoding a confidential message, we begin by deriving a code design criterion that characterizes confidentiality for finite lattice constellations. We consider wiretap lattice codes built from number fields, or more precisely ideal lattice codes. Ideal lattice codes are known to be good for reliability and we refine our code design criterion for this type of lattice codes yielding an optimization of a sum of inverse of algebraic norms. In order to construct good wiretap lattice codes for fast fading channels, we analyse sums of inverse of algebraic norms by studying the units and non-units with small norms in number fields. We compare different underlying number fields with respect to the wiretap codes they provide. Encoding of wiretap codes is done via coset encoding, where each codeword sent is chosen randomly from a coset of codewords. Motivated by the need to perform coset encoding with lattices built from number fields, we propose a generalization of Construction A of lattices over number fields from linear codes. The lattice construction is of interest on its own, but also serves for encoding slow fading wiretap codes.