Construction A of Lattices over Number Fields and Block Fading Wiretap Coding

Abstract

We propose a lattice construction from totally real and CM fields, which naturally generalizes the Construction A of lattices from $p$-ary codes obtained from the cyclotomic field $\mathbb{Q}({\zeta }_p)$, $p$ a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield $\mathbb{Q}({\zeta }_{p^r}+{\zeta }_p^{-r})$ of the cyclotomic field $\mathbb{Q}({\zeta }_{p^r})$, $r\ge 1$. Our construction has applications to coset encoding of algebraic lattice codes, and we detail the case of coset encoding of block fading wiretap codes.

Submitted to IEEE Transactions on Information Theory

References in corpus (1)

• Practical Encoders and Decoders for Euclidean Codes from Barnes-Wall Lattices

Cited by in corpus (4)

• Lattices from Codes for Harnessing Interference: An Overview and Generalizations
• Lattice Coding for Downlink Multiuser Transmission
• A Quadratic Form Approach to Construction A of Lattices over Cyclic Algebras
• Ring Compute-and-Forward over Block-Fading Channels