On The Construction of Capacity-Achieving Lattice Gaussian Codes

TL;DR

This paper introduces a new proof technique for constructing capacity-achieving lattice Gaussian codes for the AWGN channel, providing explicit parameter characterizations and a more practical existence proof.

Contribution

It presents an averaging argument applied to a generalized ensemble, offering new insights into code parameters and a practical proof of AWGN-good lattice existence.

Findings

Explicit parameter characterizations as functions of block-length

A practical proof of the existence of AWGN-good lattices

Enhanced understanding of lattice Gaussian coding schemes

Abstract

In this paper, we propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore.