Construction of LDGM lattices

TL;DR

This paper presents a method to construct LDGM lattices using Construction D and PEG algorithm, achieving good performance with low complexity, supported by theoretical bounds and simulation results.

Contribution

It introduces a novel approach to build LDGM lattices with theoretical bounds and practical construction methods, enhancing performance and efficiency.

Findings

Lattices constructed have acceptable performance under iterative decoding.

Bounds on minimum distance and coding gain are established.

Simulation confirms the effectiveness of the constructed lattices.

Abstract

Low density generator matrix (LDGM) codes have an acceptable performance under iterative decoding algorithms. This idea is used to construct a class of lattices with relatively good performance and low encoding and decoding complexity. To construct such lattices, Construction D is applied to a set of generator vectors of a class of LDGM codes. Bounds on the minimum distance and the coding gain of the corresponding lattices and a corollary for the cross sections and projections of these lattices are provided. The progressive edge growth (PEG) algorithm is used to construct a class of binary codes to generate the corresponding lattice. Simulation results confirm the acceptable performance of these class of lattices.