Capacity Achieving Low Density Parity Check Lattices

TL;DR

This paper demonstrates that a specific ensemble of regular LDPC lattices can achieve the capacity of AWGN channels and are sphere-bound-achieving, providing insights into their properties and performance metrics.

Contribution

The paper introduces and analyzes a new ensemble of regular LDPC lattices that are proven to be capacity-achieving and sphere-bound-achieving, with detailed property evaluations.

Findings

Lattices are sphere-bound-achieving.

Lattices are capacity-achieving.

Provides bounds for error probability and other properties.

Abstract

The concept and existence of sphere-bound-achieving and capacity-achieving lattices has been explained on AWGN channels by Forney. LDPC lattices, introduced by Sadeghi, perform very well under iterative decoding algorithm. In this work, we focus on an ensemble of regular LDPC lattices. We produce and investigate an ensemble of LDPC lattices with known properties. It is shown that these lattices are sphere-bound-achieving and capacity-achieving. As byproducts we find the minimum distance, coding gain, kissing number and an upper bound for probability of error for this special ensemble of regular LDPC lattices.