Threshold Improvement of Low-Density Lattice Codes via Spatial Coupling

TL;DR

This paper demonstrates that spatial coupling significantly improves the threshold of low-density lattice codes, bringing it closer to channel capacity compared to conventional LDLC, through Monte Carlo density evolution analysis.

Contribution

The paper introduces spatially-coupled LDLC constructed via protographs and shows their threshold is closer to capacity than traditional LDLC.

Findings

Spatially-coupled LDLC threshold is within 0.22 dB of channel capacity.

Conventional LDLC has a threshold of 0.5 dB from capacity.

Monte Carlo density evolution with single-Gaussian messages was used for analysis.

Abstract

Spatially-coupled low-density lattice codes (LDLC) are constructed using protographs. Using Monte Carlo density evolution using single-Gaussian messages, we observe that the threshold of the spatially-coupled LDLC is within 0.22 dB of capacity of the unconstrained power channel. This is in contrast with a 0.5 dB noise threshold for the conventional LDLC lattice construction.