Revisit the AWGN-goodness of Polar-like Lattices

TL;DR

This paper explores polar-like lattices, especially PAC lattices, demonstrating their AWGN-goodness and structural advantages through a detailed analysis of their generator matrices and connections.

Contribution

It provides a comprehensive introduction to polar-like lattices, linking them with PAC lattices and analyzing their structural properties to establish AWGN-goodness.

Findings

Polar lattices can be constructed directly from generator matrices.

PAC lattices exhibit structural advantages for AWGN-goodness.

The AWGN-goodness of PAC lattices is demonstrated through their structural analysis.

Abstract

This paper aims to provide a comprehensive introduction to lattices constructed based on polar-like codes and demonstrate some of their key properties, such as AWGN goodness. We first present polar lattices directly from the perspective of their generator matrix. Next, we discuss their connection with the recently proposed PAC (polarization adjusted convolutional) lattices and analyze the structural advantages of PAC lattices, through which the AWGN-goodness of PAC lattices can be conveniently demonstrated.