Construction of Simultaneously Good Polar Codes and Polar Lattices

TL;DR

This paper presents an explicit polarization-based method to construct lattices and codes that are simultaneously optimal for both channel and source coding, advancing the theoretical understanding of such structures.

Contribution

It introduces a new explicit construction technique for simultaneously good polar codes and polar lattices using polarization methods.

Findings

Explicit construction of simultaneously good polar codes and lattices.

Proof of existence using polarization technique.

Advancement in dual optimality for coding and source compression.

Abstract

In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding simultaneously. The existence of such kind of lattices was proven by using random lattice ensembles. Our work provides an explicit construction based on the polarization technique.