Depth versus Breadth in Convolutional Polar Codes

TL;DR

This paper explores convolutional polar codes, demonstrating that increasing convolution depth improves decoding efficiency and error performance more effectively than expanding the polarization kernel's breadth.

Contribution

It provides a numerical analysis showing that deeper convolutional structures outperform broader kernels in convolutional polar codes.

Findings

Deeper convolutional structures enhance decoding speed.

Increased convolution depth reduces decoding error probability.

Depth is more beneficial than breadth in convolutional polar codes.

Abstract

Polar codes were introduced in 2009 by Arikan as the first efficient encoding and decoding scheme that is capacity achieving for symmetric binary-input memoryless channels. Recently, this code family was extended by replacing the block-structured polarization step of polar codes by a convolutional structure. This article presents a numerical exploration of this so-called convolutional polar codes family to find efficient generalizations of polar codes, both in terms of decoding speed and decoding error probability. The main conclusion drawn from our study is that increasing the convolution depth is more efficient than increasing the polarization kernel's breadth as previously explored.