# On Distance Properties of Convolutional Polar Codes

## TL;DR

This paper establishes a lower bound on the minimum distance of convolutional polar codes, introduces a new subcode construction with improved decoding performance, and compares its decoding complexity and error probability favorably to Arikan polar codes.

## Contribution

It provides a novel lower bound on the minimum distance and proposes convolutional polar subcodes with enhanced decoding efficiency and error performance.

## Key findings

- Lower bound on minimum distance derived
- Convolutional polar subcodes outperform Arikan polar subcodes in decoding error probability
- Decoding complexity of convolutional polar subcodes is lower for large list sizes

## Abstract

A lower bound on minimum distance of convolutional polar codes is provided. The bound is obtained from the minimum weight of generalized cosets of the codes generated by bottom rows of the polarizing matrix. Moreover, a construction of convolutional polar subcodes is proposed, which provides improved performance under successive cancellation list decoding. For sufficiently large list size, the decoding complexity of convolutional polar subcodes appears to be lower compared to Arikan polar subcodes with the same performance. The error probability of successive cancellation list decoding of convolutional polar subcodes is lower than that of Arikan polar subcodes with the same list size.