On Finite-Length Performance of Polar Codes: Stopping Sets, Error Floor, and Concatenated Design

TL;DR

This paper analyzes the finite-length performance of polar codes over the BEC, focusing on stopping sets, error floors, and a concatenated design, demonstrating their advantages and proposing a practical application in optical networks.

Contribution

It provides a detailed stopping set analysis for polar codes, introduces a concatenated scheme for optical networks, and shows improved error floor performance and capacity gap closure.

Findings

Finite-length polar codes have superior error floor performance.

The proposed concatenated scheme outperforms conventional methods in OTNs.

Polar codes can be effectively combined with other schemes for real-world applications.

Abstract

This paper investigates properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief propagation as the decoding method. We provide a stopping set analysis for the factor graph of polar codes, where we find the size of the minimum stopping set. We also find the girth of the graph for polar codes. Our analysis along with bit error rate (BER) simulations demonstrate that finite-length polar codes show superior error floor performance compared to the conventional capacity-approaching coding techniques. In order to take advantage from this property while avoiding the shortcomings of polar codes, we consider the idea of combining polar codes with other coding schemes. We propose a polar code-based concatenated scheme to be used in Optical Transport Networks (OTNs) as a potential real-world application. Comparing against conventional concatenation techniques for OTNs, we show that the proposed scheme outperforms the existing methods by closing the gap to the capacity while avoiding error floor, and maintaining a low complexity at the same time.