Stopping Set Analysis for Concatenated Polar Code Architectures

TL;DR

This paper extends stopping set analysis to concatenated polar codes, deriving bounds, analyzing tightness, and proposing a new construction method that improves performance over existing designs.

Contribution

It introduces a stopping set analysis for concatenated polar codes, derives bounds on minimum stopping set size, and proposes a novel construction method for improved code architectures.

Findings

Derived an upper bound on the minimum stopping set size for concatenated polar codes.

Proposed a new construction method for concatenated polar codes based on stopping set analysis.

Simulation results show the new codes outperform existing density evolution-based designs.

Abstract

This paper investigates properties of concatenated polar codes and their potential applications. We start with reviewing previous work on stopping set analysis for conventional polar codes, which we extend in this paper to concatenated architectures. Specifically, we present a stopping set analysis for the factor graph of concatenated polar codes, deriving an upper bound on the size of the minimum stopping set. To achieve this bound, we propose new bounds on the size of the minimum stopping set for conventional polar code factor graphs. The tightness of these proposed bounds is investigated empirically and analytically. We show that, in some special cases, the exact value of the minimum stopping set can be determined with a time complexity of $O(N)$, where $N$ is the codeword length. The stopping set analysis motivates a novel construction method for concatenated polar codes. This method is used to design outer polar codes for two previously proposed concatenated polar code architectures: augmented polar codes and local-global polar codes. Simulation results demonstrate the advantage of the proposed codes over previously proposed constructions based on density evolution (DE).