Graph Search based Polar Code Design

TL;DR

This paper introduces a graph search approach to polar code design that reduces complexity and enables efficient construction of rate-compatible codes, outperforming existing heuristic methods.

Contribution

It formalizes polar code design as a graph search problem, significantly reducing design complexity and facilitating the creation of rate-compatible codes.

Findings

Reduced design complexity compared to genetic and deep learning methods

Efficient construction of rate-compatible polar codes

Analyzed error-rate performance of the proposed codes

Abstract

It is well known that to fulfill their full potential, the design of polar codes must be tailored to their intended decoding algorithm. While for successive cancellation (SC) decoding, information theoretically optimal constructions are available, the code design for other decoding algorithms (such as belief propagation (BP) decoding) can only be optimized using extensive Monte Carlo simulations. We propose to view the design process of polar codes as a graph search problem and thereby approaching it more systematically. Based on this formalism, the design-time complexity can be significantly reduced compared to state-of-the-art Genetic Algorithm (GenAlg) and deep learning-based design algorithms. Moreover, sequences of rate-compatible polar codes can be efficiently found. Finally, we analyze both the complexity of the proposed algorithm and the error-rate performance of the constructed codes.