Practical Product Code Construction of Polar Codes

TL;DR

This paper explores the structure of polar codes as product codes, providing methods to construct and decode them efficiently, leading to improved performance in latency-sensitive optical communication systems.

Contribution

It introduces a novel product code perspective for polar codes, including guidelines for frozen set computation and a two-step decoding method that reduces latency.

Findings

Product of two polar codes is a polar code.

Proposed two-step decoder significantly reduces decoding latency.

Decoding method outperforms standard polar codes and state-of-the-art codes in optical communications.

Abstract

In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets of the component polar codes. Moreover, we show how polar codes can be described as irregular product codes. We propose a two-step decoder for long polar codes taking advantage of this dual nature to heavily reduce decoding latency. Finally, we show that the proposed decoding technique outperforms both standard polar codes and state-of-the-art codes for optical communications under latency constraints.