# Construction and Decoding of Product Codes with Non-Systematic Polar Codes

## TL;DR

This paper introduces a new method for constructing product codes using non-systematic polar codes, resulting in high-throughput, low-latency error correction suitable for optical communications.

## Contribution

It presents a novel construction of product polar codes based on non-systematic polar codes and a low-complexity decoding algorithm exploiting their dual nature.

## Key findings

- High decoding speed enables long code construction
- Maintains low decoding latency with good error correction
- Suitable for optical communication systems

## Abstract

Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we present a novel construction for product polar codes based on non-systematic polar codes. We prove that the resulting product code is actually a polar code, having a frozen set that is dependent on the frozen sets of the component polar codes. We propose a low-complexity decoding algorithm exploiting the dual nature of the constructed code. Performance analysis and simulations show high decoding speed, that allows to construct long codes while maintaining low decoding latency. The resulting high throughput and good error-correction performance are appealing for optical communication systems and other systems where high throughput and low latency are required.