# On the Construction of $G_N$-coset Codes for Parallel Decoding

## TL;DR

This paper introduces a new class of $G_N$-coset codes designed for highly parallel turbo-like decoding, enabling efficient decoding with comparable performance to polar codes.

## Contribution

It proposes a novel $G_N$-coset code construction leveraging parallel decoding of component codes and a flexible information set selection method.

## Key findings

- Achieves decoding parallelism superior to traditional codes.
- Maintains coding performance comparable to polar codes.
- Demonstrates effective heuristic code construction.

## Abstract

In this paper, we propose a type of $G_N$-coset codes for a highly parallel stage-permuted turbo-like decoder. The decoder exploits the equivalence between two stage-permuted factor graphs of $G_N$-coset codes. Specifically, the inner codes of a $G_N$-coset code consist of independent component codes, thus are decoded in parallel. The extrinsic information of the code bits is obtained and iteratively exchanged between the two graphs until convergence. Accordingly, we explore a heuristic and flexible code construction method (information set selection) for various information lengths and coding rates. Simulations show that the proposed $G_N$-coset codes could achieve a coding performance comparable with polar codes but enjoy higher decoding parallelism.