# Design of Protograph Codes for Additive White Symmetric Alpha-Stable Noise Channels

## TL;DR

This paper introduces a new method for designing protograph LDPC codes tailored for additive white symmetric alpha-stable noise channels, improving error performance in impulsive noise environments.

## Contribution

It develops a novel simulation-based P-EXIT analysis and applies AWD analysis to design protograph codes specifically for AWSaSN channels, outperforming existing codes.

## Key findings

- Proposed codes outperform AR4JA and irregular codes for AWGN and AWSaSN channels.
- New analysis methods enable better decoding threshold estimation.
- Designed codes show improved error rate performance in simulations.

## Abstract

The protograph low-density parity-check (LDPC) codes possess many attractive properties, such as the low encoding/decoding complexity and better error floor performance, and hence have been successfully applied to different types of communication and data storage channels. In this paper,we design protograph LDPC codes for communication systems corrupted by the impulsive noise, which are modeled as additive white symmetric alpha-stable noise (AWSaSN) channels. We start by presenting a novel simulation-based protograph extrinsic information transfer (P-EXIT) analysis to derive the iterative decoding threshold of the protograph codes. By further applying the asymptotic weight distribution (AWD) analysis, we design new protograph codes for the AWSaSN channel. Both theoretical analysis and simulation results demonstrate that the proposed protograph codes can provide better error rate performance than the prior art AR4JA code, the irregular codes optimized for the AWGN channel, as well as the irregular codes optimized for the AWSaSN channel.