# Multi-edge-type LDPC code design with G-EXIT charts for continuous-variable quantum key distribution

## TL;DR

This paper introduces G-EXIT charts as a new, efficient analysis tool for designing multi-edge-type LDPC codes in quantum key distribution, improving decoding thresholds in low SNR regimes.

## Contribution

The paper develops G-EXIT charts for MET-LDPC codes, enabling faster and simpler analysis of code convergence and performance in quantum communication.

## Key findings

- G-EXIT charts effectively analyze MET-LDPC code convergence.
- Codes designed with G-EXIT charts achieve better decoding thresholds.
- G-EXIT charts outperform traditional density evolution in speed and simplicity.

## Abstract

Continuous-variable quantum key distribution utilizes an ensemble of coherent states of light to distribute secret encryption keys between two parties. One of the challenges is thereby the requirement of capacity approaching error correcting codes in the low signal-to-noise (SNR) regime (SNR < 0 dB). Multilevel coding (MLC) combined with multistage decoding (MSD) can solve this challenge in combination with multi-edge-type low-density parity-check (MET-LDPC) codes which are ideal for low code rates in the low SNR regime due to degree-one variable nodes. However, the complexity of designing such highly efficient codes remains an open issue. Here, we introduce the concept of generalized extrinsic information transfer (G-EXIT) charts for MET-LDPC codes and demonstrate how this tool can be used to analyze their convergence behavior. We calculate the capacity for each level in the MLC-MSD scheme and use G-EXIT charts to exemplary find codes for some given rates which provide a better decoding threshold compared to previously reported codes. In comparison to the traditional density evolution method, G-EXIT charts offer a simple and fast asymptotic analysis tool for MET-LDPC codes.