Low Rate Protograph-Based LDPC Codes for Continuous Variable Quantum Key Distribution

TL;DR

This paper presents a novel method for designing ultra low rate LDPC codes using protographs and differential evolution, significantly improving error correction performance for continuous variable quantum key distribution systems.

Contribution

It introduces type-based protographs and a differential evolution approach to efficiently design ultra low rate LDPC codes for CV-QKD, outperforming existing codes.

Findings

Codes show higher thresholds and better finite-length performance.

Design method reduces complexity and enables rapid code development.

Validated gains through Monte-Carlo simulations in CV-QKD regimes.

Abstract

Error correction plays a major role in the reconciliation of continuous variable quantum key distribution (CV-QKD) and greatly affects the performance of the system. CV-QKD requires error correction codes of extremely low rates and high reconciliation efficiencies. There are only very few code designs available in this ultra low rate regime. In this paper, we introduce a method for designing protograph-based ultra low rate LDPC codes using differential evolution. By proposing type-based protographs, a new way of representing low rate protograph-based LDPC codes, we drastically reduce the complexity of the protograph optimization, which enables us to quickly design codes over a wide range of rates. We show that the codes resulting from our optimization outperform the codes from the literature both in regards to the threshold and in finite-length performance, validated by Monte-Carlo simulations, showing gains in the regime relevant for CV-QKD.