Design of Raptor Codes in the Low SNR Regime with Applications in Quantum Key Distribution

TL;DR

This paper presents the design of highly efficient Raptor codes tailored for low SNR regimes in quantum key distribution, enabling longer-distance secure communication with higher secret key rates.

Contribution

It introduces a linear programming approach to optimize Raptor code degree distributions specifically for very low SNRs in CV-QKD systems, and proposes a new error reconciliation protocol.

Findings

Achieves over 94% efficiency at -20 dB and -30 dB SNRs.

Enables longer-distance CV-QKD with higher secret key rates.

Proposes a novel error reconciliation protocol for improved performance.

Abstract

The focus of this work is on the design of Raptor codes for continuous variable Quantum key distribution (CV-QKD) systems. We design a highly efficient Raptor code for very low signal to noise ratios (SNRs), which enables CV-QKD systems to operate over long distances with a significantly higher secret key rate compared to conventional fixed rate codes. The degree distribution design of Raptor codes in the low SNR regime is formulated as a linear program, where a set of optimized degree distributions are also obtained through linear programming. Simulation results show that the designed code achieves efficiencies higher than 94\% for SNRs as low as -20 dB and -30 dB. We further propose a new error reconciliation protocol for CV-QKD systems by using Raptor codes and show that it can achieve higher secret key rates over long distances compared to existing protocols.