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