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In this paper, we propose a design rule of rate-compatible punctured multi-edge type low-density parity-check (MET-LDPC) code ensembles with degree-one variable nodes for the information reconciliation (IR) of continuous-variable quantum key distribution (CV-QKD) systems. In addition to the rate compatibility, the design rule effectively resolves the high error-floor issue which has been known as a technical challenge of MET-LDPC codes at low rates. Thus, the proposed design rule allows one to implement rate-compatible MET-LDPC codes with good performances both in the threshold and low-error-rate regions. The rate compatibility and the improved error-rate performances significantly enhance the efficiency of IR for CV-QKD systems. The performance improvements are confirmed by comparing complexities and secret key rates of IR schemes with MET-LDPC codes whose ensembles are optimized with the proposed and existing design rules. In particular, the SNR range of positive secrecy rate increases by 1.44 times, and the maximum secret key rate improves by 2.10 times as compared to the existing design rules. The comparisons clearly show that an IR scheme can achieve drastic performance improvements in terms of both the complexity and secret key rate by employing rate-compatible MET-LDPC codes constructed with code ensembles optimized with the proposed design rule.

Rate-compatible multi-edge type low-density parity-check code ensembles for continuous-variable quantum key distribution systems