Soft-Decoding Reverse Reconciliation in Discrete-Modulation CV-QKD
For CV-QKD systems using discrete modulation, this work provides a practical method to improve secret key rates by leveraging soft information at Bob's side without leaking additional information to an eavesdropper.
The paper introduces a soft-decoding reverse reconciliation technique for discrete-modulation CV-QKD that achieves a secret key rate closely approaching the upper bound, with significant gain over hard-decision reverse reconciliation.
In continuous-variable quantum key distribution, information reconciliation is required to extract a shared secret key from correlated random variables obtained through the quantum channel. Reverse reconciliation (RR) is generally preferred, since the eavesdropper has less information about Bob's measurements than about Alice's transmitted symbols. When discrete modulation formats are employed, however, soft information is available only at Bob's side, while Alice has access only to hard information (her transmitted sequence). This forces her to rely on hard-decision decoding to recover Bob's key. In this work, we introduce a novel RR technique for PAM (and QAM) in which Bob discloses a carefully designed soft metric to help Alice recover Bob's key, while leaking no additional information about the key to an eavesdropper. We assess the performance of the proposed technique in terms of achievable secret key rate (SKR) and its bounds, showing that the achievable SKR closely approaches the upper bound, with a significant gain over hard-decision RR. Finally, we implement the scheme at the coded level using binary LDPC codes with belief-propagation decoding, assess its bit-error rate through numerical simulations, compare the observed gain with theoretical predictions from the achievable SKR, and discuss the residual gap.