A Novel Lattice-Capable Error Correction Framework for Quantum Communication and QKD Integration

This technical report proposes a unified error correction and reconciliation framework designed specifically for improving the secure key rate of Quantum Key Distribution (QKD) protocols, particularly in Continuous-Variable (CV-QKD) systems. Problem Addressed: Existing QKD reconciliation methods rely on standard binary codes, which fail to leverage the inherent geometry of the lattice channels used in CV-QKD. This leads to reduced efficiency, especially when the signal quality is low (low SNR). Key Innovations: Lattice-Native Coding: The design employs Low-Density Parity-Check (LDPC) codes defined natively over integer rings (Z-sub-q), allowing direct alignment with the geometric structure of the quantum channel. Geometry-Preserving Interleaving: A novel, low-discrepancy interleaver is introduced to optimize error spreading while maintaining local geometric structure during encoding and decoding. Leak-Aware Reconciliation Ledger: A dynamic ledger is used to precisely track all information leakage (syndrome sum) during the error correction process. This tracked leakage directly sets the length for Privacy Amplification, ensuring rigorous and composable finite-key security bounds.