Efficiently Encodable Multi-Edge Type LDPC Codes for Long-Distance Quantum Cryptography

Reconciliation is a key procedure in quantum cryptography to share the same secret key between two remote parties. For long-distance quantum cryptography, the reconciliation is often realized with multi-edge type low-density parity-check (MET-LDPC) codes due to unique advantages of MET-LDPC codes, e.g. a suitable structure for decoder implementation and capacity-approaching performances especially at very low rates. However, to make the realization practically viable, the encoding complexity of MET-LDPC codes must also be properly addressed, which unfortunately has been well touched. This work proposes a simple but efficient MET-LDPC code structure which allows a linear-time encoding complexity of MET-LDPC codes without compromising their error-correcting performances.