Key Reconciliation with Low-Density Parity-Check Codes for Long-Distance Quantum Cryptography

Mario Milicevic, Chen Feng, Lei M. Zhang, P. Glenn Gulak
Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada
arXiv:1702.07740 [quant-ph], (24 Feb 2017)


   title={Key Reconciliation with Low-Density Parity-Check Codes for Long-Distance Quantum Cryptography},

   author={Milicevic, Mario and Feng, Chen and Zhang, Lei M. and Gulak, P. Glenn},






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The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms for key reconciliation. Multi-edge low-density parity-check (LDPC) codes with low code rates and long block lengths were proposed for CV-QKD, in order to extend the maximum reconciliation distance between the two remote parties. Key reconciliation over multiple dimensions has been shown to further improve the error-correction performance of multi-edge LDPC codes in CV-QKD, thereby increasing both the secret key rate and distance. However, the computational complexity of LDPC decoding for long block lengths on the order of 10^6 bits remains a challenge. This work introduces a quasi-cyclic code construction for multi-edge LDPC codes that is highly suitable for hardware-accelerated decoding on a modern graphics processing unit (GPU). When combined with an 8-dimensional reconciliation scheme, the LDPC decoder achieves a raw decoding throughput of 1.72Mbit/s and an information throughput of 7.16Kbit/s using an NVIDIA GeForce GTX 1080 GPU, at a maximum distance of 164km with an effective secret key rate of 8.24×10^{-7} bits/pulse for a rate 0.02 multi-edge code with block length of 10^6 bits. For distances beyond 130km, the decoder delivers an information throughput between 2745x and 9138x higher than the maximum secret key rate achievable with a 1MHz light source, thereby showing that LDPC decoding is no longer the computational bottleneck in long-distance CV-QKD.
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