@article{milicevic_feng_zhang_gulak_2017, 
  title={Key Reconciliation with Low-Density Parity-Check Codes for Long-Distance
  Quantum Cryptography}, 
  abstractNote={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 (QC) 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 160km with a secret key rate of 4.10x10^-7 bits/pulse for a rate
0.02 multi-edge code with block length of 10^6 bits when finite-size effects
are considered. This work extends the previous maximum CV-QKD distance of 100km
to 160km, while delivering between 1.07x and 8.03x higher decoded information
throughput over the upper bound on the secret key rate for a lossy channel. The
GPU-based QC-LDPC decoder achieves a 1.29x improvement in throughput over the
best existing GPU decoder implementation for a rate 1/10 multi-edge LDPC code
with block length of 2^20 bits. These results show that LDPC decoding is no
longer the computational bottleneck in long-distance CV-QKD.}, 
  author={Milicevic and Feng and Zhang and Gulak}, 
  year={2017}, 
  month={Apr}
  }