Repeat-accumulate codes for reconciliation in continuous variable quantum key distribution

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise (BI-AWGN) channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approxiamtions. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.

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“…We have also compared rate 1/10 and 1/50 MET-LDPC codes designed in [21] and several RA codes in [19] in Fig. 6.…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

Raptor Codes in the Low SNR Regime

Shirvanimoghaddam

Johnson

2016

IEEE Trans. Commun.

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“…Rate efficiency versus the SNR for a Raptor code with the optimized degree distribution and different message lengths, when D = 300. The code length for RA codes [5] is 64800 and the code length for MET-LDPC is . program (5) to find the optimal degree distribution, which has been shown to achieve efficiencies larger than 92% at those SNRs [9].…”

Section: Rate Efficiency Resultsmentioning

confidence: 99%

“…The code length for RA codes [5] is 64800 and the code length for MET-LDPC is . program (5) to find the optimal degree distribution, which has been shown to achieve efficiencies larger than 92% at those SNRs [9]. The rate efficiencies for these codes have been also shown in Fig.…”

Section: Rate Efficiency Resultsmentioning

confidence: 99%

“…For the maximum value of µ i , i.e., µo, we also have µo ≤ 2αSNR. Now suppose that SNR > µo/2α, then it is clear that ω(x) = 1 satisfies all constraints in (5), thus the optimization is feasible. In an asymptotic case, when the maximum degree is very large, α is potentially infinite, thus the optimization problem is feasible for SNR > limα→∞ µo/2α = 0.…”

Section: A Degree Distribution Optimizationmentioning

confidence: 99%

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Design of Raptor codes in the low SNR regime with applications in quantum key distribution

Shirvanimoghaddam

Johnson

Lance

2016

2016 IEEE International Conference on Communications (ICC)

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Abstract-The focus of this work is on the design of Raptor codes for continuous variable Quantum key distribution (CV-QKD) systems. We design a highly efficient Raptor code for very low signal to noise ratios (SNRs), which enables CV-QKD systems to operate over long distances with a significantly higher secret key rate compared to conventional fixed rate codes. The degree distribution design of Raptor codes in the low SNR regime is formulated as a linear program, where a set of optimized degree distributions are also obtained through linear programming. Simulation results show that the designed code achieves efficiencies higher than 94% for SNRs as low as -20 dB and -30 dB. We further propose a new error reconciliation protocol for CV-QKD systems by using Raptor codes and show that it can achieve higher secret key rates over long distances compared to existing protocols.

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“…Other error-correcting codes have also been studied for the low-SNR regime of CV-QKD, including polar codes, repeataccumulate codes, and Raptor codes. 31,68,69 However, at the time of writing, there are no hardware implementations of such codes for long-distance CV-QKD beyond 100 km. In addition to extending information theoretic security to general attacks for finite key sizes, 30,70-72 a major remaining hurdle to extending the distance in CV-QKD is reducing excess noise in the optical channel.…”

Section: Discussionmentioning

confidence: 99%

Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography

et al. 2018

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The speed at which two remote parties can exchange secret keys in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of key reconciliation. Multi-dimensional reconciliation using multi-edge lowdensity parity-check (LDPC) codes with low code rates and long block lengths has been shown to improve error-correction performance and extend the maximum reconciliation distance. We introduce a quasi-cyclic code construction for multi-edge codes that is highly suitable for hardware-accelerated decoding on a graphics processing unit (GPU). When combined with an 8dimensional reconciliation scheme, our LDPC decoder achieves an information throughput of 7.16 Kbit/s on a single NVIDIA GeForce GTX 1080 GPU, at a maximum distance of 142 km with a secret key rate of 6.64 × 10 −8 bits/pulse for a rate 0.02 code with block length of 10 6 bits. The LDPC codes presented in this work can be used to extend the previous maximum CV-QKD distance of 100 km to 142 km, while delivering up to 3.50× higher information throughput over the tight upper bound on secret key rate for a lossy channel.

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Repeat-accumulate codes for reconciliation in continuous variable quantum key distribution

Cited by 14 publications

References 21 publications

Raptor Codes in the Low SNR Regime

Raptor Codes in the Low SNR Regime

Design of Raptor codes in the low SNR regime with applications in quantum key distribution

Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography

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