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Register a new userHigh-throughput GPU layered decoder of multi-edge type low density parity check codes in continuous-variable quantum key distribution systems
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The decoding throughput in the postprocessing is one of the bottlenecks for a continuous-variable quantum key distribution (CV-QKD) system. In this paper, we propose a layered decoder to decode quasi-cyclic multi-edge type LDPC (QC-METLDPC) codes based on graphic processing unit (GPU) in continuous-variable quantum key distribution (CV-QKD) systems. We optimize the storage method of the parity check matrix, merge the sub-matrices which are unrelated, and decode multiple codewords in parallel on GPU. Simulation results demonstrate that the average decoding speed of LDPC codes with three typical code rates, i.e., 0.1, 0.05 and 0.02, is up to 64.11Mbits/s, 48.65Mbits/s and 39.51Mbits/s, respectively, when decoding 128 codewords of length 106 simultaneously without early termination.
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We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Shor-Steane (CSS) construction do not need to satisfy the dual-containing property as long as pre-shared entanglement is available to both sender and receiver. We can use this to avoid the many 4-cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement.
We suggest a new protocol for the information reconciliation stage of quantum key distribution based on polar codes. The suggested approach is based on the blind technique, which is proved to be useful for low-density parity-check (LDPC) codes. We show that the suggested protocol outperforms the blind reconciliation with LDPC codes, especially when there are high fluctuations in quantum bit error rate (QBER).
In this paper we develop instanton method introduced in [1], [2], [3] to analyze quantitatively performance of Low-Density-Parity-Check (LDPC) codes decoded iteratively in the so-called error-floor regime. We discuss statistical properties of the numerical instanton-amoeba scheme focusing on detailed analysis and comparison of two regular LDPC codes: Tanners (155, 64, 20) and Margulis (672, 336, 16) codes. In the regime of moderate values of the signal-to-noise ratio we critically compare results of the instanton-amoeba evaluations against the standard Monte-Carlo calculations of the Frame-Error-Rate.
Reconciliation is a crucial procedure in post-processing of Quantum Key Distribution (QKD), which is used for correcting the error bits in sifted key strings. Although most studies about reconciliation of QKD focus on how to improve the efficiency, throughput optimizations have become the highlight in high-speed QKD systems. Many researchers adpot high cost GPU implementations to improve the throughput. In this paper, an alternative high throughput and efficiency solution implemented in low cost CPU is proposed. The main contribution of the research is the design of a quantized LDPC decoder including improved RCBP-based check node processing and saturation-oriented variable node processing. Experiment results show that the throughput up to 60Mbps is achieved using the bi-directional approach with reconciliation efficiency approaching to 1.1, which is the optimal combination of throughput and efficiency in Discrete-Variable QKD (DV-QKD). Meanwhile, the performance remains stable when Quantum Bit Error Rate (QBER) varies from 1% to 8%.
Quantum LDPC codes are a promising direction for low overhead quantum computing. In this paper, we propose a generalization of the Union-Find decoder as adecoder for quantum LDPC codes. We prove that this decoder corrects all errors with weight up to An^{alpha} for some A, {alpha} > 0 for different classes of quantum LDPC codes such as toric codes and hyperbolic codes in any dimension D geq 3 and quantum expander codes. To prove this result, we introduce a notion of covering radius which measures the spread of an error from its syndrome. We believe this notion could find application beyond the decoding problem. We also perform numerical simulations, which show that our Union-Find decoder outperforms the belief propagation decoder in the low error rate regime in the case of a quantum LDPC code with length 3600.
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