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arXiv:1204.5882 · Quantum Information and Computation

High performance error correction for quantum key distribution using polar codes

Paul Jouguet, Sébastien Kunz-Jacques

Published Mar 1, 2014• 102 citations
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Abstract

We study the use of polar codes for both discrete and continuous variables Quantum Key Distribution (QKD). Although very large blocks must be used to obtain the efficiency required by quantum key distribution, and especially continuous variables quantum key distribution, their implementation on generic x86 Central Processing Units (CPUs) is practical. Thanks to recursive decoding, they exhibit excellent decoding speed, much higher than large, irregular Low Density Parity Check (LDPC) codes implemented on similar hardware, and competitive with implementations of the same codes on high-end Graphic Processing Units (GPUs).

DOI
10.26421/qic14.3-4-8

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We study the use of polar codes for both discrete and continuous variables Quantum Key Distribution (QKD). Although very large blocks must be used to obtain the efficiency required by quantum key distribution, and especially continuous variables quantum key distribution, their implementation on generic x86 Central Processing Units (CPUs) is practical. Thanks to recursive decoding, they exhibit excellent decoding speed, much higher than large, irregular Low Density Parity Check (LDPC) codes implemented on similar hardware, and competitive with implementations of the same codes on high-end Graphic Processing Units (GPUs).
Abstract Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 10 6 . Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.
Quantum key distribution (QKD) is a cryptographic system that generates an information-theoretically secure key shared by two legitimate parties. QKD consists of two parts: quantum and classical. The latter is referred to as classical post-processing (CPP). Information reconciliation is a part of CPP in which parties are given correlated variables and attempt to eliminate the discrepancies between them while disclosing a minimum amount of information. The elegant reconciliation protocol known as \emph{Cascade} was developed specifically for QKD in 1992 and has become the de-facto standard for all QKD implementations. However, the protocol is highly interactive. Thus, other protocols based on linear block codes such as Hamming codes, low-density parity-check (LDPC) codes, and polar codes have been researched. In particular, reconciliation using LDPC codes has been mainly studied because of its outstanding performance. Nevertheless, with small block size, the bit error rate performance of polar codes under successive-cancellation list (SCL) decoding with a cyclic redundancy check (CRC) is comparable to state-of-the-art turbo and LDPC codes. In this study, we demonstrate the use of polar codes to improve the performance of information reconciliation in a QKD system with small block size. The best decoder for polar codes, a CRC-aided SCL decoder, requires CRC-precoded messages. However, messages that are sifted keys in QKD are obtained arbitrarily as a result of a characteristic of the QKD protocol and cannot be CRC-precoded. We propose a method that allows arbitrarily obtained sifted keys to be CRC precoded by introducing a virtual string. Thus the best decoder can be used for reconciliation using polar codes and improves the efficiency of the protocol.
Quantum key distribution (QKD) leverages the principles of quantum mechanics to generate unconditionally secure keys for remote communication, even in the presence of an eavesdropper with unlimited computational power. A critical component of QKD is information reconciliation (IR), which corrects bit errors introduced by system imperfections and channel noise, ensuring the integrity of the shared key. Polar codes-based IR schemes have attracted considerable attention due to their near-Shannon-limit performance and low computational complexity. However, existing implementations primarily rely on CPUs or GPUs, which are suboptimal in terms of performance and energy efficiency. Here, we present a hardware accelerator designed specifically for discrete variable QKD (DV-QKD), targeting polar codes-based IR and implemented on a cost-effective FPGA platform. Our design achieves high throughput and scalability by employing a module-level pipeline parallel structure, a fully parallelized decoding strategy, and a hybrid memory architecture. This approach enhances decoder efficiency and optimizes resource utilization. On this platform, we demonstrate an IR throughput of 35.33 Mbps for a block size of [Formula: see text], providing a real-time, cost-efficient solution that significantly enhances the performance of QKD systems.
Abstract Error correction is a significant step in postprocessing of continuous-variable quantum key distribution system, which is used to make two distant legitimate parties share identical corrected keys. We propose an experiment demonstration of high speed error correction with multi-edge type low-density parity check (MET-LDPC) codes based on graphic processing unit (GPU). GPU supports to calculate the messages of MET-LDPC codes simultaneously and decode multiple codewords in parallel. We optimize the memory structure of parity check matrix and the belief propagation decoding algorithm to reduce computational complexity. Our results show that GPU-based decoding algorithm greatly improves the error correction speed. For the three typical code rate, i.e., 0.1, 0.05 and 0.02, when the block length is 10 6 and the iteration number are 100, 150 and 200, the average error correction speed can be respectively achieved to 30.39 Mbits/s (over three times faster than previous demonstrations), 21.23 Mbits/s and 16.41 Mbits/s with 64 codewords decoding in parallel, which supports high-speed real-time continuous-variable quantum key distribution system.
Low Density Parity Check (LDPC) error correction is a one-way algorithm that has become popular for quantum key distribution (QKD) post-processing. Graphic processing units (GPUs) provide an interesting attached platform that may deliver high rates of error correction performance for QKD. We present the details of our various LDPC GPU implementations and both error correction and execution throughput performance that each achieves. We also discuss the potential for implementation on a GPU platform to achieve Gbit/s throughput.