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Open-Source LDPC Error Correction for QKD

Adomas Baliuka, Elsa Dupraz, Rengaraj Govindaraj, Auer, Michael, Peter Freiwang, Lukas Knips, Harald Weinfurter

Published Aug 23, 2021• 2 citations
OpenAlex

Abstract

Error correction is an essential step in the classical post-processing of all quantum key distribution (QKD) protocols. We present error correction methods optimized for discrete variable (DV) QKD and make them freely available as an ongoing open-source project (github.com/XQP-Munich/LDPC4QKD). Our methods are based on irregular quasi-cyclic (QC) low density parity check (LDPC) codes and stateof-the-art rate adaption techniques [1].

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Error correction is an essential step in the classical post-processing of all quantum key distribution (QKD) protocols. We present error correction methods optimized for discrete variable (DV) QKD and make them freely available as an ongoing open-source project (github.com/XQP-Munich/LDPC4QKD). Our methods are based on irregular quasi-cyclic (QC) low density parity check (LDPC) codes and stateof-the-art rate adaption techniques [1].
Although quantum key distribution (QKD) comes from the development of quantum theory, the implementation of a practical QKD system does involve a lot of classical process, such as key reconciliation and privacy amplification, which is called post-processing. Post-processing has been a crucial element to high speed QKD systems, even the bottleneck of it because of its relatively high time consumption. Low density parity check (LDPC) is now becoming a promising approach of overcoming the bottleneck due to its good performance in processing throughput. In this article we propose and simulate an easily implemented but efficiently rate-adaptive LDPC coding approach of reconciliation, different from the previously proposed puncturing- and shortening-based approach. We also give a measure for choosing the optimal LDPC parameter for our rate-adaptive approach according to error rates.
Quantum cryptography provides methods for secret key distribution between the two distant users. An important step in quantum key distribution protocols is the correction of errors that occur during the transmission and implementation of the protocol. Here we consider error estimation and error correction with linear codes such as repetition code, Hamming code, low density parity check (LDPC) code. The paper investigates the increase in the efficiency of error correction using a combination of a repetition code and a LDPC code for a high error probability.
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.
We present the Low Density Parity Check (LDPC) forward error correction algorithm adapted for the Quantum Key Distribution (QKD) protocol in a form readily applied by developers. A sparse parity check matrix is required for the LDPC algorithm and we suggest using some that have been defined by the IEEE and ETSI standards organizations for use in various communication protocols. We evaluate the QKD performance of these various parity check matrices as a function of the quantum bit error rate. We also discuss the computational precision required for this LPDC algorithm. As QKD evolves towards deployment, complete algorithm descriptions and performance analysis, as we present, will be required.
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).
In this paper, the parity-check matrices that can be used in low density parity check (LDPC) based error correction method for quantum key distribution are analyzed. The quantum key distribution system has inevitable errors in sifted key that must be corrected by an error correction algorithm to create a secure key. In this analysis, 1000-bit sifted keys are divided into 50 parts. The algorithm creates 50 syndromes corresponding to each part by multiplying 10 × 20 bit parity-check matrices. The algorithm sends the generated syndrome to the other side, which also divides the sifted key into 50 parts, creates a syndrome from each part, and compares with the received syndrome. If the syndromes are different, these sifted key parts are discarded. However, there may be situations where different parts may have the same syndromes. Therefore, it is necessary to find such an optimal matrix that removes the probability of getting the same syndromes at different parts of the sifted key.