Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Quantum Engineering

Rateless Protograph LDPC Codes for Quantum Key Distribution

Alberto Tarable, Rudi Paolo Paganelli, Marco Ferrari

Published Jan 1, 2024• 13 citations
Publisher

Abstract

Information Reconciliation (IR) is a key step in Quantum key distribution (QKD). In recent years, blind reconciliation based on low-density parity-check (LDPC) codes has replaced Cascade as a standardde facto, since it guarantees efficient information reconciliation without a priori quantum bit error rate estimation and with limited interactivity between the parties, which is essential in high key-rate and long distance QKD links. In this paper, a novel blind reconciliation scheme based on rateless protograph LDPC codes is proposed. The rate adaptivity, essential for blind reconciliation, is obtained by progressively splitting LDPC check nodes, which ensures a number of degrees of freedom larger than puncturing in code design. The protograph nature of the LDPC codes allows to use the same designed codes with a large variety of sifted-key lengths, enabling a blocklength flexibility, which is important in largely varying key-rate link conditions. The code design is based on a new protograph Discretized Density Evolution tool.

DOI
10.1109/tqe.2024.3361810

Related papers

Flexible Blind Information Reconciliation for QKD based on Rateless Protograph LDPC codes

Marco Ferrari, Alberto Tarable, Rudi Paolo Paganelli

Information Reconciliation (IR) is a crucial step in the process of distillation of unconditionally secure keys in Quantum key distribution (QKD). Novel IR rateless codes based on protograph low-density parity-check (LDPC) codes have been recently designed to replace Cascade. In this paper, a blind IR protocol is described that exploits all the features of rateless protograph LDPC codes.

International Conference on Transparent Optical Networks•Jul 14, 2024•1 citation

Blind Reconciliation with Protograph LDPC Code Extension for FSO-Based Satellite QKD Systems

Cuong T. Nguyen, Hoang D. Le, Vuong V. Mai +2 more

A significant breakthrough in space-based quantum key distribution (QKD) inaugurated by the Micius satellite has brought us closer to the era of global QKD networks. An essential step in the post-processing QKD is key reconciliation (KR), which eliminates the mismatch in the raw keys between two legitimate users. However, the fluctuation in the quantum bit-error rate (QBER) caused by the free-space optical (FSO) turbulence channels poses various challenges for the KR design. This paper addresses the design of blind KR schemes for FSO-based low Earth orbit (LEO) satellite QKD systems, which allow operating without a prior QBER estimation. Specifically, we present a novel blind KR scheme with a protograph low-density parity check (LDPC) code extension. The proposed LDPC structure is constructed by gradually extending and exhaustively searching among all possible solutions. The proposed design is evaluated in terms of the final key rate performance over the QKD systems using a dual-threshold/direct detection (DT/DD) scheme. Simulation results confirm the effectiveness of our proposed design compared to the state-of-the-art design in different turbulence channel conditions.

International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)•Jul 17, 2024•3 citations

Blind reconciliation

Jesús Martínez-Mateo, David Elkouss, Vicente Martín

Information reconciliation is a crucial procedure in the classical post-processing of quantum key distribution (QKD). Poor reconciliation efficiency, revealing more information than strictly needed, may compromise the maximum attainable distance, while poor performance of the algorithm limits the practical throughput in a QKD device. Historically, reconciliation has been mainly done using close to minimal information disclosure but heavily interactive procedures, like \textit{Cascade}, or using less efficient but also less interactive ---just one message is exchanged--- procedures, like the ones based in low-density parity-check (LDPC) codes. The price to pay in the LDPC case is that good efficiency is only attained for very long codes and in a very narrow range centered around the quantum bit error rate (QBER) that the code was designed to reconcile, thus forcing to have several codes if a broad range of QBER needs to be catered for. Real world implementations of these methods are thus very demanding, either on computational or communication resources or both, to the extent that the last generation of GHz clocked QKD systems are finding a bottleneck in the classical part. In order to produce compact, high performance and reliable QKD systems it would be highly desirable to remove these problems. Here we analyse the use of short-length LDPC codes in the information reconciliation context using a low interactivity, \textit{blind}, protocol that avoids an a priori error rate estimation. We demonstrate that $2 \times 10^3$ bits length LDPC codes are suitable for blind reconciliation. Such codes are of high interest in practice, since they can be used for hardware implementations with very high throughput.

arXiv:1205.5729•Quantum Information and Computation•Sep 1, 2012•46 citations

Efficient Rate-Adaptive Reconciliation Based on LDPC Accumulate Codes for Quantum Key Distribution

Tharathorn Phromsa‐ard, Patcharapong Treeviriyanupab, Paramin Sangwongngam +4 more

In this paper, a rate-adaptive method is proposed an alternative reconciliation protocol by employing the LDPC-accumulate codes to the practical implementation in the quantum key distribution (QKD). The proposed rate-adaptive reconciliation is adapted in the Slepian-Wolf scheme where specific low-density parity-check (LDPC) codes are constructed by accumulated syndrome encoding/decoding. Its objective is to skip the step of quantum bit error rate (QBER) estimation by the traditional key sampling that increases the final secret key length in practice. From the numerical results, the proposed method achieves a good performance in terms of the number of disclosed bits and reconciliation efficiency comparable to the conventional Winnow, Cascade, and fixed-rate compatible LDPC based protocols. Moreover, it can cover the possible cases of error rates in the QKD system. Therefore, method is suitable for the highspeed discrete-variable QKD applications.

International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC)•Jun 1, 2015•0 citations

Information reconciliation for QKD with rate-compatible non-binary LDPC codes

Kenta Kasai, Ryutaroh Matsumoto, Kohichi Sakaniwa

We study the information reconciliation (IR) scheme for quantum key distribution (QKD) protocols. The IR for the QKD can be seen as the asymmetric Slepian-Wolf problem, which low-density parity-check (LDPC) codes can solve with efficient algorithms, i.e., the belief propagation. However, the LDPC codes are needed to be chosen properly from a collection of codes optimized for multiple key rates, which leads to complex decoder devices and performance degradation for unoptimized key rates. Therefore, it is desired that establish an IR scheme with a single LDPC code which supports multiple rates. To this end, in this paper, we propose an IR scheme with a rate-compatible non-binary LDPC code. Numerical results show the proposed scheme achieves IR efficiency comparable to the best know conventional IR scheme with lower decoding error rates.

International Symposium on Information Theory and its Applications•Oct 1, 2010•24 citations

Key Reconciliation with RC-LDPC/Error Estimation for Satellite-based FSO/QKD Systems

Cuong T. Nguyen, Hoang D. Le, Anshul Jaiswal +2 more

Satellite-based free-space optics (FSO) quantum key distribution (QKD) systems have recently attracted significant research interest due to their potential to enable globally secured applications. However, the inherent uncertainty of FSO channels, caused by weather conditions and satellite mobility, induces severe fluctuations in quantum bit-error rate (QBER) between legitimate users. This makes designing an efficient key reconciliation, an essential step in the QKD post-processing, particularly challenging. In this work, we propose a key reconciliation scheme that combines protograph rate-compatible (RC) low-density parity-check (LDPC) codes with a syndrome-based error estimation method. The proposed error estimation method reduces the number of communication rounds without requiring additional information disclosure. Furthermore, to our best knowledge, an analytical framework is first developed to evaluate end-to-end secret-key throughput (SKT), accounting for the impact of imperfect error estimation and dynamic FSO channel conditions. Numerical results demonstrate that the proposed scheme consistently outperforms conventional blind reconciliation under diverse FSO channel conditions and provide practical guidelines for system parameter selection. Finally, we validate the proposed framework through a case study that incorporates data from a Starlink low-Earth orbit (LEO) satellite and moving ground vehicles.

arXiv:2609.25646•IEEE Transactions on Vehicular Technology•Jan 1, 2026•0 citations
Information Reconciliation (IR) is a key step in Quantum key distribution (QKD). In recent years, blind reconciliation based on low-density parity-check (LDPC) codes has replaced Cascade as a standardde facto, since it guarantees efficient information reconciliation without a priori quantum bit error rate estimation and with limited interactivity between the parties, which is essential in high key-rate and long distance QKD links. In this paper, a novel blind reconciliation scheme based on rateless protograph LDPC codes is proposed. The rate adaptivity, essential for blind reconciliation, is obtained by progressively splitting LDPC check nodes, which ensures a number of degrees of freedom larger than puncturing in code design. The protograph nature of the LDPC codes allows to use the same designed codes with a large variety of sifted-key lengths, enabling a blocklength flexibility, which is important in largely varying key-rate link conditions. The code design is based on a new protograph Discretized Density Evolution tool.
A significant breakthrough in space-based quantum key distribution (QKD) inaugurated by the Micius satellite has brought us closer to the era of global QKD networks. An essential step in the post-processing QKD is key reconciliation (KR), which eliminates the mismatch in the raw keys between two legitimate users. However, the fluctuation in the quantum bit-error rate (QBER) caused by the free-space optical (FSO) turbulence channels poses various challenges for the KR design. This paper addresses the design of blind KR schemes for FSO-based low Earth orbit (LEO) satellite QKD systems, which allow operating without a prior QBER estimation. Specifically, we present a novel blind KR scheme with a protograph low-density parity check (LDPC) code extension. The proposed LDPC structure is constructed by gradually extending and exhaustively searching among all possible solutions. The proposed design is evaluated in terms of the final key rate performance over the QKD systems using a dual-threshold/direct detection (DT/DD) scheme. Simulation results confirm the effectiveness of our proposed design compared to the state-of-the-art design in different turbulence channel conditions.
Information reconciliation is a crucial procedure in the classical post-processing of quantum key distribution (QKD). Poor reconciliation efficiency, revealing more information than strictly needed, may compromise the maximum attainable distance, while poor performance of the algorithm limits the practical throughput in a QKD device. Historically, reconciliation has been mainly done using close to minimal information disclosure but heavily interactive procedures, like \textit{Cascade}, or using less efficient but also less interactive ---just one message is exchanged--- procedures, like the ones based in low-density parity-check (LDPC) codes. The price to pay in the LDPC case is that good efficiency is only attained for very long codes and in a very narrow range centered around the quantum bit error rate (QBER) that the code was designed to reconcile, thus forcing to have several codes if a broad range of QBER needs to be catered for. Real world implementations of these methods are thus very demanding, either on computational or communication resources or both, to the extent that the last generation of GHz clocked QKD systems are finding a bottleneck in the classical part. In order to produce compact, high performance and reliable QKD systems it would be highly desirable to remove these problems. Here we analyse the use of short-length LDPC codes in the information reconciliation context using a low interactivity, \textit{blind}, protocol that avoids an a priori error rate estimation. We demonstrate that 2×1032 \times 10^32×103 bits length LDPC codes are suitable for blind reconciliation. Such codes are of high interest in practice, since they can be used for hardware implementations with very high throughput.
In this paper, a rate-adaptive method is proposed an alternative reconciliation protocol by employing the LDPC-accumulate codes to the practical implementation in the quantum key distribution (QKD). The proposed rate-adaptive reconciliation is adapted in the Slepian-Wolf scheme where specific low-density parity-check (LDPC) codes are constructed by accumulated syndrome encoding/decoding. Its objective is to skip the step of quantum bit error rate (QBER) estimation by the traditional key sampling that increases the final secret key length in practice. From the numerical results, the proposed method achieves a good performance in terms of the number of disclosed bits and reconciliation efficiency comparable to the conventional Winnow, Cascade, and fixed-rate compatible LDPC based protocols. Moreover, it can cover the possible cases of error rates in the QKD system. Therefore, method is suitable for the highspeed discrete-variable QKD applications.
We study the information reconciliation (IR) scheme for quantum key distribution (QKD) protocols. The IR for the QKD can be seen as the asymmetric Slepian-Wolf problem, which low-density parity-check (LDPC) codes can solve with efficient algorithms, i.e., the belief propagation. However, the LDPC codes are needed to be chosen properly from a collection of codes optimized for multiple key rates, which leads to complex decoder devices and performance degradation for unoptimized key rates. Therefore, it is desired that establish an IR scheme with a single LDPC code which supports multiple rates. To this end, in this paper, we propose an IR scheme with a rate-compatible non-binary LDPC code. Numerical results show the proposed scheme achieves IR efficiency comparable to the best know conventional IR scheme with lower decoding error rates.
Satellite-based free-space optics (FSO) quantum key distribution (QKD) systems have recently attracted significant research interest due to their potential to enable globally secured applications. However, the inherent uncertainty of FSO channels, caused by weather conditions and satellite mobility, induces severe fluctuations in quantum bit-error rate (QBER) between legitimate users. This makes designing an efficient key reconciliation, an essential step in the QKD post-processing, particularly challenging. In this work, we propose a key reconciliation scheme that combines protograph rate-compatible (RC) low-density parity-check (LDPC) codes with a syndrome-based error estimation method. The proposed error estimation method reduces the number of communication rounds without requiring additional information disclosure. Furthermore, to our best knowledge, an analytical framework is first developed to evaluate end-to-end secret-key throughput (SKT), accounting for the impact of imperfect error estimation and dynamic FSO channel conditions. Numerical results demonstrate that the proposed scheme consistently outperforms conventional blind reconciliation under diverse FSO channel conditions and provide practical guidelines for system parameter selection. Finally, we validate the proposed framework through a case study that incorporates data from a Starlink low-Earth orbit (LEO) satellite and moving ground vehicles.