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International Conference Education and Creativity for a Knowledge-based Society – Informatics

INFORMATION RECONCILIATION IN QKD: A COMPARATIVE ANALYSIS OF CASCADE, LDPC AND POLAR CODES

Liliana Zisu, Ciprian Răcuciu

Published Jun 11, 2026• 0 citations
Publisher

Abstract

Quantum Key Distribution (QKD) provides unconditional security, but requires a robust information reconciliation step to eliminate errors introduced by the quantum channel. The efficiency of this step directly determines the net secret key generation rate. The paper presents a detailed comparative analysis of three major reconciliation techniques: CASCADE, LDPC (Low-Density Parity-Check), and Polar Codes. The analysis focuses on seven essential metrics, including reconciliation efficiency (f), maximum error tolerance (QBERmax,), final secure key rate (R), frame error rate (FER), and computational complexity. Simulations are performed on a realistic QKD channel model (BB84 with depolarization), with QBER varying between 0.1% and 16%, covering experimental conditions. Keywords: QKD, Information Reconciliation, LDPC, CASCADE, Polar Codes, Secret Key Rate

DOI
10.66793/titui19proceeding10

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Quantum Key Distribution (QKD) provides unconditional security, but requires a robust information reconciliation step to eliminate errors introduced by the quantum channel. The efficiency of this step directly determines the net secret key generation rate. The paper presents a detailed comparative analysis of three major reconciliation techniques: CASCADE, LDPC (Low-Density Parity-Check), and Polar Codes. The analysis focuses on seven essential metrics, including reconciliation efficiency (f), maximum error tolerance (QBERmax,), final secure key rate (R), frame error rate (FER), and computational complexity. Simulations are performed on a realistic QKD channel model (BB84 with depolarization), with QBER varying between 0.1% and 16%, covering experimental conditions. Keywords: QKD, Information Reconciliation, LDPC, CASCADE, Polar Codes, Secret Key Rate
With the rapid improvement of quantum computing technology, quantum key distribution(QKD) is a hot technology. Information reconciliation is a key step of QKD which is useful for correcting key error. Classical message interaction is necessary in a practical information reconciliation scheme, which makes the efficiency of these protocols decreased. Therefore, some one-way information reconciliation schemes based on low-density parity-check(LDPC) codes and polar codes are proposed. Here we propose a concatenated method of IR schemes which can achieve any given error rate level without the need of interactions. Compared with the one-way IR schems based on LDPC codes and polar codes, the IR schemes based on the proposed concatenated method can get lower bit error rates after error correction, which can also reduce the communication delay and system complexity of QKD, improve the final key generation rate and enhance the practicability of QKD system.
Quantum Key Distribution (QKD) is a revolutionary security technology that exploits the laws of quantum mechanics to achieve information-theoretic secure key exchange. QKD enables two parties to “grow” a shared secret key without placing any limits on an adversary’s computational power. Error reconciliation protocols have been developed that preserve security while allowing a sender and receiver to reconcile the errors in their respective keys. The most famous of these is the Cascade protocol, which is effective but suffers from a high communication complexity and low throughput. The Winnow protocol reduces the communication complexity over Cascade, but has the disadvantage of introducing errors. Finally, Low Density Parity Check (LDPC) codes have been shown to reconcile errors at rates higher than those of Cascade and Winnow, but with greater computational complexity. In this paper we evaluate the effectiveness of LDPC codes by comparing the runtime, throughput and communication complexity empirically with the Cascade and Winnow algorithms. The effects of inaccurate error estimation, non-uniform error distribution and varying key length on all three protocols are evaluated for identical input key strings. Analyses are performed on the results in order to characterize the strengths and weaknesses of each protocol.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string —the key— known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals —the raw key— must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of theQKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secretkey agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
CASCADE protocol is an error detection and correction (EDC) method proposed firstly for use in quantum key distribution (QKD) systems. It is used to detect and correct all the errors in keys transmitted over a noisy quantum channel. This is done by sending some redundant information about the key to receiver as usual. However, just as differently, this extra information is sent over another noiseless classical channel after the quantum transmission is completely finished. Briefly, all the errors in noisy quantum communication are detected and corrected by a later noiseless classical communication using CASCADE protocol. In QKD literature, this EDC process is also called as information reconciliation (IR) or secret key reconciliation (SKR). For an IR protocol in QKD, one of the main performance measures is efficiency which depends on the amount of redundant information sent to make EDC possible. Since this extra information is transmitted over public channels, everyone can get it easily. Because this can damage the secrecy of keys that must be kept secret from third parties, more efficient, that is revealing less information about keys, IR methods are needed. In this paper, we present more efficient implementations of CASCADE protocol, using some inherent information already available in the protocol, exactly known bits and already known parities. This information is used in error detection and correction steps of the protocol to decrease the redundancy in redundant information. Our experiments have shown that the resulting protocols have higher efficiency than both all the previous CASCADE versions and several other more recently proposed IR methods.
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.