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International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON)

BCH-based Slepian-Wolf coding with feedback syndrome decoding for quantum key reconciliation

Patcharapong Treeviriyanupab, Paramin Sangwongngam, Keattisak Sripimanwat, O. Sangaroon

Published May 1, 2012• 14 citations
Publisher

Abstract

The quantum key reconciliation is an essential step of QKD protocol. Its main objective is to correct the transmission error after the distribution of quantum objects over a quantum channel, where two legitimate parties use a classical interactive communication for agreeing on their common key. This paper presents an alternative quantum key reconciliation method based on the Slepian-Wolf coding scheme with the chosen optimal set of BCH code rates as close to the Slepian-Wolf bound. In the proposed scheme, the BCH decoder is modified by adding one-bit feedback based on syndrome decoding to detect uncorrectable errors whenever the decoding process fails. The performance evaluation of this proposed scheme can achieve the reconciliation efficiency and reduce the cost of interactive communication via an error-free public channel comparable to the well-known reconciliation protocols. It is then suitable to apply for higher-speed discrete-variable QKD applications.

DOI
10.1109/ecticon.2012.6254266

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The quantum key reconciliation is an essential step of QKD protocol. Its main objective is to correct the transmission error after the distribution of quantum objects over a quantum channel, where two legitimate parties use a classical interactive communication for agreeing on their common key. This paper presents an alternative quantum key reconciliation method based on the Slepian-Wolf coding scheme with the chosen optimal set of BCH code rates as close to the Slepian-Wolf bound. In the proposed scheme, the BCH decoder is modified by adding one-bit feedback based on syndrome decoding to detect uncorrectable errors whenever the decoding process fails. The performance evaluation of this proposed scheme can achieve the reconciliation efficiency and reduce the cost of interactive communication via an error-free public channel comparable to the well-known reconciliation protocols. It is then suitable to apply for higher-speed discrete-variable QKD applications.
Due to imperfection in quantum key distribution (QKD) an uncorrected secret key transmitted via quantum channel exists at the receiver side. This paper presents an alternative method to recover those quantum key by using BCH codes - a class of error control coding (ECC). Application of BCH codes to source coding with side information is described for quantum key reconciliation. Unlikely to many previous protocols, the proposed scheme aims to reduce public communication with acceptable quantum bit error rate and a number of disclosed bits; therefore, it is suitable to applications of high speed QKD.
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.
The purpose of reconciliation, one of classical aspects of quantum key distribution (QKD) protocol, is to mitigate errors after the distribution of quantum information over a quantum channel. In this paper, a rate-adaptive method is proposed by means of a channel coding scheme where specific low-density parity-check (LDPC) codes are adapted in the Slepian-Wolf coding system. Puncturing and shortening techniques are adopted to optimize their coding rates with all possible cases of error in QKD. This successful method utilizes the knowledge of the quantum bit error rate (QBER) based on the maximum-likelihood estimator with respect to the syndrome information. Its benefit is that avoids wasting sample keys in the traditional channel estimation and thus increases the size of the final secret key. Evidently, simulation results confirm an improvement in the reconciliation efficiency with minimal interaction that suitable for high QKD throughput applications.
An effective post-processing algorithm is essential for achieving high rates of secret key generation in quantum key distribution. This work introduces an approach to quantum key distribution post-processing by integrating the three main steps into a unified procedure: syndrome-based error estimation, rate-adaptive reconciliation, and subblock confirmation. The proposed scheme employs low-density parity-check codes to estimate the quantum bit error rate using the syndrome information, and to optimize the channel coding rates based on the Slepian-Wolf coding scheme for the rate-adaptive method. Additionally, this scheme incorporates polynomial-based hash verification in the subblock confirmation process. The numerical results show that the syndrome-based estimation significantly enhances the accuracy and consistency of the estimated quantum bit error rate, enabling effective code rate optimization for rate-adaptive reconciliation. The unified approach, which integrates rate-adaptive reconciliation with syndrome-based estimation and subblock confirmation, exhibits superior efficiency, minimizes practical information leakage, reduces communication rounds, and guarantees convergence to the identical key. Furthermore, the simulations indicate that the secret key throughput of this approach achieves the theoretical limit in the context of a BB84 quantum key distribution system.
A quantum key distribution protocol(QKD), known as BB84, was developed in 1984 by Charles Bennett and Gilles Brassard. The protocol works in two phases which are quantum state transmission and conventional post processing. In the first phase of BB84, raw key elements are distributed between two legitimate users by sending encoded photons through quantum channel whilst in the second phase, a common secret-key is obtained from correlated raw key elements by exchanging messages through a public channel e.g.; network or internet. The secret-key so obtained is used for cryptography purpose. Reconciliation is a compulsory part of post processing and hence of quantum key distribution protocol. The performance of a reconciliation protocol depends on the generation rate of common secret-key, number of bits disclosed and the error probability in common secrete-key. These characteristics of a protocol can be achieved by using a less interactive reconciliation protocol which can handle a higher initial quantum bit error rate (QBER). In this paper, we use a simple Bose, Chaudhuri, Hocquenghem (BCH) error correction algorithm with simplified syndrome table to achieve an efficient reconciliation protocol which can handle a higher quantum bit error rate and outputs a common key with zero error probability. The proposed protocol efficient in removing errors such that it can remove all errors even if QBER is 60%. Assuming the post processing channel is an authenticated binary symmetric channel (BSC).
Quantum key reconciliation is an essential process of quantum key distribution (QKD). It aims to correct the transmission errors after the distribution of quantum objects over a quantum channel, where two legitimate parties use a classical public authenticated channel to disclose correlated bits for agreeing on their common key. This work proposes an alternative promising method employing LDPC-codes bit-flipping decoding to practical implementation of quantum key reconciliation. In our proposed scheme, the low-complexity code bit-flipping decoding based on syndrome decoding is modified and applied to conventional Winnow protocol to achieve both error correcting performance and low complexity of hardware realization, i.e. FPGA logic cells and/or memory. From numerical simulation while the performance of our proposed scheme in terms of final bit error rate (BER) and disclosed bits is superior to conventional Winnow and CASCADE protocols, it yields low complexity in LDPC decoding comparable to the existing LDPC-based reconciliation protocols. Therefore, the technique is promising to high-speed discrete-variable QKD applications.