Quantum key distribution (QKD) is a cryptographic communication protocol that utilizes quantum mechanical properties for provable absolute security against an eavesdropper. The communication is carried between two terminals using random photon polarization states represented through quantum states. Both these terminals are interconnected through disjoint quantum and classical channels. Information reconciliation using delay controlled joint decoding is performed at the receiving terminal. Its performance is characterized using data and error rates. Achieving low error rates is particularly challenging for schemes based on error correcting codes with short code lengths. This article addresses the decoding process using ordered statistics decoding for information reconciliation of both short and medium length Bose–Chaudhuri–Hocquenghem codes over a QKD link. The link’s quantum channel is modeled as a binary symmetric quantum depolarization channel, whereas the classical channel is configured with additive white Gaussian noise. Our results demonstrate the achievement of low bit error rates, and reduced decoding complexity when compared to other capacity achieving codes of similar length and configuration.
Quantum key distribution (QKD) is a cryptographic communication protocol that utilizes quantum mechanical properties for provable absolute security against an eavesdropper. The communication is carried between two terminals using random photon polarization states represented through quantum states. Both these terminals are interconnected through disjoint quantum and classical channels. Information reconciliation using delay controlled joint decoding is performed at the receiving terminal. Its performance is characterized using data and error rates. Achieving low error rates is particularly challenging for schemes based on error correcting codes with short code lengths. This article addresses the decoding process using ordered statistics decoding for information reconciliation of both short and medium length Bose–Chaudhuri–Hocquenghem codes over a QKD link. The link’s quantum channel is modeled as a binary symmetric quantum depolarization channel, whereas the classical channel is configured with additive white Gaussian noise. Our results demonstrate the achievement of low bit error rates, and reduced decoding complexity when compared to other capacity achieving codes of similar length and configuration.
Abstract In Quantum Key Distribution (QKD), two users extract a shared secret key using a quantum communication channel in the presence of an eavesdropper. Among QKD protocols, the ones based on Energy-Time (ET) entanglement of photons have been studied extensively due to their ability to generate high key rates from the arrival times of entangled photons. For the information reconciliation (IR) stage of ET-QKD protocols (where the users communicate using a classical channel in order to reconcile differences in their data), a scheme called multi-level coding (MLC) was proposed by Zhou et al. in prior work. The MLC scheme splits the raw key symbols into bit layers and utilizes binary Low-Density Parity-Check (LDPC) codes to encode each layer. Although binary LDPC codes are able to offer low complexity decoding for IR, they have poor error-correcting performance compared to their non-binary counterparts, thus leading to low key rates. Additionally, existing LDPC codes do not fully utilize the properties of the QKD channel to optimize the key rates. In this paper, we mitigate the above issues by proposing a flexible protocol for IR in ET-QKD systems called Non-Binary Multi-Level Coding NB-MLC(a) which is parameterized by a positive integer a. The NB-MLC(a) protocol is a generalization of the MLC scheme and utilizes NB-LDPC codes from a Galois field of size 2^a. We show that by using a small value of a, the NB-MLC(a) protocol significantly improves the key rate without much increase in complexity. To further improve the key rates of the NB-MLC(a) protocol, we propose i) a joint rate and degree distribution optimization (JRDO) algorithm to design the NB-LDPC codes for the protocol; ii) an interleaved decoding and communication (IDC) scheme to decode the different layers of the NB-MLC(a) protocol. The JRDO algorithm is designed to use the QKD channel information and we show that it results in a higher key rate than codes used in prior work. Additionally, the IDC scheme improves the key rate compared to the decoding and communication methods utilized previously in literature. Overall, the NB-MLC(a) protocol that uses JRDO LDPC codes and the IDC scheme results in a significant 40 − 60% improvement in key rates compared to prior work for ET-QKD systems.
This thesis deals with soft-information based information reconciliation and data sifting for Quantum Key Distribution (QKD). A novel composite channel model for QKD is identified, which includes both a hard output quantum channel and a soft output classic channel. The Log-Likelihood Ratios, - also called soft-metrics - derived from the two channels are jointly processed at the receiver, exploiting capacity achieving soft-metric based iteratively decoded block codes. The performance of the proposed mixed-soft-metric algorithms are studied via simulations as a function of the system parameters. The core ideas of the thesis are employing Forward Error Correction (FEC) coding as opposed to two-way communication for information reconciliation in QKD schemes, exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement, and providing a security versus secret-key rate trade-off to the end-user within the context of QKD systems.
This paper deals with the use of sparse-graph codes (and in particular, Low density Parity Check - LDPC - codes) for information reconciliation and pre-data sifting in Quantum Key Distribution (QKD). We model the overall channel used in QKD as the parallel of the quantum channel, where the actual quantum key is transmitted, and a public Additive White Gaussian Noise (AWGN) channel, where the parity check bits are transmitted. The metrics derived from the two channels are jointly processed at the receiver by properly combining the metrics derived from the two channels and exploiting capacity achieving soft-metric based iteratively decoded sparse-graph codes. The information derived from the iterative decoder are used to (1) perform error correction of the received q-bits; (2) detect the possible presence of unauthorized eavesdroppers; (3) perform pre-data sifting. The performance of the proposed mixed-soft-metric algorithms are studied via simulations as a function of the system parameters. The core ideas of the paper are: a) employing FEC coding as opposed to two-way communication for information reconciliation, minimizing the interactions between transmitter and receiver; b) exploiting all the available information for data processing at the receiver including information available from the quantum channel; c) using convergence properties of the code to estimate QBER and presence of an eavesdropper.
We establish conditions and give proofs on how an error-correcting code can attain infinite diversity in a time-entanglement quantum key distribution (TE-QKD) reconciliation. The shocking result, never encountered in the literature on coding and communication theory, is that a decoder exhibits an infinite diversity order while the channel has finite diversity and the code has a relatively short finite length.
This paper studies the diversity order of coded TE-QKD reconciliation, defined by the asymptotic slope of the error probability at high signal-to-noise ratio. For bounded-distance algebraic decoding, we derive a necessary and sufficient condition in terms of the number of photons per codeword and the decoding radius.
For soft-decision decoding, we introduce the maximal finite diversity (MFD) property and prove that infinite diversity is achieved if and only if the code is MFD deficient. The infinite diversity in TE-QKD has no counterpart in classical fading channels, where decoding can only multiply a finite diversity order by a finite factor.
Examples of short codes based on Golay, Reed-Solomon, Bose-Chaudhuri-Hocquenghem (BCH), and Reed-Muller codes validate the analysis and illustrate how the TE-QKD system parameters and the relatively short code parameters affect the achievable diversity for both hard and soft information reconciliation.
This paper investigates the potential improvements that may be obtained in terms of the secret key transmission rate in a Quantum Key Distribution (QKD) scheme whereby photon-counting detectors are used at the receiver. To take full advantage of such detectors, soft information is generated in the form of Log-Likelihood Ratios (LLRs) using a Bayesian estimator of phase of the signal pulse which is used to carry the information. The technique is general in a sense that any optical communication scheme whereby the received mean photon count is relatively small, but not necessarily below one and uses the polarization state of light to transmit the binary data may benefit from the soft information processing proposed, although in this paper, we have focused on the QKD application. We demonstrate using simulations the significant reduction in the residual Bit Error Rate (BER) and Frame Error Rate (FER) that is achievable using the proposed soft information processing scheme for a given Quantum BER (QBER) on the quantum link, after the information reconciliation process using LDPC Forward Error Correction (FEC) coding.
The focus of this research activity is to work on pragmatic information reconciliation applied to QKD schemes based on single photon or weak pulse laser (WPL) sources, so as to use feed-forward techniques which minimize the interaction between transmitter and receiver. The core ideas of the thesis are employing Forward Error Correction (FEC) coding as opposed to two-way communication for information reconciliation in QKD schemes, exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement, and providing a security versus secret-key rate trade-off to the end-user within the context of QKD systems. Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate -QBER may have a high value), both because of the inherent characteristics of the system, and of the presence of a possible attacker. In order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit. Furthermore, since the more redundancy is added by the channel code, the more the corresponding information can be used to decipher the private message itself, it becomes necessary to design high-rate codes obtained by puncturing a low-rate mother code, possibly achieving a redundancy such that elements of the secret message cannot be uniquely determined from the redundancy itself, so for that purpose we designed high rate LDPC codes. Using high rate codes increases the security with trade-off to performance. Other low photon number applications have also been considered, such as weak-laser pulses (WLP) communication. For that purpose, a low-complexity photon-counting receiver has been considered which may be employed in long-distance amplification-free classical optical communication schemes, and which is typically modeled as an equivalent Binary Symmetric Channel (BSC). We have developed a time varying Binary Input-Multiple Output (BIMO) channel model for this low-complexity photon-counting receiver, and analyzed its performance in presence of soft-metric based capacity approaching iteratively decoded error correcting codes, such as soft-metric based Low Density Parity Check (LDPC) codes and polar codes. We show that the classical channel capacity of the suggested BIMO model is higher than the capacity of the BSC model, and that the use of the BIMO model allows to feed the channel decoder with soft information, in the form of Log-Likelihood Ratios (LLRs), achieving a significant reduction in Bit Error Rate (BER) and Frame Error Rate (FER) with respect to classical hard-metric-based schemes which should be used in conjunction with a BSC channel model.