1.
Liu, Xin; Xu, Chao; Ng, Soon Xin; Hanzo, Lajos
OTFS-Based CV-QKD Systems for Doubly Selective THz Channels Journal Article
In: IEEE Transactions on Communications, vol. 73, no. 8, pp. 6274–6289, 2025, ISSN: 1558-0857.
Abstract | Links | BibTeX | Tags: Array signal processing, continuous variable quantum key distribution (CV-QKD), Faces, Fading channels, low-density parity check (LDPC), multiple-input multiple-out (MIMO), OFDM, Orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), Parity check codes, Random variables, secret key rate (SKR), Symbols, Terahertz (THz), Terahertz communications, Time-frequency analysis, Vectors
@article{liu_otfs-based_2025,
title = {OTFS-Based CV-QKD Systems for Doubly Selective THz Channels},
author = {Xin Liu and Chao Xu and Soon Xin Ng and Lajos Hanzo},
url = {https://ieeexplore.ieee.org/document/10857395},
doi = {10.1109/TCOMM.2025.3535889},
issn = {1558-0857},
year = {2025},
date = {2025-08-01},
urldate = {2025-10-08},
journal = {IEEE Transactions on Communications},
volume = {73},
number = {8},
pages = {6274–6289},
abstract = {The feasibility of continuous variable quantum key distribution (CV-QKD) is considered in the Terahertz (THz) band, experiencing time-varying and frequency-selective fading. Advanced multi-carrier modulation is required for improving the secret key rate (SKR). However, the hostile quantum channel requires powerful classical channel coding schemes for maintaining an adequate reconciliation performance. Against this background, for the first time in the open literature, we propose a multi-carrier quantum transmission regime that incorporates both orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) transmission over doubly selective fading THz channels. Furthermore, we propose a modified multi-dimensional reconciliation algorithm for CV-QKD, facilitating the integration of OFDM/OTFS quantum transmission with low-density parity check (LDPC) coded key reconciliation. Moreover, we harness multiple-input multiple-output (MIMO) beamforming for mitigating the severe THz path loss. Our SKR analysis results demonstrate that the proposed OTFS-based and LDPC-assisted CV-QKD system is capable of outperforming its OFDM counterpart in mobile wireless scenarios. Moreover, we also demonstrate that increasing the MIMO dimension reduces the transmission power required for achieving the secure transmission distance target.},
keywords = {Array signal processing, continuous variable quantum key distribution (CV-QKD), Faces, Fading channels, low-density parity check (LDPC), multiple-input multiple-out (MIMO), OFDM, Orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), Parity check codes, Random variables, secret key rate (SKR), Symbols, Terahertz (THz), Terahertz communications, Time-frequency analysis, Vectors},
pubstate = {published},
tppubtype = {article}
}
The feasibility of continuous variable quantum key distribution (CV-QKD) is considered in the Terahertz (THz) band, experiencing time-varying and frequency-selective fading. Advanced multi-carrier modulation is required for improving the secret key rate (SKR). However, the hostile quantum channel requires powerful classical channel coding schemes for maintaining an adequate reconciliation performance. Against this background, for the first time in the open literature, we propose a multi-carrier quantum transmission regime that incorporates both orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) transmission over doubly selective fading THz channels. Furthermore, we propose a modified multi-dimensional reconciliation algorithm for CV-QKD, facilitating the integration of OFDM/OTFS quantum transmission with low-density parity check (LDPC) coded key reconciliation. Moreover, we harness multiple-input multiple-output (MIMO) beamforming for mitigating the severe THz path loss. Our SKR analysis results demonstrate that the proposed OTFS-based and LDPC-assisted CV-QKD system is capable of outperforming its OFDM counterpart in mobile wireless scenarios. Moreover, we also demonstrate that increasing the MIMO dimension reduces the transmission power required for achieving the secure transmission distance target.
2.
Wang, Dingzhao; Liu, Xin; Xu, Chao; Ng, Soon Xin; Hanzo, Lajos
Short-Block Polar-Coded Reverse and Direct Reconciliation in CV-QKD Journal Article
In: IEEE Open Journal of Vehicular Technology, vol. 6, pp. 2195–2209, 2025, ISSN: 2644-1330.
Abstract | Links | BibTeX | Tags: Complexity theory, Continuous-variable quantum key distribution (CV-QKD), Fading channels, Maximum likelihood decoding, multidimensional reconciliation, Parity check codes, polar code, Polar codes, Protection, Protocols, Quantum key distribution, secret key rate, Simulation, Wireless networks
@article{wang_short-block_2025,
title = {Short-Block Polar-Coded Reverse and Direct Reconciliation in CV-QKD},
author = {Dingzhao Wang and Xin Liu and Chao Xu and Soon Xin Ng and Lajos Hanzo},
url = {https://ieeexplore.ieee.org/abstract/document/11087626},
doi = {10.1109/OJVT.2025.3591417},
issn = {2644-1330},
year = {2025},
date = {2025-01-01},
urldate = {2025-10-08},
journal = {IEEE Open Journal of Vehicular Technology},
volume = {6},
pages = {2195–2209},
abstract = {Continuous-variable quantum key distribution (CV-QKD) is a promising technique of supporting quantum-safe wireless networks in the emerging 6 G era, mapping quantum information onto the amplitude or phase of electromagnetic waves. However, conventional CV-QKD reconciliation methods often assume ideal classical side-information channels, which is an unrealistic scenario in practical deployments. To address this critical challenge, we propose a novel protection scheme integrating Polar and low-density parity-check (LDPC) codes. Specifically, Polar codes safeguard quantum transmissions due to their superior performance for short block lengths, while LDPC codes robustly protect the classical side information exchanged over auxiliary classical channels. We further enhance the CV-QKD performance by harnessing a soft-decision Polar decoding method combined with protocols specifically tailored for reverse reconciliation (RR) and direct reconciliation (DR). In the RR scheme, conceived decoding complexity is strategically distributed: Polar decoding is performed by Alice, and LDPC decoding by Bob, hence significantly reducing the computational demands compared to traditional schemes where both decoding processes are invoked at a single node. Simulation results validate the effectiveness of our approach, demonstrating that Polar codes consistently outperform LDPC codes in quantum transmission scenarios having short block lengths under 512 bits. These findings emphasize the strong potential of Polar coding-assisted CV-QKD in achieving secure and efficient quantum-safe control information transmissions, paving the way for practical implementation in next-generation wireless networks.},
keywords = {Complexity theory, Continuous-variable quantum key distribution (CV-QKD), Fading channels, Maximum likelihood decoding, multidimensional reconciliation, Parity check codes, polar code, Polar codes, Protection, Protocols, Quantum key distribution, secret key rate, Simulation, Wireless networks},
pubstate = {published},
tppubtype = {article}
}
Continuous-variable quantum key distribution (CV-QKD) is a promising technique of supporting quantum-safe wireless networks in the emerging 6 G era, mapping quantum information onto the amplitude or phase of electromagnetic waves. However, conventional CV-QKD reconciliation methods often assume ideal classical side-information channels, which is an unrealistic scenario in practical deployments. To address this critical challenge, we propose a novel protection scheme integrating Polar and low-density parity-check (LDPC) codes. Specifically, Polar codes safeguard quantum transmissions due to their superior performance for short block lengths, while LDPC codes robustly protect the classical side information exchanged over auxiliary classical channels. We further enhance the CV-QKD performance by harnessing a soft-decision Polar decoding method combined with protocols specifically tailored for reverse reconciliation (RR) and direct reconciliation (DR). In the RR scheme, conceived decoding complexity is strategically distributed: Polar decoding is performed by Alice, and LDPC decoding by Bob, hence significantly reducing the computational demands compared to traditional schemes where both decoding processes are invoked at a single node. Simulation results validate the effectiveness of our approach, demonstrating that Polar codes consistently outperform LDPC codes in quantum transmission scenarios having short block lengths under 512 bits. These findings emphasize the strong potential of Polar coding-assisted CV-QKD in achieving secure and efficient quantum-safe control information transmissions, paving the way for practical implementation in next-generation wireless networks.
3.
Liu, Xin; Xu, Chao; Wang, Stephen; Ng, Soon Xin; Hanzo, Lajos
Hybrid Beamforming Assisted OTFS-Based CV-QKD Systems for Doubly Selective THz Channels Journal Article
In: IEEE Transactions on Communications, pp. 1–1, 2025, ISSN: 1558-0857.
Abstract | Links | BibTeX | Tags: Array signal processing, Channel estimation, continuous variable quantum key distribution (CV-QKD), Decoding, Fading channels, hybrid beamforming (HBF), low-density parity check (LDPC), multiple-input multiple-out (MIMO), OFDM, Orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), Parity check codes, secret key rate (SKR), Terahertz (THz), Terahertz communications, Time-frequency analysis, Vectors, Wireless communication
@article{liu_hybrid_2025,
title = {Hybrid Beamforming Assisted OTFS-Based CV-QKD Systems for Doubly Selective THz Channels},
author = {Xin Liu and Chao Xu and Stephen Wang and Soon Xin Ng and Lajos Hanzo},
url = {https://ieeexplore.ieee.org/document/11069272},
doi = {10.1109/TCOMM.2025.3585501},
issn = {1558-0857},
year = {2025},
date = {2025-01-01},
urldate = {2025-10-08},
journal = {IEEE Transactions on Communications},
pages = {1–1},
abstract = {Continuous-variable quantum key distribution (CV-QKD) maps information onto the quadrature components of electromagnetic waves, so that off-the-shelf wireless transceivers can be utilized. This motivates the move from optical to Terahertz (THz) bands. However, wireless THz channels suffer from severe path loss, while the mobility of wireless users imposes doubly selective fading. Against this background, we propose a new CV-QKD regime that relies on hybrid beamforming (HBF) assisted multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) system, where the channel’s transmissivity and robustness against double selectivity are overcome by HBF and OTFS, respectively. Secondly, in order to provide channel state information (CSI) for both the transmitter (CSI-T) and receiver (CSI-R), practical channel estimation methods are conceived. They operate in the time-frequency domain for OFDM and in the delay-Doppler domain for OTFS. Thirdly, soft-decision detection is devised for our MIMO OFDM/OTFS aided multi-dimensional reconciliation (MDR) scheme. Low-density parity-check (LDPC) coding is invoked for further improving secure CV-QKD transmission distance in the THz band. Our simulation results demonstrate that the proposed HBF MIMO OTFS-based CV-QKD system relying on realistic estimated CSI is capable of achieving an adequate secret key rate (SKR) and secure transmission distance in hostile doubly selective THz channels.},
keywords = {Array signal processing, Channel estimation, continuous variable quantum key distribution (CV-QKD), Decoding, Fading channels, hybrid beamforming (HBF), low-density parity check (LDPC), multiple-input multiple-out (MIMO), OFDM, Orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), Parity check codes, secret key rate (SKR), Terahertz (THz), Terahertz communications, Time-frequency analysis, Vectors, Wireless communication},
pubstate = {published},
tppubtype = {article}
}
Continuous-variable quantum key distribution (CV-QKD) maps information onto the quadrature components of electromagnetic waves, so that off-the-shelf wireless transceivers can be utilized. This motivates the move from optical to Terahertz (THz) bands. However, wireless THz channels suffer from severe path loss, while the mobility of wireless users imposes doubly selective fading. Against this background, we propose a new CV-QKD regime that relies on hybrid beamforming (HBF) assisted multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) system, where the channel’s transmissivity and robustness against double selectivity are overcome by HBF and OTFS, respectively. Secondly, in order to provide channel state information (CSI) for both the transmitter (CSI-T) and receiver (CSI-R), practical channel estimation methods are conceived. They operate in the time-frequency domain for OFDM and in the delay-Doppler domain for OTFS. Thirdly, soft-decision detection is devised for our MIMO OFDM/OTFS aided multi-dimensional reconciliation (MDR) scheme. Low-density parity-check (LDPC) coding is invoked for further improving secure CV-QKD transmission distance in the THz band. Our simulation results demonstrate that the proposed HBF MIMO OTFS-based CV-QKD system relying on realistic estimated CSI is capable of achieving an adequate secret key rate (SKR) and secure transmission distance in hostile doubly selective THz channels.