Quantum key distribution (QKD) enables two authenticated parties to share secret keys with the ability to detect any attempts to eavesdrop the keys theoretically. As a crucial step, information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CV-QKD) systems. To improve the secret key rate in practical CV-QKD systems with time-varying quantum channel, we propose an efficient rate-adaptive multidimensional information reconciliation protocol based on polar codes. Simulation results verify that our proposed rate-adaptive reconciliation protocol can enhance the secret key rate compared to that of the conventional reconciliation protocol.

Rate-adaptive reconciliation with polar coding for continuous-variable quantum key distribution

https://onlinelibrary.wiley.com/doi/pdf/10.1049/cmu2.12083

A blind detection method for spatial modulation in MIMO communications

The use of quaternion orthogonal designs (QODs) to describe point-to-point communication among dual-polarized antennas has the potential to provide higher rate orthogonal and quasi-orthogonal complex designs exploiting polarization diversity among space and time diversities. Furthermore, it is essential to have a space time block code (STBC) which offers a linear and decoupled decoder which quasi-orthogonal designs fail to attain. In this paper, we show how the realm of quaternions unexpectedly offers us a possible solution and codes obtained from quaternion designs mostly achieve both linear and decoupled decoders. This motivated us to perform an indispensable search for QODs such that the code rate is bounded below by 1/2 and does not sharply decrease as the number of transmit antennas increases. It is shown that three famous recursive techniques do not satisfy this criteria and their code rates decrease rather rapidly. Therefore, we propose another method of constructing quaternion designs suitable for any number of transmit antennas and verify that these attain linear and decoupled decoders with the system model based on quaternionic channel. It is shown that such designs outperform others in terms of transmit diversity, code rates and the optimality of the proposed decoder is validated through simulation results.

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Quaternion Codes in MIMO System of Dual-Polarized Antennas

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future. 

Low-Density Parity-Check Codes: Research Status and Development Direction

In this letter, we propose a dual-polarized precoding-aided spatial modulation (DPPSM) scheme, which introduces the polarization dimension into conventional precoding-aided spatial modulation (PSM) to transmit an additional information bit, avoiding the occupation of additional physical space while offering extra transmit diversity. We obtain an upper bound on the average bit error probability (ABEP) of the proposed DPPSM scheme over correlated fading channels. We also derive an approximate upper bound on the ABEP to show the diversity order. Simulation results show that the upper bound is tight for a high signal-to-noise ratio (SNR) range, and the bit error rate (BER) performance of the proposed DPPSM scheme is better than that of the conventional PSM scheme at the same spectral efficiency when equipped with an equal amount of antennas. Furthermore, the proposed DPPSM scheme is more robust to Gaussian channel error when the channel estimation imperfection is considered.

Precoding-Aided Spatial Modulation With Dual-Polarized Antennas Over Correlated Channels

The well-known multidimensional reconciliation is a significant stage of a continuous-variable quantum key distribution (CVQKD) system, which uses $d$-dimensional rotations to build a virtual channel between authenticated parties, Alice and Bob. Generally, a block low-density parity-check code with a belief-propagation (BP) iterative decoding algorithm, which is optimized for an additive white Gaussian noise channel, is always used in multidimensional reconciliation for the CVQKD system. In this paper, we study the signal-to-noise ratio (SNR) of the virtual channel of multidimensional reconciliation in CVQKD and prove that the noise of the virtual channel follows the Student's $t$-distribution. Therefore, we propose a $t$-BP decoding algorithm, which can be better applied to multidimensional reconciliation. Simulation results show that the frame error rate (FER) with the proposed $t$-BP decoding algorithm is superior to that with the conventional BP decoding algorithm applied to multidimensional reconciliation. Subsequently, the FER improvement results in significant influence on reconciliation efficiency and secret key rate of the CVQKD system.

Virtual channel of multidimensional reconciliation in a continuous-variable quantum key distribution

Information reconciliation in the continuousvariable quantum key distribution (CVQKD) plays a vital role on affecting secret key rate as well as maximum transmission distance. It is necessary to search good error-correcting codes in order to improve the performance of reconciliation efficiency. In this work, we construct Quasi-Cyclic (QC) low-density paritycheck (LDPC) codes based on LDPC codes in the digital video broadcasting second generation terrestrial (DVB-T2) standard, and then combine these codes with information reconciliation in the CVQKD system, which can extremely ameliorate the performance of secret key rate and maximum transmission distance. The simulation results show that our proposed QC-LDPC codes can achieve higher reconciliation efficiency of 93.05% compare to DVB-T2 LDPC codes, which means our proposed QC-LDPC codes can obtain better performance of secret key rate and longer maximum transmission distance.

Runhe Qiu

Papers

Precoding-Aided Spatial Modulation With Dual-Polarized Antennas Over Correlated Channels

Virtual channel of multidimensional reconciliation in a continuous-variable quantum key distribution

High Efficiency Continuous-Variable Quantum Key Distribution Based on Quasi-Cyclic LDPC Codes