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A NOMA-based Quantum Key Distribution System
over Poisson Atmospheric Channels
Xiaojun Yu
∗
, Xiaolin Zhou
∗
, Chongbin Xu
∗
, Lingda Wang
†
, Dailin Shen
∗
and Haitao Zhou
∗
∗
The Key Laboratory for Information Science of Electromagnetic Waves,
School of Information Science and Technology, Fudan University, Shanghai, China 200433
†
Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, 61801, USA
Email: zhouxiaolin@fudan.edu.cn
Abstract—Quantum wireless communications (QWC) is gain-
ing much attention for its incomparable advantages of secure
key transmission in free-space scenarios. In this paper, a novel
iterative multi-user quantum key distribution (MQKD) non-
orthogonal multiple-access (NOMA) system over Poisson at-
mospheric channels is proposed. Considering the atmospheric
attenuation and quantum direct product operation, a MQKD
parallel interference cancellation (PIC) approach is designed at
the receiver. In particular, a quantum nonlinear Poisson shot
noise limited sum-product interference cancellation algorithm is
derived. Simulation results show that the proposed scheme is
capable of mitigating the multi-user interference effectively, even
considering the polarization mismatch. Quantitatively, for the 4-
user scenario, it can achieve the classical Bit Error Rate (BER) of
3 × 10
−6
at 2.5 km distance with polarization mismatch factor
of 0.05. Moreover, the proposed NOMA-MQKD scheme can have
obviously higher secure key rate than the conventional WDMA-
MQKD approach[9].
I. INTRODUCTION
Quantum cryptography allows two legal parties, namely
Alice and Bob, to achieve the information-theoretic security
over public channels. Among those, wireless quantum key
distribution (QKD) has become a research hotspot recently
for building future highly secure free-space communication
networks [1]–[4].
Owning to extremely sensitive to environmental impacts,
such as atmospheric attenuation, background noise, the imple-
mentation of wireless QKD faces many challenges. In [5], a
wavelength division multiplexing (WDM) and orthogonal an-
gular momentum (OAM) based multiple-input-multiple-output
(MIMO) QKD system is studied for achieving the high-speed
secure key transmission over atmospheric turbulent channels.
In [6], a network-coded cooperative QKD system is conceived
over Free Space Optical (FSO) channels, in which network
coding is adopted for improving the key exchange in multiple-
user QKD systems. In [7], a subcarrier intensity modulated
(SIM) QKD scheme with dual-threshold/direct detection (D-
T/DD) receiver is designed. It proves that QKD protocol can
be implemented in the standard pulse-based optical signal
systems.
Another key requirement of QKD networks is expansion
from point-to-point to multiple-access QKD communications
[8]–[10]. In [8], Time / Code Division Multiple Access
(TDMA/CDMA) approaches are considered in the star-coupler
quantum networks, where multiple QKD users can exchange
Quantum
Transmitter
Telescope
Atmospheric
Attenuation
Channels
Telescope
Quantum
Receiver
Multiuser
NOMA
Detection
Bob
Alices
þ1ÿ
BS
þ0ÿ
þͰÿ
basis
BS
þ1ÿ
þ0ÿ
þĴÿ
basis
BS
þ1ÿ
BS
þ0ÿ
þͰÿ
basis
BS
þ1ÿ
þ0ÿ
þĴÿ
basis
BS
)(&
)(&
þ1ÿ
BS
þ1ÿ
BS
þ
0ÿ
þ0ÿ
PBS
þ1ÿ
BS
þ1ÿ
BS
þ
0ÿ
þ0ÿ
PBS
Interleaving
Process
Multiuser
Free
Space
Channel
Bob
(a)
Alice k-1 Alice k Alice k+1
ĂĂ
Interleaving
Process
Repetition
Coding
ISVN SSCN MAN TSVN
(b)
Fig. 1. The schematic of the proposed NOMA-MQKD QKD system. (a) the
illustration of the system over atmospheric noise channels, (b) the factor graph
of NOMA transmitter (ISVN: Information Sequence Variable Node, SSCN:
Spread Spectrum Constraint Node, MAN: Multiple Accessing Node, TSVN:
Transmitted Sequence Variable Node)
secret keys simultaneously. In [9], a Wavelength Division
Multiplexing Access QKD system (WDMA-QKD) is designed
and analyzed. Compared to a point-to-point link, this proposal
can have a higher secure key rate for per user. In [10], an
Orthogonal Frequency Division Multiplexing QKD (OFDM-