Three Lower Bounds on Secrecy Capacity for
Indoor Visible Light Communications
Cheng Liu
∗
, Jin-Yuan Wang
†‡§
, Jun-Bo Wang
∗
, Jian-Xia Zhu
∗
, and Ming Chen
∗
∗
National Mobile Communications Research Laboratory, Southeast University, Nanjing 211111, China.
†
Key Laboratory (Research Base) of Signal and Information Processing, Xihua University, Chengdu 610039, China.
‡
Key Lab of Broadband Wireless Communication and Sensor Network Technology, Ministry of Education,
Nanjing University of Posts and Telecommunications, Nanjing 210003, China.
§
Jiangsu Key Laboratory of Traffic and Transportation Security, Huaiyin Institute of Technology, Huaian 223003, China.
E-mail: 220160880@seu.edu.cn, jywang@njupt.edu.cn
Abstract—Recently, the physical-layer security, which exploits
the channel characteristics in order to hide information from
unauthorized receivers and does not reliance on the upper-layer
encryption, has been proposed as a promising complement to the
traditional security schemes. In this paper, the lower bounds on
secrecy capacity for indoor visible light communications (VLC)
are investigated. The noise is assumed to be Gaussian, which
is independent of the input signal. The non-negativity and the
average optical intensity constraint are taken into consideration.
Based on the system model, three lower bounds on secrecy
capacity for VLC are derived, respectively. Numerical results
show that method 2 is better than the other two methods at high
signal-to-noise ratio (SNR) regime, while method 3 is the best
method at low SNR regime.
I. INTRODUCTION
Recently, visible light communication (VLC) employing
white light-emitting diodes (LEDs) has attracted considerable
attention. Due to the combination of communication and
illumination, VLC is regarded as one of the most important
wireless communication technologies for future indoor access
[1].
In the last decade, the point-to-point (P2P) VLC has
achieved rapid development in many aspects, especially in
channel modelling [2], modulation [3], coding [4], equalization
[5], channel estimation [6], channel capacity analysis [7]–
[10], and transceiver design [11]. At present, the research
focus is being changed from the P2P VLC to the VLC net-
works. In VLC networks, data privacy and confidentiality are
becoming a major concern for users. Therefore, information
security in VLC becomes one of the most urgent issues to be
solved. Recently, the physical-layer security, which exploits
the channel characteristics in order to hide information from
unauthorized receivers and does not reliance on the upper-layer
encryption, has been proposed as a promising complement to
the traditional security schemes.
Secure transmission is very important for radio frequen-
cy (RF) wireless communication networks. The information-
theoretic security was firstly investigated by C. E. Shannon
in 1949, who proposed the concept of perfect secrecy over
noiseless channels [12]. Under the noisy channels, A. D. Wyn-
er investigated the secrecy capacity via the wiretap channel
model [13]. In [14], the secrecy capacity of the single-input
single-output Gaussian wiretap channel was derived. Under the
non-degraded wiretap channel, a single-letter characterization
of the secrecy capacity was derived in [15]. For multi-input
multi-output Gaussian wiretap channels, the secrecy capacities
were considered in [16]–[19]. Although much work has been
done to analyze the secrecy capacity for RF wireless communi-
cations, the developed theory and analysis are not directly ap-
plicable to VLC. In other words, VLC has some characteristics
that are different from RF wireless communications. Specif-
ically, the transmitted signal in RF wireless communications
can be bipolar, while the signal in VLC must be non-negative,
since the signal is modulated as the instantaneous optical
intensity. Moreover, the mean square of a signal as the average
power is a resource measure in RF communications, but the
signal mean is important in VLC, since the light intensity
is the signal. Therefore, the aforementioned characteristics
should be considered in practical VLC systems. In [20], the
secrecy capacity was analyzed for amplitude-constrained VLC.
However, average optical intensity constraint and dimming
control are not considered in [20]. Moreover, the corrupting
noise in [20] is assumed to be independent of the input signal.
Due to the random nature of photon emission in the LED,
the noise depends on the signal itself [21]. Motivated by [20]
and [21], the secrecy capacity for VLC should be investigated
systematically.
Based on the information theory, this paper investigates the
lower bounds on secrecy capacity for indoor VLC. In this
paper, the noise is assumed to be Gaussian and is independent
of the input signal. The non-negativity and the average opti-
cal intensity constraint are considered. Based on the system
model, three theoretical methods are employed. According to
the three methods, three lower bounds on secrecy capacity are
derived. Numerical results verify the derived lower bounds on
secrecy capacity.
The reminder of this paper is organized as follows. Section
II describes the system model. Section III derives the secrecy
capacity bounds for three methods. Numerical results are
presented in Section IV. Finally, the conclusions are given in
Section V.
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