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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 38, NO. 20, OCTOBER 15, 2020 5733
Dimming-Aware Deep Learning Approach for
OOK-Based Visible Light Communication
Cong Zou, Student Member, IEEE, and Fang Yang , Senior Member, IEEE
Abstract—Visible light communication (VLC) is a secure, low-
cost, and high-rate communication method. On-off keying (OOK)
is one of the modulation schemes of VLC, turning each light either
on or off to generate binary signals. Recently, deep learning (DL)
technologies have made a series of breakthroughs for dimming
in VLC system. This task is actually quite challenging for DL,
since the VLC system needs to be able to support various dim-
ming targets on account of the different preferences from users in
practical applications, resulting in an optimization problem with
multiple constraints. This article presents a DL framework for
the dimming-aware binary VLC system, which can meet arbitrary
dimming requirements by a universal neural network, named uni-
versal auto-encoder (UAE). The proposed UAE creatively utilizes
a multi-branch architecture with several carefully designed con-
catenated patches, and a novel multi-stage training strategy for
the optimization problem with multiple dimming constraints. The
experiments indicate that the proposed DL approach outperforms
existing techniques in terms of the average bit error rate, the
satisfaction of the dimming constraints, and the robustness for
imperfect optical channels.
Index Terms—Constant weight code, constrained optimization,
deep learning, on-off keying, visible light communication.
I. INTRODUCTION
VISIBLE light communication (VLC) [1]–[3], using light-
emitting diodes (LEDs) to transmit information, becomes
an emerging and promising optical wireless communication
(OWC) technology. Compared with radio frequency (RF) com-
munication, VLC has a number of strengths, such as high-
speed transmission, low cost, no electromagnetic interference,
enhanced security, etc., which result in widespread concern and
research.
In VLC, the message is conveyed via high-rate temporal
changes in light intensity of LEDs, so that intensity modulation
and direct detection (IM/DD) is the critical technique. The
Manuscript received March 20, 2020; revised May 29, 2020; accepted June
22, 2020. Date of publication June 24, 2020; date of current version October
15, 2020. This work was supported in part by the National Natural Science
Foundation of China under Grant 61871255, in part by the Natural Science
Foundation of Guangdong Province under Grant 2015A030312006, in part by
the National Key Research and Development Program of China under Grant
2017YFE0113300, and in part by the Fok Ying-Tung Education Foundation
(Corresponding author: Fang Yang.)
Cong Zou and Fang Yang are with the Department of Electronic Engineering
Beijing National Research Center for Information Science and Technology,
Tsinghua University, Beijing 100084, China, and also with the Key Laboratory
of Digital TV System of Guangdong Province and Shenzhen City, Research
Institute of Tsinghua University in Shenzhen, Shenzhen 518057, China (e-mail:
zouc19@mails.tsinghua.edu.cn; fangyang@tsinghua.edu.cn).
Color versions of one or more of the figures in this article are available online
at https://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2020.3004664
modulation schemes [4], [5] include on-off keying (OOK) [6]–
[9], pulse position modulation (PPM) [10], [11], pulse width
modulation (PWM) [12] and orthogonal frequency division mul-
tiplexing (OFDM) [13], [14], and this paper will pay attention to
the OOK-based VLC systems generating binary messages. At
the same time, the LEDs also serve as lighting sources, giving
rise to intensity constraint problem because of the illumination
requirements from users and LED property. Thus, for the OOK-
based VLC systems, the key issue is the constant weight codes
(CWCs) designing problem.
However, the optimal design of CWCs [15], [16] only fo-
cused on the mathematical properties like minimum Hamming
distance, instead of the system performance like bit error rate
(BER), which is still a challenging task. Furthermore, the im-
perfections of the optical channel [17] in the practical imple-
mentation, such as the inter-symbol interference (ISI) problem,
the thermal noise and the signal-dependent shot noise, also
raise much difficulties for these coding techniques. To deal
with this issue, recently, a number of deep learning (DL) based
methods have made a series of breakthroughs for the VLC
system design [18]–[21]. In [18] and [19], an auto-encoder
(AE) and a convolutional AE are employed to learn a set of
CWCs, respectively. However, the trained neural network can
only satisfy a specific dimming intensity. In [20], though the
universal support of arbitrary dimming targets is achieved, it can
only learn a set of semi-CWC [22], which means the dimming
intensity is controlled by the average Hamming weight over a
codebook, resulting in an unstable dimming intensity. Therefore,
the goal of this paper is to explore a dimming-aware CWC-based
VLC system using a novel DL framework.
In this paper, an AE with multiple branches aiming to meet
different dimming intensities, named universal auto-encoder
(UAE), is creatively proposed. As the difference among the AE
with different dimming constraints in [18] is only the regular-
ization term, it is not necessary to retrain another network for a
different dimming target, which is quite time-consuming. Hence,
in the proposed UAE, a certain part of the structure is shared in
various branches. This idea is similar to hard parameter sharing
in multi-task learning (MLT) [23], which shares the hidden lay-
ers among all tasks, while keeping several task-specific output
layers. But in the proposed UAE, the output layers are shared,
while the hidden layers are dimming-specific. By this means, the
risk of overfitting as well as the Rademacher complexity can be
reduced, which is crucial for VLC system with imperfect chan-
nels. Furthermore, there are two performance improvements can
be made based on UAE. Firstly, too many branches still lead to
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5734 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 38, NO. 20, OCTOBER 15, 2020
considerable computational complexity. Therefore, a specially
designed binary patch is concatenated to the codeword, so that
the weight of the spliced codeword can be adjusted by changing
the number of ones in the patch. In this way, a few branches
are sufficient to meet arbitrary dimming requirements, which
significantly reduces the computational complexity. Secondly,
since there are multiple dimming constraints in UAE, it is
unpractical to preset an appropriate penalty parameter for each
constraint artificially. Hence, to avoid the process of selecting
hyper-parameters, we propose a multi-stage training strategy,
which jointly optimizes the network parameters and the penalty
parameters via a single stochastic gradient descent (SGD) up-
date, making the proposed UAE more feasible and adaptive.
In summary, the contributions of this paper are as fol-
lows. Firstly, the DL framework is utilized to avoid the time-
consuming search process of optimizing the binary CWC code-
words in conventional VLC systems, and to improve system
robustness against the imperfect channels. Secondly, we propose
an innovative universal AE with several branches, where for each
branch, the other branches act as regularizer. Thus, the risk of
overfitting and the ability to fit the noise are reduced, resulting in
better BER performance over the channels with thermal noise,
shot noise and ISI problem. Thirdly, the multi-branch structure
with concatenated patches makes the proposed UAE able to
meet arbitrary dimming requirements with a single training
process, which reduces computational complexity and improves
practicability. Finally, a novel multi-stage training strategy is
investigated for optimization problem with multiple constraints,
which enhances the satisfaction of the dimming targets.
The rest of the paper is organized as follows. Section II
contains a brief review of OOK-based VLC system. The network
architecture of the proposed UAE, the corresponding training
strategy and practical application are investigated in Section III.
Section IV contains the implementation details and the experi-
mental results. Finally, Section V includes the conclusion of the
paper.
Notations: Throughout this paper, boldface lowercase letters
(e.g., a) denote vectors, boldface capital letters (e.g., A) denote
matrices, and boldface Euler script letters (e.g., A) denote sets.
[a]krepresents the k-th element of vector a,[A]ij represents
the (i, j)-th element of matrix A. Besides, |A|represents the
number of elements in set A.
II. SYSTEM MODEL
The OOK-based VLC system is mainly concerned with
transmitting Mdifferent messages bi∈M={b1,...,b
M}in
the form of OOK optical pulses emitted by LEDs, which can
be symbolized as binary codewords s∈Sof dimension N,
where Srepresents the code-book. To reflect the imperfec-
tions of the optical channel in the practical implementation,
the signal is added with thermal noise nth ∈RN∼N(0,σ
2)
and signal-dependent shot noise nsh ∈RN∼N(0,sψ2σ2),
where ψ2stands for the shot noise variance scaling factor.
Thus, the received signal ydetected by a photo-detector (PD) is
given by
y=Hs +nth +nsh,(1)
Fig. 1. The ISI problem from signal reflection.
where H∈RN×Nstands for an optical communication channel
matrix. When H=IN, the channel is an additive noise channel.
However, in practical indoor VLC environment, the reflection
of wall will lead to ISI problem, as shown in Fig. 1 [24]. In this
way, the received signal is
y(t)=h(1)(t)⊗x(t)+h(2) (t)⊗x(t−τd)+nth(t)+nsh (t),
(2)
where h(1)(t)and h(2) (t)are the corresponding impulse re-
sponses for LED and reflection on the wall. τdis time delay
calculated as τd=(d1+d2−d)/c, and cis the speed of light.
Thus, the optical communication channel matrix His expressed
as
[H]ij =⎧
⎨
⎩
1+γ(1 −Δ),for j=i
γΔ,for j=i−1
0,else
(3)
where γ=h(2)/h(1) =d4/(d1+d2)4,Δ=τd/T , and Tis the
bit time interval.
To meet the illumination requirements, the number of ones
in the binary codewords s, i.e., the Hamming weight, should be
equal to the required dimming intensity I∈0,1,...,N, that is
N
i=1
[s]i=I, for s∈S,(4)
and the code-book Sis called CWC.
III. THE PROPOSED UNIVERSAL AUTOENCODER
The structure of the proposed dimming-aware neural network,
UAE, is introduced in this section. While training, the proposed
UAE is constructed with an encoding network, a binarization
operation, a dimming constraint operation, a patch concatenation
operation, an optical channel and a decoding network, as shown
in Fig. 2, which will be discussed in detail in the following.
A. Encoding and Decoding Network
The input data of the encoding network is the one-hot repre-
sentation xof message bi∈M, which sets the value of the i-th
element of a M-dimensional zero vector to one. The encoding
network consists of two fully connected (FC) layers: The first
hidden layer has input size of M(Mis the number of different
messages) and output size of N(Nis the dimension of the binary
codeword s), with the rectified linear unit (ReLU) applied as
the activation function. To make UAE able to satisfy various
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ZOU AND YANG: DIMMING-AWARE DEEP LEARNING APPROACH FOR OOK-BASED VISIBLE LIGHT COMMUNICATION 5735
Fig. 2. The whole structure of the proposed UAE while training.
dimming constraints, the second hidden layer is divided into B
branches, each of which is trained to meet a specific dimming
target, and is provided with input size of N, output size of N.
Thus, the output of the encoding network can be expressed as
h2[k]=W2[k]×ReLU(W1x+b1)+b2[k],k=1,...,B.
(5)
The input data of the decoding network is the received sig-
nal y[k]as (1). The decoding network is almost symmetrical
to the encoding network, which also consists of two FC layers:
The third hidden layer is divided into Bbranches, each of which
has its own parameters {W3[k],b3[k]}(k=1,...,B)with the
ReLU function applied as the activation function, and is provided
with input size of N, output size of M. The fourth hidden layer
has input size of Mand output size of N, with the softmax
function applied as the activation function. Thus, the output of
the decoding network can be expressed as
h4[k]=softmax W4×ReLU W3[k]+b3[k]+b4,(6)
and each element of h4[k], denoted as [h4[k]]j, stands for the
probability that the input message bbelongs to the j-th one.
Hence, according to the maximum likelihood theorem, the re-
constructed message is obtained as
ˆ
b[k]=arg max
1≤j≤M[h4[k]]j,k=1,...,B. (7)
By optimizing the network parameters Θ={Wl,bl|l=
1,...,4}, our goal is to minimize the cost function, i.e.,
min
ΘC(Θ)= 1
K
B
k=1
log [h4[k]]bi,(8)
which is the cross entropy between the probability distribution
vector h4[k]and the input message bi. The parameters Θcan be
optimized by SGD algorithm step by step as follows
Θt=Θt−1−η∇ΘCΘt−1,(9)
where Θtrepresents the value of Θat the t-th step, ηdenotes
the learning rate and the gradient ∇C(Θ)is obtained by the back
propagation algorithm [25].
In this way, training only one network, instead of training
different networks for different dimming constraints like
[18], [19], can meet multiple dimming needs at the same
time. Thus, to meet Bdifferent dimming intensities, the
computational complexity of the encoding network is
reduced from O(BMN +BN2)to O(MN +BN2), and
the same is true for decoding network. Besides, the first
and the last hidden layer are shared among all branches,
that decreases the number of network parameters to be
trained from {Wl[k],bl[k]|l=1,...,4,k=1,...,B}to
{W1,b1,W2[k],b2[k],W3[k],b3[k],W4,b4|k=1,...,B}.
Further, for any of these branches, the other branches act as
regularizer, that reduces the risk of overfitting and the ability to
fit the additive noise from the imperfect channels.
B. Binarization
To implement OOK modulation, the binarization operation
needs to convert the output of the encoding network h2[k](k=
1,...,B), which is continuous in nature, to binary code e[k].
The most direct way is to apply the unit step function on h2[k].
However, since the unit step function is unsmooth and the
gradient is zero for all nonzero [h2[k]]j(j=1,...,N), which
further leads to the gradient of cost function with respect to the
parameters of encoding network diminishing to zero. According
to (9), these parameters cannot be optimized, which gives rise
to the vanishing gradient issue [26].
To tackle this problem, this paper implements a multi-stage
training strategy for binarization [27], which gradually anneals
a soft binarization procedure to a hard one. Since it is known
that the scaled sigmoid function with a scaling parameter β,
sigmoid(βz)= 1
1+e−βz ,β>0,(10)
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5736 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 38, NO. 20, OCTOBER 15, 2020
Algorithm 1: The Binarization Algorithm.
Input:Θ[0] and β[i],i=1,...,P;
1: for g=1to Pdo
2: Initialize Θ0=Θ[g−1];
3: Set β=β[g];
4: Set t=1;
5: repeat
6: Θt=Θt−1−η∇ΘC(Θt−1);
7: t=t+1;
8: until the converged parameters Θ[g]are obtained;
9: end for
is smooth and as the value of βincreases, the scaled sigmoid
function will become more unsmooth and closer to the unit step
function. Thus, we can replace the unit step function with the
scaled sigmoid function, i.e., [e[k]]j=sigmoid(β[h2[k]]j), and
employ a multi-stage training strategy for binarization to obtain
binary outputs.
As the sigmoid function is a common and effective activa-
tion function which can be successfully trained, the scaling
parameter βis initialized as β[0] = 1, then, for the following
stages, βis increased such that β[0] <β[1] <··· <β[P].At
each stage g, the parameters of the proposed UAE is initialized
with the converged parameters Θ[g−1] obtained at the previous
stage g−1, and the proposed UAE at stage gis trained until
convergence with β=β[g]. After that, the converged param-
eters Θ[g]of stage gwill be used as initialization in the next
stage, and the overall binarization algorithm is illustrated in
Algorithm 1. Thus, with the previous pre-training as base-
ment, the parameters just need to be fine-tuned at each stage,
which makes the binarization operation easier to converge and
equipped with better performance. When βis large enough, this
binarization operation can generate exactly binary codes just as
the unit step function does.
C. Dimming Constraint
To satisfy the dimming constraints, the unconstrained opti-
mization problem in (8) is converted to the one with multiple
constraints, i.e.,
min
ΘC(Θ)
s.t. Hk(Θ)=Ik,k=1,2,...,B,
(11)
where Hk(Θ)=N
i=1[d[k]]i, and Ik(k=1,2,...,B)are B
various dimming constraints in Fig. 2. Since DL approaches
are only effective for unconstrained optimization problem, a
popular way to remove these constraints is adding regularization
terms Rk=Hk(Θ)−Ik(k=1,2,...,B)behind the original
cost function as
min
ΘC(Θ)+
B
k=1
λkR2
k,(12)
Algorithm 2: The Proposed Constrained Training Algo-
rithm.
Input:Θ[0] and λ[0];
1: for g=1to pdo
2: Initialize Θ0=Θ[g−1];
3: Set t=1;
4: repeat
5: Θt=Θt−1−η(∇ΘC(Θt−1)+B
k=1 2λk[g−
1] ×(Hk(Θt−1)−Ik)∇ΘHk(Θt−1));
6: t=t+1;
7: until the converged parameters Θ[g]are obtained;
8: Initialize λ0=λ[g−1];
9: Set t=1;
10: repeat
11: λt=[λt−1
1,...,λt−1
B]T+η[(H1(Θ[g]) −I1)2,··· ,
(HB(Θ[g]) −IB)2]T;
12: t=t+1;
13: until the converged parameters λ[g]are obtained;
14: end for
where λ=[λ1,...,λB]Tare positive hyper parameters, con-
trolling the weigh between the cost function and the regular-
ization terms. On the one hand, if λis too large, the output
reconstructed message will be quite likely to differ from the input
message b, leading to high BER. On the other hand, if λis too
small, the dimming targets cannot be achieved. The determina-
tion of the value of λis usually relied on a trial-and-error based
searching process, which has shown a satisfying performance
for DL with a single constraint like [18], [19]. However, with
multiple constraints, the proposed UAE using trial-and-error is
extremely time-consuming and troublesome. Thus, instead of
presetting the value of λby hand, we improve the constrained
training algorithm in [28], which will be discussed in detailed
next.
The Lagrange duality method [29] is an effective way to
achieve our goal. The Lagrange function is just the cost function
with regularization terms as (12), which is given by
L(Θ,λ)=C(Θ)+
B
k=1
λkR2
k,(13)
Then, the dual function is represented as
G(λ)=min
ΘL(Θ,λ),(14)
and the dual problem is given by
max
λG(λ)
s.t. λk≥0,k=1,...,B.
(15)
Based on the weak duality, the Lagrange function and the dual
function can be iteratively optimized to gradually approximate
the optimal solution. Whereas instead of updating Θand λonly
once in each iteration as [28], which is not easy to converge,
we also propose a multi-stage training strategy for dimming
constraint in this section. At each stage g, the network param-
eters and penalty parameters are initialized as Θ0=Θ[g−1]
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ZOU AND YANG: DIMMING-AWARE DEEP LEARNING APPROACH FOR OOK-BASED VISIBLE LIGHT COMMUNICATION 5737
Fig. 3. The operation of the patch concatenation layer.
and λ0=λ[g−1], respectively, where Θ[g−1] and λ[g−1]
are the converged parameters obtained at the previous stage g−
1. The Lagrange function is optimized firstly, where the network
parameters Θare updated by SGD algorithm step by step until
getting Θ[g]as follows
Θt=Θt−1−η∂ΘL(Θt−1,λ[g−1])
=Θt−1−η∇ΘC(Θt−1)+
B
k=1
2λk[g−1]
×Hk(Θt−1)−Ik∇ΘHk(Θt−1)
.(16)
Then, the dual function is optimized based on Θ[g], where the
penalty parameters λare also updated by SGD algorithm till
getting λ[g]as
λt=λt−1+η∂λG(λ)
=⎡
⎣
λt−1
1
···
λt−1
B
⎤
⎦+η⎡
⎣
(H1(Θ[g]) −I1)2
···
(HB(Θ[g]) −IB)2⎤
⎦.(17)
After that, the converged parameters Θ[g]and λ[g]of stage g
will be used as initialization in the next stage, and the overall
constrained training algorithm is illustrated in Algorithm 2.
This algorithm makes the penalty parameters λ, which need
to be preset in [18], [19], also become trainable and adjustable.
In this way, the time-consuming trial-and-error based searching
process can be avoided, and the penalty parameters are automat-
ically adjusted according to the change of the tradeoff between
cost function and regularization terms during the training pro-
cess, bringing about more outstanding performance that will be
shown in the experimental results.
D. Patch Concatenation
After dimming constraint, a binary patch of length Lis con-
catenated to the codeword d[i]as Fig. 3, so that the Hamming
weight of the spliced codeword can be adjusted by changing
the number of ones in the patch, in other words, the dimming
intensity Iis adjustable, where I∈{0,1,...,N +L}.It’s
worth noting that, the length of the patch should be carefully
determined, because if Lis too large, the length of the spliced
codeword will become too long to cause excessive pressure on
the channel capacity. Conversely, if Lis too small, the adjustable
range of dimming intensities will become pretty limited, so that
the goal of dimming-aware VLC system cannot be achieved.
Thus, an appropriate value of Lneed to be settled, which is the
Algorithm 3: The Overall Training Algorithm.
Input: Θ[0],λ[0] and β[i],i=1,...,P;
1: for g=1to Pdo
2: Set β=β[g];
3: Initialize Θ0=Θ[g−1];
4: Set t=1;
5: repeat
6: Sample a mini-batch set Tm⊂T;
7: Θt=Θt−1−η(∇ΘC(Θt−1)+B
k=1 2λk[g−
1] ×(Hk(Θt−1)−Ik)∇ΘHk(Θt−1));
8: t=t+1;
9: until the converged parameters Θ[g]is obtained;
10: Initialize λ0=λ[g−1];
11: Set t=1;
12: repeat
13: Sample a mini-batch set Tm⊂T;
14: λt=[λt−1
1,...,λt−1
B]T+η[(H1(Θ[g]) −I1)2,··· ,
(HB(Θ[g]) −IB)2]T;
15: t=t+1;
16: until the converged parameters λ[g]is obtained;
17: end for
minimum value that can be achieved when most of the range of
dimming intensities can be covered.
For the k-th branch, suppose the dimming target is Ik, and
through changing the number of ones in the patch, the set of
the achievable dimming intensities is Ik={I∈N|Ik≤I≤
Ik+L}, where Nis the natural number set. In order to get as
many dimming intensities as possible, the maximum value of the
elements in set Ikshould not be less than the minimum value
of the elements in set Ik+1, then the optimization problem with
regard to Lis
min L
s.t. Ik+L≥Ik+1,k=1,...,B, (18)
and it is obvious that
min L=max{Ik+1 −Ik,k=1,...,B−1}.(19)
Then, if Ik+1 −Ik=L,|IkIk+1|=1. While if Ik+1 −Ik<
L,|IkIk+1|>1, which will result in a waste of resources. To
avoid this issue, we define that
Ik+1 −Ik=L, ∀k=1,...,B, (20)
and it can be obtained that Ik=I1+(k−1)L.
To meet all of the dimming requirements, the following equa-
tions need to be satisfied
I1=0
IB+L=N+L⇒L=N
B−1.(21)
As the number of binary length-Nsequences of Hamming
weight Iis N
I, to get more CWCs, the dimming requirement is
generally not less than 0.1 Nand not larger than 0.9 N. Hence,
to further optimize the value of Land relieve the pressure of the
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5738 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 38, NO. 20, OCTOBER 15, 2020
optical channel, eqn.(21) is improved as
⎧
⎪
⎨
⎪
⎩
I1=1
10(N+L)
IB+L=9
10(N+L)
⇒L=N
5
4B−1,(22)
from which it can be noticed that Lis negatively correlated
with the number of branches B. Therefore, Bshould also be
carefully designed, as a large Bwill lead to quite considerable
computational complexity and network storage space, while a
small Bwill bring about a long patch. In the experiments, we
find that when B=4,Lis just N/B, which is more concise,
and the results prove that it achieves a good tradeoff.
E. The Overall Training Strategy
The overall training strategy is summarized in this section,
with the training set constructed as T={b(1),...,b(Nt)},
where b(j)∈Mis the randomly generated message and Nt
is the number of training data. We apply the mini-batch SGD
algorithm, which is a stochastic optimization tool to reduce
memory space via randomly sampling a mini-batch set Tm⊂T
of size Jat each training epoch. Then, the objection function to
be minimized, which is just the improved Lagrange function in
(13), is defined as
L(Θ,λ)= 1
J
J
j=1
B
k=1 log [h4[k]]b(j)
+λkN
i=1 db(j)
[k]i−Ik2,
(23)
where db(j)
[k]is the binary code of the k-th branch and input b(j).
The first term of (23) is the cost function C(Θ)as (8), and the
second term is the regularization terms Rk(k=1,...,B).
Next, as mentioned in Section III-B and III-C, there are two
multi-stage training strategies in our proposed UAE, one for
binarization and one for dimming constraint. In the overall
training strategy we proposed, these two multi-stage methods
are merged into a single one, as shown in Algorithm 3. Thus,
the trained UAE can be used as a dimming-aware VLC system,
which is more effective with lower BER and computational
complexity.
F. Practical Application
In practical application, the binarization and dimming con-
straint operation can be removed from the trained UAE, whose
structure is shown in Fig. 4. As mentioned above, the set of
the achievable dimming intensities of the k-th branch is Ik=
{I∈N|Ik≤I≤Ik+L}. Therefore, if the desired dimming
intensity Ibelongs to Ik, then the one-hot representation x
will be encoded by the k-th branch of the encoding network,
and be decoded by the k-th branch of the decoding network.
The output of the encoding network is directly binarized by the
unit step function to get the binary code d[k], whose Hamming
weight is just the dimming target of the k-th branch Ik.To
meet the desired dimming intensity I, the number of ones in the
Fig. 4. The structure of the trained UAE for practical application.
concatenated patch is set as I−Ik. Thus, the trained encoding
network as well as the patch concatenation operation can map
message bto (N+L)-length CWCs with desired Hamming
weight I, and the trained decoding network can be used for
message reconstruction.
IV. EXPERIMENTAL RESULTS
In this section, we describe the concrete structure of the
proposed UAE and compare the performance of our method
to that of other state-of-the-art VLC systems in term of BER,
the satisfaction of the dimming constraints and the robustness
for imperfect optical channels.
A. Implementation Details
Our proposed UAE network is constructed based on the
Tensorflow package [30]. We randomly generate a training set
with 104samples and a test set with 2×104samples. While
the validation set is a reference set consisting of Mmessages,
e.g., M={b1,...,b
M}. The network parameters Θ[0] and
the penalty parameters λ[0] are updated using the Adam opti-
mizer [31] with learning rate ηattenuating from 0.001 to 0.0001,
and the mini-batch size is set as 256. The number of training
stage P=15and the scaling parameter βis multiplied by 21/3
at each stage with β[0] = 1. Thus, at the final stage, the scaled
sigmoid function is almost the same with the unit step func-
tion, so that the scaled sigmoid function can be replaced with
the unit step function while testing. To simulate the practical
optical channel, the encoded signal s[k]is added with thermal
noise nth ∼N(0,σ
2)and shot noise nsh ∼N(0,s[k]ψ2σ2).
SNR is defined as SNR =Es/σ2=I/(Nσ2), and the pro-
posed UAE is trained at a certain SNR, which is determined
by the validation process, while it is tested for SNR from 0 dB
to 20 dB.
B. The Superiority of the Proposed Training Algorithm
To show the impact of out proposed training algorithm as
Algorithm 3, we compare it with two conventional training ap-
proaches. The first one is the proposed training strategy without
the multi-stage for binarization as Algorithm 1, which trains the
proposed UAE with βalways equaling to β[P]. Fig. 5 illustrates
the convergence behavior of our proposed training algorithm
and the first conventional training approach with same training
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ZOU AND YANG: DIMMING-AWARE DEEP LEARNING APPROACH FOR OOK-BASED VISIBLE LIGHT COMMUNICATION 5739
Fig. 5. The convergence behavior with N=16,H=IN,ψ2=0 and
SNR =10dB.
TAB L E I
THE DIMMING ACCURACY WITH M=64,N=16,H=IN,ψ2=0,
SNR =10dB, AND DIMMING TARGET =14
epochs, M={64,32},N=16,H=IN,ψ2=0and SNR =
10 dB. It can be found that the value of the cost function can
converge to a lower value by our proposed training algorithm,
because it make the easy-to-train sigmoid function gradually
approach to the hard-to-train unit step function, which leads to a
smoother training process. While the first conventional training
approach encounters the vanishing gradient problem caused by
the unit step function, which results in a poor performance.
Notice that the increase in cost function value at the beginning of
the training process comes from maximizing the dual function,
and in the following epochs, both the value of the cost function
and the dual function are close to optimal, which is almost
the same, so that the cost function converges according to the
Karush-Kuhn-Tucker Conditions(KKT).
The second conventional training approach is the proposed
training strategy without the multi-stage for dimming constraints
as Algorithm 2, which trains the proposed UAE with fixed
penalty parameters λas (12). Fig. 6 and Table I shows the
performance of our proposed training algorithm and the second
conventional training approach in each validation stage with
M=64,N=16,H=IN,ψ2=0,SNR=10dB and dim-
ming target I=14. The dimming accuracy is defined as Nd/M ,
where Ndis the amount of validation data that meet the dimming
targets as (4). It is discovered that, with smaller value of λsuch
as 0.03, the second conventional training approach can achieve
lower BER, but the dimming accuracy is always zero, which
means this approach does not constrain the dimming intensity,
Fig. 6. The average BER with M=64,N=16,H=IN,ψ2=0, SNR =
10 dB, and dimming target =14.
Fig. 7. The variety of λduring training process.
whereas the second conventional approach with larger value of λ
reflects an opposite situation. However, our proposed training
strategy outperforms the second conventional one in dimming
accuracy, no matter what the value of λis, which implies that
fixed penalty parameters are not sufficient and adjustable for
multi-constraint problems, and the variety of λin our proposed
training strategy is demonstrated in Fig. 7.
C. Comparison With Existing Methods
To show the performance of our proposed UAE, we compare
it with the AE network in [18], which is taken as the baseline
in this paper. We set B=4,N=16 and L=4. It can be
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5740 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 38, NO. 20, OCTOBER 15, 2020
Fig. 8. The average BER for various test SNR with H=INand N=16.
TAB L E I I
THE DIMMING ACCURACY FOR EACH INTENSITY WITH M=64,
N=16,H=INAND ψ2=0
calculated that the dimming constraints of these four branches
are {2,6,10,14}and the achievable dimming intensities of
each branch are I1={I∈N|2≤I≤6},I2={I∈N|
6≤I≤10},I3={I∈N|10 ≤I≤14}, and I4={I∈
N|14 ≤I≤18}, respectively. The codewords with various
dimming intensities can be obtained by training UAE only
once, whereas the baseline can only satisfy a specific dimming
intensity, in other words, to compare with the proposed UAE,
the baseline needs to be trained with different parameters for
different dimming constraints. That is, the baseline requires to
be trained for a total of 18 −2+1=17times, which leads to
high computational complexity.
With H=IN,ψ2={0,5},M={64,32}, Fig. 8 depicts
the average BER for various test SNR, in addition, Table II
TABLE III
THE DIMMING ACCURACY FOR EACH INTENSITY WITH M=32,
N=16,H=INAND ψ2=5
and Table III illustrate the dimming accuracy for each dimming
intensity of the UAE and the baseline schemes. It is worth noting
that, no matter what the value of ψ2is, the proposed UAE
performs better than the baseline in terms of BER, which proves
that the proposed UAE is efficient for both thermal noise and
shot noise. This is because the multi-branch structure acts as a
regularizer, which reduces the ability to fit the additive noise
from the imperfect channels. Besides, it can be found from
Table II that, when the dimming constraint is larger than 12, the
baseline with fixed small penalty parameter λ=0.03 is unable to
effectively control the dimming intensity. This is because higher
dimming targets require larger penalty parameters, whereas
larger penalty parameters cause poorer BER performance, that
means fixed penalty parameters cannot lead to a good tradeoff
between BER and dimming accuracy performance. But with
trainable penalty parameters, whose variety is just shown in
Fig. 7, the proposed UAE demonstrates satisfying performance
in the aspect of both BER and dimming accuracy regardless of
the dimming constraints. Moreover, Table III illustrates that the
dimming accuracy of the proposed UAE is still pretty high with
signal-dependent noise, while that of the baseline is below 50%
for all dimming intensity regimes.
Also, it can be realized that the dimming accuracy of the
second and the third branches are higher than the first and
the fourth branches. As mentioned above, the number of bi-
nary length-Nsequences of Hamming weight Iis N
I, which
is higher with I={6,10}than with I={2,14}. Thus, the
ratio M/N
Iare different among these branches, leading to
different minimum Hamming distances, further resulting in
different dimming accuracy. While with N=24and various M
and I, similar ratio M/N
Iare obtained in Fig. 9, where the
BER performances of the proposed UAE are pretty close, and
the dimming accuracy under these conditions are all 100%.
Again, both the BER and dimming accuracy performance of
the proposed UAE are superior than those of the baseline.
To stimulate the ISI problem in realistic VLC system, we
assume that LED and PD are equipped on the center of the
ceiling and the floor of a two-dimensional 3 m-by-3 m room,
that is the coordinate of LED and PD are (1.5, 3) and (1.5,
0), respectively. The detector physical length of the PD is
0.2 m, which means the light can be detected in the range
of (1.5±0.1,0). Thus, to capture the general feature of the ISI
channel, we randomly generate the location of the detected light
as [p, 0] while training, where pis the uniform random variable
within [1.4, 1.6]. Fig. 10 shows the average BER over ISI channel
specified by (3) with ψ2=0,N=32,M= 128,B=4and
the bit time interval T=10
−8sec. It can be calculated that
the patch length L=8and the dimming constraints of these
four branches are {4,12,20,28}. Compared with the baseline,
the proposed baseline can still generate efficient OOK symbol
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ZOU AND YANG: DIMMING-AWARE DEEP LEARNING APPROACH FOR OOK-BASED VISIBLE LIGHT COMMUNICATION 5741
Fig. 9. The average BER for various test SNR with H=IN,ψ2=0,N=
24 and similar ratio M/N
I.
Fig. 10. The average BER over ISI channel with ψ2=0,N=32 and
M= 128.
set and learn the general feature of a more complex channel
environment. Besides, as the ratio M/N
Iof these four branches
are all relatively small, the dimming accuracy of the achievable
dimming intensities 4≤I≤36 are all almost 100%.
V. C ONCLUSION
In this paper, we proposed a novel dimming-aware DL frame-
work named UAE for VLC system, which is equipped with a
innovative structure with several branches and binary patches
and a novel multi-stage training strategy to solve this optimiza-
tion problem with multiple dimming constraints. Compared with
existing approaches, our proposed UAE can meet arbitrary dim-
ming targets with a single network, instead of training different
networks for different dimming constraints. Experiments show
that the proposed UAE achieves a superior performance with
lower BER and higher dimming accuracy, and has satisfying
robustness to channel noise.
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Cong Zou (Student Member, IEEE) is a Ph.D. student with the Department
of Electronic Engineering, Tsinghua University, Beijing, China. Her research
interests lie in the field of visible light communication and deep learning for
communications.
Fang Yang (Senior Member, IEEE) received the B.S.E. and Ph.D. degrees in
electronic engineering from Tsinghua University, Beijing, China, in 2005 and
2009, respectively. He is currently working as an Associate Professor with the
Department of Electronics Engineering, Tsinghua University. He has published
over 120 peer-reviewed journal and conference papers. He holds over 40 chinese
patents and two PCT patents. His research interests lie in the fields of channel
coding, channel estimation, interference cancellation, and signal processing
techniques for communication system, especially in power line communication,
visible light communication, and digital television terrestrial broadcasting. Dr.
Yang received the IEEE Scott Helt Memorial Award (Best Paper Award in IEEE
TRANSACTIONS IN BROADCASTING) in 2015. He is the Secretary General of the
Sub-Committee 25 of the China National Information Technology Standardiza-
tion (SAC/TC28/SC25). He currently serves as an Associate Editor for the IEEE
ACCESS and is the fellow of IET.
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