Constrained Coding for Hardware-friendly Intensity Modulation
Gilbert J. M. Forkel, Tom J. Wettlin and Peter A. Hoeher
Faculty of Engineering, Kiel University, Kaiserstr. 2, D-24143 Kiel, Germany
Keywords:
Binary Superposition Modulation, IM/DD, VLC, OWC, Constrained Coding.
Abstract:
An advanced signal design for boosting the performance of binary-modulated IM/DD communication systems
is presented. Multiple light sources are jointly modulated so that the optical signals superimpose at the receiver.
The superimposed signal is of high rate. The switching sequences are constrained to match the physical
properties of the transmit hardware. A graph-based representation is used to design a low-complexity block
code, enabling the use of the binary superposition modulation scheme under investigation in a practical IM/DD
setup. Based on this coded signal design measurement results on power consumption and simulation results
on bit error rate performance are presented.
1 INTRODUCTION
Superimposing multiple binary-modulated light sour-
ces improves the performance of intensity modula-
tion and direct detection (IM/DD) communication sy-
stems. This is a twofold effect.
On the one hand, the throughput is typically upper
bounded by bandwidth limitations at the transmitter.
An improvement of the maximum possible data rate
can be realized by overlaying multiple binary inten-
sities (Fath et al., 2013; Armstrong, 2013; Dobesch
et al., 2014; Forkel and Hoeher, 2015) for forming
a multilevel intensity modulated signal. Furthermore
this receiver-side sum signal is possibly of higher rate
then the state changes at the individual light sources
(Forkel and Hoeher, 2016). The constrained superpo-
sition intensity modulation (CSIM) method under in-
vestigation exploits both techniques at the same time
(Forkel and Hoeher, 2017).
On the other hand, the amount of power spent for
modulation, i.e., for charging or discharging the ca-
pacities in the optical emitter and the driver circuitry,
can be reduced by using the proposed superposition
modulation scheme. This is possible by lowering the
number of switching operations per source bit, com-
pared for example to on-off keying (OOK) modula-
tion.
The key contribution of this paper is a channel co-
ding design which is matched to CSIM.
The overall work is organized as follows: In the
next section we define a CSIM scheme to mitigate the
physical limitation of the individual transmit LEDs by
superimposing multiple low-rate sequences. We in-
troduce a constrained capacity and evaluate the num-
ber of switching operations per source bit. Having
derived a Moore-graph representation of the transmit-
ter constraints, block coding is applied in Section 3.
A constrained superposition intensity coding (CSIC)
method allows CSIM sequences to be used for repre-
senting actual transmit data. Then simulation results
comparing CSIC with OOK are presented. Finally
conclusions are drawn in Section 4.
2 CONSTRAINED
SUPERPOSITION
MODULATION
The novel CSIC encoder, cf. Fig. 1, generates a vector
x of integer numbers given a binary source data vector
u. The time duration of one vector element is denoted
as one slot in the following. A mapper transforms the
integer numbers x into switching patterns s
l
G
n
2
,
l =
{
0, . .., L 1
}
, where L is the number of light
sources. These switching patterns control the light
sources, as shown in Fig. 2. Subsequently, we assume
an illumination fixture where the LEDs are in close
distance to each other (Mossaad et al., 2015). Cor-
respondingly, all L light sources superimpose with
equal weight on the channel. Therefore the channel
gain H is the same for all light sources. Furthermore
292
Forkel, G., Wettlin, T. and Hoeher, P.
Constrained Coding for Hardware-friendly Intensity Modulation.
DOI: 10.5220/0006715802920296
In Proceedings of the 6th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2018), pages 292-296
ISBN: 978-989-758-286-8
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
y
R
n
u
G
k
2
ˆ
u
G
k
2
x
{0, ...,L}
n
Simplified IM/DD Channel Model
CSIC
Encoder
Mapper
CSIC
Decoder
s
L1
s
0
s
1
.
.
.
G
n
2
+
H
+
n
AWGN
Figure 1: Proposed system model. The block lengths are denoted in the exponent of the variable names.
s
0
s
1
V
s
L1
y
TIA
H
H
H
Figure 2: Transmitter configuration for binary intensity su-
perposition modulation using L light sources and a single
direct-detection receiver (represented by a photodiode with
transimpedance amplifier). The optical signals superimpose
at the receiver, weighted by the channel gain H.
additive white Gaussian noise (AWGN) is assumed:
y = H
L1
l=0
s
l
+ n . (1)
In the field of mass storage technology it is com-
mon to match symbol sequences to the physical li-
mitations of the storage hardware. Similarly we ma-
tch binary sequences to the limitations of light sour-
ces, namely the restricted dynamic behavior caused
by their junction capacities. Each individual LED se-
quence s
l
is therefore constrained with (d
0
|d
1
), where
d
0
is the minimum number of slots the LED is hold in
state “off” and d
1
is the minimum number of slots the
light source has to remain in state “on”. A correspon-
ding graph is exemplarily given in Fig. 3. E.g. GaN-
based LEDs (Kishi et al., 2014) exhibit high depletion
capacities that lead to slower 1 0 than 0 1 tran-
sitions. This can be taken care of by setting d
0
> d
1
.
In the following, we assume that each light source
is individually binary-modulated employing a (d
0
|d
1
)
Node notation:
x
1
0
0
11
Figure 3: State diagram of a single (2|3) constrained light
source. The number of minimum “off slots is d
0
= 2 and
the minimum number of “on” slots is d
1
= 3.
2 2
2
2
0
0
1
0
1
1
1
1
2
2
Node notation:
x
Init
Figure 4: State diagram for (2|3)
2
- CSIM, when superim-
posing two (2|3) constrained sequences.
constrained sequence s
l
. The evolving superimposed
signal is denoted as (d
0
|d
1
)
L
and a graph representa-
tion of permissible sequences x is exemplarily shown
in Fig. 4. A corresponding signaling example is de-
picted in Fig. 5, including a measurement result for a
receive signal using three LEDs and a single direct-
detection receiver.
Constrained Coding for Hardware-friendly Intensity Modulation
293
0
1
2
0
1
2
3
Slot
s
l
y
/H
Figure 5: Example for (2|3)
3
- CSIM signaling with in-
dividually constrained switching sequences s
l
, l = 0,.. ., 2
and the measured receive signal y at a comparatively high
signal-to-noise ratio.
With the CSIM construction it is possible to re-
duce the modulation bandwidth limitations of binary-
type IM/DD modulation formats. Following Shan-
non’s famous Mathematical Theory of Communica-
tion (Shannon, 1948), we can analytically derive the
constrained capacity from the CSIM graph descrip-
tion. This is the capacity of a noiseless channel, where
N (T ) is the number of admissible sequences of length
T :
C = lim
T
logN(T )
T
. (2)
From now on we use a (5|5)
5
- CSIM superposition
modulation format with a constrained capacity of
C
(5|5)
5
- CSIM
1.55
bit
/slot (3)
as an example, and OOK modulation as reference sy-
stem. Regarding the light source switching require-
ments, OOK is thereby equalized to (5|5)
5
- CSIM by
setting the symbol duration of OOK to five slots, lea-
ding to a constrained capacity for OOK of
C
OOK
=
1
/L
bit
/slot = 0.2
bit
/slot . (4)
Thus the constrained capacity is increased by a factor
of
C
(5|5)
5
- CSIM
C
OOK
7.75 (5)
using the selected CSIM example.
In terms of power efficiency of the transmitter we
use the number of switching operations necessary to
encode one source bit as figure of merit. This is rea-
sonable since the switching elements, typically field-
effect transistors (FETs), exhibit no significant loss in
DC operation when compared to the state transition
phases. Additionally the junction capacities of the
LEDs have to be charged or depleted for each state
55
60
65
70
75
80
0 40 80 120 160
Electrical input power P in W
Data rate R
b
in Mbps
OOK
(5|5)
5
- CSIM
Figure 6: Measurement result on rate dependent
transmitter-side power consumption.
transition consuming additional power. The power
consumption of each switching operation is equal to
the energy stored in the capacitors:
E =
1
2
CV
2
. (6)
Thus the overall transmitter-side power consumption
is proportional to the number of switching operations
per source bit. For a fair comparison, we assume the
transmitter to consist of L light sources both for CSIC
and OOK. In the case of OOK, with a probability of
one half all light sources have to change their state
to encode one source bit of an uniformly distributed
random sequence, which leads to
L
/2 switching ope-
rations per bit. The analytic results show a reduction
in the amount of required switching operations per
bit from 2.5 for OOK to about 0.4 for CSIM, when
L = 5 light sources are used. Effectively this is a re-
duction of the switching-dependent power consump-
tion by a factor of approximately
2.5
/0.4 = 6.25 while
preserving the data rate of the system.
Measurement results of the transmitter power con-
sumption, supporting this reasoning, are shown in
Fig. 6. In our lab setup we use five blue-colored LED
arrays, each one supplied with 42.5V at a current
of 500 mA. The light sources are biased with 24 V
to reduce the energy required for changing the out-
put states. With this setup a reduction of the po-
wer consumption from 79.3W to 56.5 W at a data
rate of 20 Mbps (compare Fig. 6) is realized by using
CSIM as replacement for OOK. This translates to
a receiver-side SNR improvement of 2.94 dB in the
electrical domain. By removing the static power-
consumption of 52W we can show that CSIM re-
duces the switching-dependent power consumption
from 27.3 W to 4.5 W. This is a reduction by a factor
of 6.07, and reasonably close to the analytic result of
6.25 and thus supports that power consumption in the
PHOTOPTICS 2018 - 6th International Conference on Photonics, Optics and Laser Technology
294
transmitter is proportional to the number of switching
operations per source bit.
3 CODING ON CONSTRAINED
SEQUENCES
Having introduced a graph-based representation of
the constrained optical superposition transmitter, we
now adapt a block coding scheme originally deve-
loped in the mass storage community. The recur-
sive elimination algorithm by Franaszek (Franaszek,
1968; Franaszek, 1969) provides a mapping from the
binary input sequences u to the modulation sequen-
ces x. The algorithm is able to identify a subset
of the original system states, called principal states
q
i
, i = 0, .. ., Q 1, given the CSIM state-transition
matrix D
n
. The requirement for a valid code is that
each code word set W (q
i
) contains 2
k
code words
of length n. If a state does not satisfy the condition, it
is eliminated and the condition gets rechecked, until
either all states have been eliminated or until a valid
set of principal states has been found. If more than 2
k
codes are in one set we remove the code words with
the worst Euclidean distance profile in an iterative
process. The resulting CSIC code is state-dependent.
The code rate
k
/n is defined as the number of source
bits k mapped to one symbol block with a duration of
n slots. It is smaller or equal than the CSIM constrai-
ned capacity.
We have chosen a coding scheme with rate
1.25
bit
/slot for the (5|5)
5
- CSIM example, mapping
k = 5 source bits onto n = 4 symbol slots. The
short block length results in some rate degradation
compared to the maximum possible capacity of ap-
proximately 1.55
bit
/slot for CSIM, but it offers enco-
ding/decoding with relatively low complexity and low
memory footprint with a requirement of Q = 1680
principle states and 2
k
= 32 admissible code words
per state.
Mapping the code words, i.e. the output symbols
x to switching sequences s
l
, is done by symbol-wise
evolving the light sources output states while follo-
wing the per light source constraints. For perfor-
mance reasons s
l
, l = 0,...,L 1, can be computed
offline and used in the transmitter as replacement for
the code words x, effectively joining the CSIC enco-
der and the mapper. By this method, we are able to
implement a purely lookup-table based encoder.
Decoding is performed using maximum-
likelihood (ML) decoding according to
ˆ
u = argmax
u
(y W
u
(q
i
)) ,
0.5
10
5
10
4
10
3
10
2
10
1
5 0 5 10 15 20 25
Bit error rate
E
b
/N
0
in dB
(5|5)
5
- CSIC with error prop.
(5|5)
5
- CSIC w/o error prop.
OOK
Figure 7: Simulation results using five constrained light
sources. The triangle-style CSIC curve represents the
“real-world” decoder performance (including error propa-
gation effects), while for the circle-style CSIC curve perfect
receiver-side knowledge of the system state q is assumed.
were q
i
is the previous system state and W
u
(q
i
) is the
code word from the set W (q
i
) assigned to the source
word u. This typically leads to error propagation due
to the state dependency. The bit error rate (BER) re-
sults in Fig. 7 show that both curves with and without
the error propagation are converging at low BER va-
lues.
Finally we use the Monte Carlo simulation results
to evaluate the performance of CSIC. Specifically we
compare the developed (5|5)
5
- CSIC system to OOK.
We have shown before that CSIM is superior to OOK
in terms of constrained capacity and transmitter-side
power consumption. As penalty, power efficiency is
reduced by 11.4 dB at a bit error rate of 10
5
, cf.
Fig. 7. This degradation is partly mitigated by the
transmitter-side power savings.
4 CONCLUSIONS
In this work, we present a superposition IM/DD
scheme, where multiple binary-modulated light sour-
ces are combined to boost the data rate. For this su-
perposition of individually constrained switching se-
quences a graph-based representation is introduced.
Based on an example using five light sources we
achieve a capacity boost of almost factor eight, and
at the same time we are able to reduce the transmitter-
side power consumption by a factor of six. Note-
worthy the transmitter-side power savings are of par-
ticular importance in practical visible-light commu-
nication (VLC) scenarios, where high optical output
powers are required for the purpose of illumination.
The receiver-side SNR penalty may be of minior inte-
Constrained Coding for Hardware-friendly Intensity Modulation
295
rest in many scenarios. Furthermore, a block coding
scheme is adapted to this communication scenario and
its feasibility is supported by bit error rate simulations
and measurements.
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