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

∈ G

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

∈ R

∈ G

∈ {0, ...,L}

Simpliﬁed IM/DD Channel Model

CSIC

Encoder

Mapper

CSIC

Decoder

L−1

∈ G

AWGN

Figure 1: Proposed system model. The block lengths are denoted in the exponent of the variable names.

L−1

TIA

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

L−1

∑

l=0

+ 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

is therefore constrained with (d

), where

is the minimum number of slots the LED is hold in

state “off” and d

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

> d

In the following, we assume that each light source

is individually binary-modulated employing a (d

)

Node notation:

Figure 3: State diagram of a single (2|3) constrained light

source. The number of minimum “off” slots is d

= 2 and

the minimum number of “on” slots is d

= 3.

2 2

Node notation:

Init

Figure 4: State diagram for (2|3)

- CSIM, when superim-

posing two (2|3) constrained sequences.

constrained sequence s

. The evolving superimposed

signal is denoted as (d

)

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

Slot

Figure 5: Example for (2|3)

- CSIM signaling with in-

dividually constrained switching sequences s

, 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 )

. (2)

From now on we use a (5|5)

- CSIM superposition

modulation format with a constrained capacity of

(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)

- CSIM by

setting the symbol duration of OOK to ﬁve slots, lea-

ding to a constrained capacity for OOK of

OOK

bit

/slot = 0.2

bit

/slot . (4)

Thus the constrained capacity is increased by a factor

(5|5)

- CSIM

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

0 40 80 120 160

Electrical input power P in W

Data rate R

in Mbps

OOK

(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 =

. (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

/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

, i = 0, .. ., Q − 1, given the CSIM state-transition

matrix D

. The requirement for a valid code is that

each code word set W (q

) contains ≥ 2

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

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

/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)

- 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

= 32 admissible code words

per state.

Mapping the code words, i.e. the output symbols

x to switching sequences s

, 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 = 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

u = argmax

(y −W

)) ,

0.5

−5

−4

−3

−2

−1

−5 0 5 10 15 20 25

Bit error rate

in dB

(5|5)

- CSIC with error prop.

(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

is the previous system state and W

) is the

code word from the set W (q

) 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)

- 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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