![](bg4.png)
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
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