B. Fong et al.: Forward Error Correction with Reed-Solomon Codes for Wearable Computers
917
Forward Error Correction with Reed-Solomon Codes for
Wearable Computers
B. Fong,
Senior Member, IEEE,
P. B. Rapajic,
Senior Member, IEEE,
G. Y. Hong,
Member, IEEE,
and A. C. M. Fong,
Member, IEEE
Abstract
— High-speed multimedia data transmission is
vulnerable to burst errors primarily due to its frame structure.
Forward error correction (FEC) codes mitigate the effects of
multipath fading as some form of time diversity by adding
redundancies into the transmitted data. This paper evaluates
the performance of Reed-Solomon codes on transmitting ATM
data for lightweight wearable computers using single carrier
modulation. The aim is to maximize link availability and
minimize the impact of atmospheric conditions on bit error
rate (BER) performance. The performance is compared with
signals transmitted without any forward error correction
scheme.
This scheme is particularly suitable for small
wearable computers with high portability due to simplicity of
circuitry making it suitable for consumers on the move.
Index Terms —
Burst error, Link availability, Single-
carrier Modulation, Wearable computers.
I.
I
NTRODUCTION
H
IGH
speed wireless Asynchronous Transfer Mode (ATM)
networks are widely used for multicast distribution of
multimedia data over a locality. Microwave links that carry
the data suffer from fading due to rain attenuation,
depolarization, multipath, and frequency fading [1]. The
quality of service (QoS) of a wireless network is largely
dependent on maximizing the link availability between the
basestation modem unit (BMU) and the customer-premises
equipment (CPE).
Wearable computers are found appealing in the ever
growing consumer electronics industry as multimedia service
enhancements make small devices such as PDA (personal
digital assistant) and WAP (Wireless Application Protocol)
compatible cellular phones are able to provide a range of
network services for subscribers on the move. A number of
challenges exist for reliable operation of wearable computers
in an outdoor environment particularly under the influence of
heavy and persistent rainfall [2]. The need for reliable error
correction is therefore crucial for maximizing system QoS to
ensure adequate network availability.
B. Fong is with Auckland University of Technology, Private Bag 92006,
Auckland 1020, New Zealand (e-mail: bfong@ieee.org)
P.B. Rapajic is with School of Electrical Engineering and
Telecommunications University of New South Wales, Sydney 2052,
Australia.
G. Y. Hong is with Massey University- Albany Campus, Private Bag 102904,
North Shore Mail Center, Auckland, New Zealand
A. C. M. Fong is School of Computer Engineering, Nanyang Technological
University, Singapore
Contributed Paper
Manuscript received May 15, 2003
Earlier research [3], [4] have found that Reed-Solomon
codes (R-S) are effective in minimizing the impairment caused
by burst errors in delivery of high speed data traffic, which is
the most significant type of error associated with ATM
multimedia traffic because of its data frame structure. A
reduction in the bit error rate (BER) can be realized by FEC,
this consequently leads to an increase in microwave link
availability in the expense of slightly lowering the effective
available bandwidth due to redundancies. FEC codes have
been widely used in consumer electronics equipment such as
audio compact discs (CD) [5] and random access memory
(RAM) [6]. Earlier work on applying FEC to broadband
networks have been performed by [7], [8]. Results show that
FEC is generally effective when there is a high degree of
correlation in the error and its performance is largely
dependent on the spread of error. Our work seeks to evaluate
the performance of R-S code on the improvement for
delivering ATM traffic to mobile receivers.
The link availability is measured by the percentage of time
in which it can provide a BER of 10
-6
or better. Factors that
affect the link performance that ultimately determines the
maximum coverage range are mainly due to geographical
conditions with both stationary and moving obstacles causing
signal degradation due to phenomena such as shadowing,
multipath, and environmental conditions resulting from rain
and snow. Improvement in the link BER performance by
using R-S encoding has been studied in this paper.
II.
PROBLEM STATEMENT
Wireless links are harsh environments for data transmission
due to conditions such as multipath fading and attenuation.
Wideband communication is particularly vulnerable to such
signal degradation. It is also realized that most of the error
involved is burst errors in multimedia traffic. Overheads for
FEC can be added to data frames to improve QoS as a result of
BER improvement. Frame relay networks are susceptible to
burst errors.
While the IEEE 802.11 standard provides
specifications on wireless networks, it does not specify the
type of modulation scheme and error correction mechanism for
deployment as there is no single optimal solution that offers
best performance.
Rain causes scattering, depolarization and phase rotation to
radio waves. Highly robust error correction is important in
ensure maximum reliability for wearable computers with high
mobility in an outdoor environment.
0098 3063/00 $10.00 © 2003 IEEE
918
IEEE Transactions on Consumer Electronics, Vol. 49, No. 4, NOVEMBER 2003
ATM
Network
Backbone
DS3 E3
Line-of-Sight
Radio
hub
12 Mbps
Subscriber Internal
End-user
Access connection
node
System
Fig. 1 System Layout for providing multimedia services to wearable computers
R-S
Encoder
Multimedia
S/P
data
T
s
2
R-S
Encoder
Cross
correlator
Filter
e
u (t)
I
I(t)
f
c
Q(t)
Filter
90
o
Σ
u
Q
(t)
e
Fig. 2 Encoding mechanism
III.
S
YSTEM
L
AYOUT
A wireless local area network (WLAN) system operating at
a carrier frequency of 5 GHz has been used. This system
offers distinctive advantages in network capacity [9]. The
system block diagram is shown in Fig. 1. This system consists
of three main parts, Switching that connects the access system
to its network backbone using a fixed E3 connection via the
radio hub. The Transport segment relays data to the BMU
where data is transmitted over the link. The Access part is a
subscriber radio unit and a subscriber access system which
process the received data and the data is then collected for a
notebook computer to perform data analysis. The objective is
to improve the tolerance to burst error with wearable nodes.An
outdoor line-of-sight (LOS) link is established between the
antennas of the transmitter and the receiver. The link is
evaluated under conditions when persistent heavy rainfall
causes maximum degradation to the link performance in a
tropical region of ITU-P [10].
The maximum range of the microwave link as a function of
the percentage of time that the link maintains a BER of no
worse than 10
-6
is shown in Fig. 3. The main causes of link
outage are due to weather conditions such as rain and fog.
Such effects can usually be compensated by adjustment made
to the fade margin. The result shown indicates the maximum
link range for a transmission rate of 12 Mbps using a 5 GHz
carrier with LOS and no rainfall. The range for 99.99%
availability is 18 km. Each ATM cell consists of only 8 error
checking header bits. Any cell that is received with an error
Fig. 3 Maximum link coverage
not corrected by the FEC is relayed to the subscriber access
system with the error still present.
The system performance is also largely determined by its
modulation scheme. While there are a number of options
available depending on factors such as bandwidth efficiency,
transmission power and cell-to-cell interference. Multicarrier
modulation offer a number of advantages for wireless
multimedia transmission as described in [11], single carrier
modulation schemes is selected for their high level of
narrowband noise immunity due to inherent capability by use
of adaptive equalization and reduced receiver structure
B. Fong et al.: Forward Error Correction with Reed-Solomon Codes for Wearable Computers
919
TABLE I
T
HE
GF(2
M
) R-S C
ODES
Field GF( )
R-S Code
(N= 2
m
–1, k, d= 2
m
-k)
(15, 8, 8)
(31, 8, 24)
(63, 8, 56)
(127, 8, 120)
(255, 8, 248)
complexity because of simplified decoding mechanism with
the added advantage of being more tolerant to noise and
interference.
The system is set up to evaluate the effects of Reed-
Solomon codes on the radio link availability as shown in Fig.
1. Forward Error Correction (FEC) technique provides a
means to reduce the BER. Data frames are sent across an LOS
radio link supporting a data rate of 12 Mbps.
The data is transmitted using QPSK modulation for its
robustness and relatively good tolerance to noise and
interference with ease of implementation [12]. Fig. 2 shows
the structure of transmitter with R-S encoding mechanism.
The symbol sequence polynomial is given by
2
m
16
32
64
128
256
Where
k
is chosen as 8 bit.
v
(
x
)
=
v
0
+
v
1
x
+
...
+
v
n
−
1
x
n
−
1
whereas the information polynomial can be represented as
(6)
a
(
x
)
=
a
k
−
1
x
k
−
1
+
a
k
−
2
x
k
−
2
+
...
+
a
1
x
+
a
0
(1)
u
(
x
)
=
u
0
+
u
1
x
+
...
+
u
k
−
1
x
k
−
1
(7)
The code words are encoded using the product of the generator
polynomial g(x) and the information block such that:
This information polynomial can be transformed as the code
polynomial v(x) with the generator polynomial
g
(
x
)
=
∏
(
x
−
a
i
)
i
=
0
15
(2)
g
t
(
x
)
=
LCM
[
φ
i
(
x
)]
1
≤
i
≤
2t
(8)
g
(
x
)
=
x
+
∑
g
i
x
i
16
i
=
0
15
v
(
x
)
=
x
n
−
k
u
(
x
)
+
x
n
−
k
u
(
x
)
g
t
(
x
)
(3)
where x
n-k
u(x) is divided by g
t
(x) to obtain the remainder x
n-k
u(x)
m
gt(x)
. For an RS(n,k) code with symbols from GF(2 ), there will be
an m
2
number of cells. The codes of GF(
2
m
) are listed in Table 1.
IV.
D
ECODING
A
LGORITHM
A burst erasure correction R-S code [7] is used for FEC.
The notation
RS(N,k)
represents a code block of
N
symbols
length that contains
k
information symbols. This code is
defined in a Galois field as GF(2
m
) where
m
represents the bit
length of a code symbol. With an
N
point GF DFT defined as
V
k
=
∑
v
i
α
ik
k
=
0
N
−
1
b. Rate of erroneous correction
The network delivers a range of data from different multimedia
applications such as audio and video data. In our system, bulk
data transfer with a single burst source of a fixed number of cells
is used for ease of implementation.
The burst error received is fed into the R-S decoder for burst
correction. The probability of incorrectly manipulating the burst
error with a burst of length exceeding 16 is shown in Fig. 4.
(4)
v
i
=
∑
V
k
α
−
ik
k
=
0
N
−
1
(5)
where a primitive N-root of
α
is the kernel. By solving these
equations in the frequency domain that yields an error locator
polynomial having a root of
α
-i
, an error occurs at position
i
of
the received data block.
a. Reed-Solomon Coding
GF(2 ) denotes the finite field of 2
m
elements with
n
defined as (2
m
-1). An RS(63, 56) code has
63
code symbols
and
56
information symbols in each block with
8
bits. The
code symbols can be represented as the coefficients of code
polynomial
m
Fig. 4 Probability of correction error
920
IEEE Transactions on Consumer Electronics, Vol. 49, No. 4, NOVEMBER 2003
c. Over radio channels
The radio channel is assumed to be slow fading with the signal
of the forward channel defined as a Rayleigh random variable
with pdf
p
(
a
)
=
2
a
. exp(
−
a
2
)
(9)
It is assumed that the channel is not frequency-selective and
the effects of signal degradation caused by multipath fading is
eliminated by using an equalization method as described in
[13]. A code symbol error occurs when there is a code symbol
that is failed to be detected as an erasure. The received
symbol that contains errors can be represented by
corrected. Such cut off is performed manually at the receiving
end.
A comparison between no error correcting mechanism and
the deployment of FEC codes has been made over the same
microwave link under identical operating environments. The
system’s E
b
/N
o
performance is shown in Fig. 6 without error
correction. The BER performance with an 8% overhead of
check bits are measured and results are shown in Fig. 7. The
insertion of Reed-Solomon FEC codes yields an improvement
on the link availability at the expense of a marginal increase in
data rate due to redundancies.
The results show that at BER = 10
–6
, when the link is at the
boundary of barely available, the E
b
/N
o
ratio with FEC is
increased by 4 dB. The improvement is even more significant
as the BER further decreases.
r
(
a
)
=
s
(
a
)
+
e
(
a
)
=
∑
r
i
a
i
i
=
0
15
(10)
where
s
and
e
denote the transmitted signal and error as a
function of
a,
respectively. This yields to the syndrome
polynomial coefficients as
S
i
(
a
)
=
r
(
a
i
)
=
s
(
a
i
)
+
e
(
a
i
)
1
≤
i
≤
2t
(11)
The processing time of the R-S decoder is show in Fig. 5
where it is noted that the decoding time for up to a burst length
of 30 symbols is acceptable that takes less than 450 machine
clock cycles to complete.
Fig. 6 System performance
Fig. 5 Processing time of R-S decoder with burst length between 15 and
30 symbols.
Fig. 7 Performance of Reed-Solomon FEC codes
V.
R
ESULTS
Multimedia traffic is transmitted over the link as described
in Section II above and the received data is collected for data
analysis. The receiver is suspended whenever the link is
unavailable, that is, when its BER falls below 10
-6
. This is
because even with FEC, large amount of errors cannot be
It is also noted from Fig. 7 that the rate of E
b
/N
o
improvement with FEC is significantly reduced due to the
much steeper slope of the performance curve. This means that
a small change in E
b
/N
o
causes very high fluctuation of BER.
As a result, the link availability will be changed between
available and unavailable much more frequently than in the
case where no error correcting mechanism is used.
B. Fong et al.: Forward Error Correction with Reed-Solomon Codes for Wearable Computers
921
VI.
C
ONCLUSIONS
This paper presents the performance of Reed-Solomon
codes for error correction in wearable computers. The harsh
operating environment of small wearable computers in the
open is particularly vulnerable to transmission error.
ATM traffic is susceptible to burst errors and the effects of
performance degradation can be compensated by the use of
Reed-Solomon codes for error correction. A slight increase in
data rate due to 8% overhead yields a noticeable improvement
in BER performance that consequently leads to a higher
availability of the radio link as a minimum BER of 10
-6
can be
attained at a much lower E
b
/N
o
. Results with QPSK show that
E
b
/N
o
is dropped from 11.2 dB to 7.3 dB when the link is
barely available. A further improvement is noted when the
BER is lowered to 10
-8
where the difference of almost 5 dB in
E
b
/N
o
is offered by FEC. It is shown that although FEC is
unable to fully correct errors due to burst errors, it does offer a
significant improvement on the link availability.
Bernard Fong
(M’93) graduated in Electrical Engineering
from the University of Manchester (UMIST), United
Kingdom.
He is currently a faculty member in
telecommunication engineering and multimedia with the
Department of Electrotechnology, Auckland University of
Technology, New Zealand
He was previously a Staff Engineer with Hewlett-
Packard. His research interests include wireless communications, Internet
technologies and engineering project management.
Predrag B. Rapajic
(M’89-SM’99) received the B.E
degree from the University of Banja Luka, Yugoslavia, in
1982, and the M. E. degree from The University of
Belgrade, Belgrade, Yugoslavia, in 1988. He received the
Ph.D. degree from The University of Sydney, Sydney,
Australia in 1994.
In 1996, he was appointed Head of the
Communications Group, Motorola Australian Research Center. Since 2000,
he has been a Senior Lecturer at The University of New South Wales, Sydney,
Australia. His research interests include adaptive multiuser detection,
equalization, error control coding, mobile communication systems and
multiuser information theory.
R
EFERENCES
[1]
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2003, pp. 13- 14
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Causing Uncertainties in Outdoor Wireless Wearable Communications”,
to appear in IEEE Pervasive Computing, Vol. 2 No. 2, April 2003.
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G. Y. Hong
(M’95) received her Ph.D. degree from the
National University of Singapore. She is currently with
Massey University (Albany Campus).
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
A. C. M. Fong
received his degrees from the University of
Auckland and Imperial College, London.
He is currently an Assistant Professor in Computer
Engineering at Nanyang Technological University.
His research interests include various aspects of
Internettechnology, information theory, and video and
image signal processing. He is a Chartered Engineer.
[13]
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