Analisa Kinerja Algoritma Soft Output Viterbi (sova) Pada Struktur ...
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Performance of Iterative Soft Output Viterbi Algorithm (SOVA) Decoder on Turbo Coding
under Fading Channel
Miftahul Huda*, Achmad Affandi**, Suwadi**, Tri Budi Santoso*, Arifin*, Aries P*.
(e-mail: huda@eepis-its.edu)
*Wireless Research Group of
Electronic Engineering Polytechnic Institute of Surabaya
** Electric Engineering Department –Industrial Engineering Faculty
Institut Teknologi Sepuluh Nopember Surabaya (ITS)
Abstract
FEC technique base on this structure was proposed for the
Classical turbo coding base on Parallel Concatenated
first time at 1993 on coding community [6]. The important
Convolutional Code has been used for forward error
point in this technique is the possibility to develop the
correcting (FEC). From some research reports [1,2,3,5]
excellent communication system with power efficiency near
this technique show new hope to get the coding technique
to Shannon region. Under AWGN channel, with code rate of
at near Shanon limitation. This paper explains how
1/2 the performance of this system is 10-5 of BER on 0.7 dB
SOVA decoder works on classical turbo coding.
of Eb/No. Jian-Qi [7] reports that the performance of turbo
Performance analysis of SOVA decoder is observed by
code under AWGN channel is better than under Rayleigh
measure the number of bit error (BER). The simulation
fading channel.
is set up under Rayleigh Fading channel, where two types
Rayleigh fading generation are considered, that are
2.
Classical Turbo Coding
correlated and uncorrelated Rayleigh fading. Simulation
parameters to evaluate the decoder performance are
The Classical structure of turbo coding consists of two
signal to noise ratio (Eb/No), frame size, code rate, and
recursive systematic convolutional (RSC) which are parallel
number of iteration. In this paper the effect of additional
concatenated, PAD block, interleaver block, puncturing
interleaver to interleave the code word on BER also
block, and data multiplex block.
discussed.
From simulation, we found that increasing number of
iteration not much helpful in the low region of Eb/No. In
the middle to high region (Eb/No > 3 dB) the
performance of SOVA decoder improve drastically.
Increasing frame size it will produce larger distance by
using an interleaver, and resulting a better decoder
performance. Increasing the parity check bit also
increases the decoder performance significantly, but
consequently the requirement bandwidth also increases.
Figure 1. Structure of classical turbo encoding
Data block u enters the turbo code system. PAD will add tail
Key words:
bit to reset the encoder state. Each data block enters RSC1
iterative SOVA decoder, correlated and uncorrelated
and RSC2. Interleaver is a block for interleaving data
Rayleigh fading
sequence on pseudo random sequence. The output bit from
RSC acts as a parity check bit, ci. Through puncturing block
the parity check bit will be punctured or un-punctured
resulting on difference code rate. The parity check bit is
1.
Introduction
multiplexed with original data and resulting a code word.
After transmitting through fading channel, the receiving data
The classical structure of turbo coding base on Parallel
are decoded by iterative SOVA decoder.
Concatenated Convolutional Code has been implemented for
forward error correcting (FEC). From some research reports
[1,2,3,4,5] this technique show new hope to get the coding
technique at near Shanon limitation.
This paper explain the SOVA Decoder performance on
classical structure of turbo coding through evaluate the value
of BER. The simulation parameters are: number of decoding
iteration, ratio of energy bit and noise power spectral
(Eb/No), frame sizes, and application of additional
interleaver.
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In this simulation there are two types of Rayleigh fading
generations, they are correlated and uncorrelated Rayleigh
fading. Correlated Rayleigh fading is generated by Jack
model, while uncorrelated Rayleigh fading; aR is generated
by equation 2:
2
2
n + n
1
2
a =
…
2
R
2
Figure 2. Structure of iterative SOVA decoder
Where n1 and n2 are Gaussian random number.
3.
Iterative SOVA Decoder
pdf of Ray leigh Random Dis tribution
The SOVA decoder is a modification of classical Viterbi
1
0.8
Algorithm (VA). In VA, the maximum likelihood (ML) path
0.6
is considered by survivor path only. But in the SOVA, the
)
(
x
fx 0.4
ML path is considered by both of survivor and competition
0.2
paths. The SOVA decoders evaluate the a-priori value of
0
information sequences u, L (u) and weighted signal, L
0
0.5
1
1.5
2
2.5
3
cy. The
value of x
a-priori value is obtained from previous decoder. If there is
Cdf of Ray leigh Random Dis tribution
1
no previous a-priori value then L (u) is set to zero. The
0.8
output from SOVA decoder is estimated value (u’) and
0.6
)
extrinsic value, L (u’) that will be iterated to the other SOVA
(
x
Fx 0.4
decoder. The structure of SOVA decoder is depicted on
0.2
Figure 2.
0
0
0.5
1
1.5
2
2.5
3
value of x
4.
Simulation Model
A model used in this paper is as shown in Figure 3. The
Figure 4. pdf and Cdf of Rayleigh random distribution
simulation procedure could be explained as follows:
After demodulation and deinterleaver, iterative SOVA
The source block generates random information u, u∈{0,1}
decoder decodes the received code word. The SOVA
then the random information is encoded by turbo encoding,
decoder steps is shown as on below flowchart [10].
x∈{-1,1}. Using optional interleaver, the code word is
interleaved on pseudo random sequence {-1,1}, then the
modulated code word, X∈{-Λ,Λ} is transmitted through the
fading channel [8,9]. The received signal, y is expressed as:
y = aX + n …
(1)
Where a is fading coefficient which has Rayleigh
distribution, X is transmitted data, and n is white Gaussian
noise. Figure 4 is probability density function and collective
density function of Rayleigh distribution generation (dash
line) and theoretical (solid line).
Intrinsic information
exchange
Figure 3. Simulation Model
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-1
10
EbN0 = 4 dB
EbN0 = 3 dB
t
e
a
r R -2
10
rro
i
t
E
B
1
2
3
4
5
Iterasi
Figure 7. Effect of decoder number iteration
on BER. Frame size = 5000 (uncorrelated fading) at EbN0 =
3 and 4 dB
0
10
-1
10
-2
10
te
a
r
R
-3
10
r
ro
it E
-4
B
Figure 5. The SOVA decoder flowchart
10
-5
co de rate = 1/2
10
co de rate = 1/3
-6
10 1
2
3
4
5
6
5.
Simulation Result and Data Analysis
EbN0 (dalam dB)
Figure 8. Effect of code Rate on.
After developing and running the simulation program under
Matlab environment, the simulation result can be observed
0
10
through Figure 6 to Figure 11. Figure 6 and Figure 7 give an
384r1/3
impression that increasing number of iteration not much
1200r1/3
-1
helps in the low region of Eb/No. In the middle to high
10
region (Eb/No > 3 dB) the performance of SOVA decoder
-2
t
e
improves drastically. This is due to the decoder 1 and
a 10
r R
decoders 2 shares the information and makes decision more
rro
accurate.
-3
i
t
E 10
B
0
10
EbN0 = 1 dB
-4
10
EbN0 = 2 dB
-5
10 1
2
3
4
5
6
t
e
EbN0 (dalam dB)
a
r R
Figure 9. Effect of frame size on BER
rro
i
t E
B
Figure 8 gives information that changing the code rate from
1/2 to 1/3 will increase SOVA decoder performance
significantly. This is because of the parity check bit on 1/3
-1
rate larger then on 1/2 rate; hence the code word is rather
10 1
1.5
2
2 .5
3
3.5
4
4.5
5
Iterasi
immune to noise. As a consequence the requirement
Figure 6. Effect of decoder number iteration
bandwidth will increase.
On BER. Frame size = 5000 (uncorrelated fading) at EbN0 =
1 and 2 dB
Figure 9 illustrates the effect of frame size on BER of SOVA
decoder. From this figure we found that increasing frame size
resulting better decoder performance. This is due to the
larger frame size produce the larger distance caused by
interleaver. The disadvantage of increasing frame size is
delay time before getting complete decoder also increase.
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0
5.
Because the less correlation of fading process, the
10
Uncorrelated Fading
decoder performance under correlative Rayleigh
Correlated Fading
-1
generator is worse than under uncorrelative Rayleigh
10
generator.
-2
t
e
10
r
Ra
6.
Optional interleaver can increase the decoder
r
r
o
performance especially for the large frame size.
-3
E 10
Bit
-4
10
-5
10 1
2
3
4
5
6
7.
References
EbN0 (dalam dB)
Figure 10. Effect of Rayleigh generator on BER. The
simulation parameter are, Frame size = 5000, code rate = 1/2,
[1.] Matthew C. Valenthi, “Turbo Code and Iterative
number of iteration = 3.
Processing”, Mobile and Portable Radio Research
Group, Virginia Polytechnic Institute and State
From Figure 10, it can be shown that the performance of
University, Blacksburg, USA, 1999
decoder under uncorrelative Rayleigh generator better than
correlative Rayleigh generator. This means the less
[2.] Jun Tan and Gordon L. Stuber, “Soft Output Viterbi for
correlation of fading process will give the better decoder
Non-Binary Turbo Codes”, Electrical and Computer
performance.
Engineering, Georgio Institute of Technology,
(Proceeding of ISIT-2000), USA, 2000
0
10
Without optional Int
With optional interleaver
[3.] Jun Tan and Gordon L. Stuber, “A MAP Equivalent
-1
10
SOVA for NON-Binary Turbo Codes”, Electrical and
-2
10
Computer Engineering, Georgio Institute of
te
Technology, USA, 2000
r
Ra
-3
10
r
r
o
E
[4.] Jason P. Woodard and Lajos Hanzo,
Bit
-4
10
“ComparativeStudy of Turbo Decoding Techniques: An
-5
10
Overview”, IEEE Transaction on Vehicular
Technology, Vol. 49, No. 6, November 2000
-6
10 1
2
3
4
5
6
7
EbN0 (dalam dB)
[5.] Barbulescu, Sorin Andrian, “Iterative Decoding of
Figure 11. Effect of optional interleaver on BER. The
Turbo Codes and Other Concatenated Codes”,
simulation parameter, frame size 1.200, code rate 1/3, after 4
Dissertation, Faculty of Engineering, University of
iteration
South Australia, 1996
Figure 11 gives the illustration that the use of optional
[6.] C. Berrou, A. Glavieux, and P. Thitimasjshima; “Near
interleaver can increase the decoder performance. As a
Shanon limit error-correcting coding and decoding”:
general sense that the burst error is hard to be corrected by
Turbo Codes(1). Proc., IEEE Int. Conf. On Commun.,
viterbi algorithm. The using of optional interleaver can
(Geneva, Switzerland), 1993
produce a high-weighted code, especially for the large frame
size.
[7.] Jian Qi, “Turbo Code in IS-2000 Code Division
Multiple Access Communication under Fading”, Master
6.
Conclusion
Thesis of Wichitia State University, 1999
After making discussion the following conclusion could be
[8.] Gayatri S. Prabhu and P. Mohana Shankar, ”Simulation
drawn:
of Flat Fading Using Matlab for Classroom
Instruction”, Lecture note, Department of Electrical and
1.
As an error correcting technique, performance of
Computer Engineering, Drexel University
SOVA decoder on turbo coding is good enough.
[9.] Fatin Said, Dr., “Introduction to the Mobile Radio
2.
Effect of number of decoder iteration is much helpful
Channel”, Center for Telecommunication Research,
especially on the middle to high region of Eb/No (> 3
King College London
dB)
[10.] Huang, Fu-Hua; “Evaluation of Soft Output Viterbi
3.
Increasing frame size also increasing the decoder
Decodingfor Turbo Codes”, Virginia Polytechnic
performance, even though the delay time will also
Institute and State University, Master Thesis, 1997
increase.
4.
Increasing code rate also can reach better decoder
performance, but the requirement bandwidth must be
considered.
Document Outline
