1. PERFORMANCES OF PARALLEL CONCATENATED CODES FOR
NON LINEAR SATELLITE CHANNEL
Leila Zine, Rachid Amraoui and Rachid Hadj Ameur
Zine.leila@gmail.com, amra_rachid@yahoo.fr, harachid.ing@gmail.com
SET laboratory, Department of Electronic, Saad Dahleb Blida University, Algeria
ABSTRACT The purpose of this work is
analysis and evaluation of performance of parallel
concatenated codes (parallel turbo codes) or iterative
This work focuses on the elements causing the decoding for error probability BER as compared with the
degradation of a signal transmitted through a nonlinear Viterbi decoding.
satellite channel, limited bandwidth. The amplification of
the satellite often operates near the saturation point. It 2. SYSTEM DESCRIPTION
introduces the nonlinear distortion amplitude (conversion
AM / AM) and phase (conversion AM / PM). This leads to The block diagram of the chain of digital satellite
degradation of performance which are analyzed and transmission adopted by the simulation is given in figure
evaluated through computer simulation. This simulation 1.
is achieved through modeling of different devices in the Instead of using a simple convolutional code or a single
chain of transmission. Then, the work focuses on block code, it is also possible to combine them and create
correcting the received signal with concatenated codes a parallel concatenated code.
(parallel turbo codes) and iterative decoding. The turbo-parallel code shown in Figure 2 that we
consider in this work consists of two identical recursive
encoders and systematic separated by an interleaver. It
goes without saying that if we took three coders, we have
1. INTRODUCTION two interleavers and so on.
Because of the increase experienced by requests for
services by satellite, the transmission channel is limited in emitted parallel MPSK
both bandwidth and power. To cope with these demands, signal turbo code modulation
(PCCC)
it is necessary to use the spectrum more efficiently. And
it is also necessary to operate the amplifiers satellites TWT
devices (Traveling Wave Tubes TWT) at the point of
saturation or near the saturation point for the efficient use
received MPSK AWGN
of power output. Iterative
demodulation
signal decoding
These amplifiers introduce two types of distortion on the PCCC
output signal affecting its amplitude and phase [1] [2].
This leads to the existence of interference in each satellite
channel. In addition, spread spectrum beyond the channel Figure 1. Model of satellite system transmission
is a source of radio interference between adjacent
channels. Therefore, the quality of transmission is
degraded.
When a sequence of symbols dk arrives at the
This work focuses on the parallell convolutional encoder, it passes through two parallel steps. The first
concatenated codes. This new form of concatenation corresponds to the first encoder to upstairs. This step is
combined with iterative decoding has given rise to a new simply the convolutional coding of this sequence. The
class of error correcting codes: the Turbo-codes, input sequence goes in parallel with the encoder lower
introduced in 1993 by Claude Berrou and Alain Glavieux after having been interleaved.
[3] who first introduced a turbo decoder to transmit data
at less than 1 dB of the Shannon limit with an error rate
less than 10-5 [4].

2. dK
If we denote by m (t) modulated wave, n (t) the downlink
noise; the signal at the reception of earth station is:
interlevear
r(t)=m(t)+n(t) (4)
P
The amplifiers of the satellite are operating most
often near the saturation point, area, where he expressed
his best performance in power. Whatever the technology
used, amplification introduces two types of distortions:
-Distortion of the signal output due to saturation of the
P : Puncturing matrix amplifiera"AM/PM".
-Distortion of the phase of the output signal based on
Fig 2. Turbo Codeur changes in the signal input "AM / PM". These distortions
Figure 2. Parallel turbo encoder. are translated by:
Parallèle.
-Interference between symbols, which are non-linear and
The purpose of puncturing, (we use case), is to remove
cannot be eliminated by a simple filtering.
some parity symbols to vary the coding rate. If we
- Spectrum spreading due to a change in the envelope of
consider the parallel concatenation of two systematic
the modulated signal as it passes by a non-linear device.
encoders whose coding rate is [5]:
Note by  (t) and (t) respectively, the amplitude and
and phase of the complex envelope mc (t) of the modulated
signal e (t):
Where:
The overall rate of turbo encoder is:
(1) m(t) = a(t) cos ( 2fot ) – b(t) sin( 2fot )
– –
Where:
a (t) = 
n
an (t- nT) and b (t) = n
bn (t- nT)
b: represents input information. mc (t) = (t) exp [j(t)]
V1: output of first encoder.
V2: output of second encoder.
 (t) = [a2(t) + b2(t) ]1/2 and (t) = tan-1[b(t) / a(t)]
Subtraction, the denominator, is due to the fact that the The signal output of the device will have nonlinear
systematic symbols are transmitted only once. This complex envelope yc(t) which can be written according to
equation is also written the expression of Salleh [7]:
(2)
Yc=([(t)]expj((t)+j[(t)] (5)
In our case of figure 2, the coding rates R1and R2 are A [.] is the function of conversion AM/AM, and  [.] the
both equal to 1 / 2. The overall rate of our turbo encoder conversion AM/PM.
is without puncturing equal to1/ 3. Where:
The output signal of the encoder blocks attacks A ( ) = et  ( ) =
modulation. Of course, the type of modulation used is the
MPSK. According to equation 3, the modulated signal
takes the form: The signal at the output of the amplifier is given by:
2E expj(2fot+i (t)) y(t)=A[m(t)]cos2fot+(t)+[m(t)] (8)
mi(t)= (3)
T
The reduced coefficients of functions A [.]  and [.] to
Where: the TWT are:
E is the energy per symbol, and T is the duration of the mA = 2 nA = 1 m = 2.77 n = 6.25
symbol.
i (t) = 2i / M and M represents the number of states.
The general structure of a parallel iterative turbo decoder
The space sector is represented by the TWT where, entry is shown in figure 3, [7] [8].
is the emitted modulated wave. The output will be
corrupted at downlink by the AWGN noise.

3. Figure 3. Iterative decoding of parallel turbo encoder.
3. RESULTS OF SIMULATION
A comparison of the performance of convolutional codes Figure 5. Quality evaluation of QPSK transmission
with parallel those of a simple convolutional code for the for 6 iterations, block size N = 1024 and different
BER was performed. At the reception, the signal is constraint lengths.
decoded using the iterative decoder. It is expected
therefore that the system performance is improved. The choice of length N blocks of the interleaver is an
Figure 4 presents the results of a simulated satellite important parameter in the design of turbo codes where it
channel using a back entrance of 0 dB and performs a plays the role of interleaver length. For this reason we
comparison between cases of transmission of an iterative proposed the simulation of a transmission chain using a
decodingandViterbidecoding. turbo-parallel code, QPSK modulation and an interleaver
Given the results, the parallel turbo encoder that we used size N of the variable. The simulation results are
(PCCCP) provides quite satisfactory performance, it presented by figure 6.
provides a low error rate compared to a Viterbi decoding.
.
0
10
PCCC
CONV
-1
10
-2
10
TEB
-3
10
-4
10
-5
10
0 2 4 6 8 10 12
Eb/No (dB)
Figure 4. Quality evaluation of QPSK transmission Figure 6. Quality evaluation of QPSK transmission
for 6 iterations. for 6 iterations, and different length of block interleaver.
This simulation gives us the opportunity to study and According to the figure above, there is a significant
evaluate the effect of different parameters such as improvement in bit error rate with increasing length of
constraint length, length of block interleaving, number of the interleaving.
iterations of the decoder and puncturing on the
performance of turbo codes. The importance of iterative decoding is concentrated in
Figure 5 presents the results of a simulated satellite the iterative decoding process that allows continuous
channel using a drop of input power of 0 dB. We improvement of the BER at each iteration. To illustrate
evaluated the effect of the length constraint on the perfectly the dominant role of the number of iterations in
performance of turbo code. For that we have given determining the performance of turbo codes, we
varying values to the constraint length K of encoders simulated the transmission chain for various numbers of
RSC's turbo encoder which is our. iterations ranging from 2 to 6, as shown in figure 7.
It is found that the received signal quality improves
with increasing constraint length K. but this increase must
be controlled, given the complexity decoding. So we can
say that the choice of the length plays a fundamental role
in the design of a turbo code.

4. linearity in amplitude and phase leading to the
degradation of transmission quality. Then we evaluated
the performance of a parallel turbo code under different
transmission effects.
The parallel turbo code is the code that performs best
decoding robustness, he exhibited against the Viterbi
decoding is closest to the limit fixed by the fundamental
theorem of Shannon.
It was verified that it is possible to improve the
performance of parallel turbo code by varying the
parameters they define are: constraint length, block size
interleaving and encoding rate
For future work, we can offer for example the use of
hybrid schemes of turbo coding, or the application of new
Figure 7. Quality evaluation of QPSK transmission techniques interleaving.
increasing number of iterations.
REFERENCES
The simulation results listed in Figure 7 show that it is
possible to verify that the higher the number of iterations, [1] K.Konstantinides, K.Yao, "Modelling and
the greater the transmission performance improves. equalization of nonlinear bandlimited satellite channels,"
IEEE, pp. 1622-1626, 1986.
Evaluate the effect of puncturing on the performance of [2] S.Benedetto, E.Biglieri,"Nonlinear equalization of
turbo code, we made two types of puncturing at the end digital satellite channels," IEEE Journ. Select. Areas
Commun. Vol. Sac-1, n°1, pp. 57-62, January 1983.
for a code rate R=1/2 then R= 2/3.
[3] R.Chaggara, " les modulations à phase continue pour
The simulation results are presented in figure 8. la conception d’une forme d’onde adaptative, application
aux futures systèmes multimédia par satellite en bande
Ka" Thèse, spécialité: télécommunication et traitement
de signal, ENST, France, 2004.
[4] C.Berou and A. Glavieux, " Near optimum error
correcting coding and decoding: turbo code. IEEE
Transactions on Communications, 44, October 1996.
[5] Grégory Royer ‘’Évaluation des entrelaceurs au sein
des Codes Turbo par simulations’’, Thèse, Spécialité :
Génie Électrique, Université De Montréal, Ecole
Polytechnique De Montréal, Canada 2000.
[6] A.Adel, M.Saleh, "Frequency-independent and
frequency-dependent nonlinear models of TWT
amplifiers», IEEE Trans. Commun., vol. COM-29, 3 pp.
1715-1720, November 1981.
[7] G.Montorsi, «Design of fixed- point iterative
decoders for concatenated codes with interleavers ",
IEEE Journal on Selected Area in Communication, pp-
871-822, Vol.19 no 05. May 2001.
Figure 8. Quality evaluation of QPSK transmission [8]J.Boutros " les turbo codes parallèles et séries et
for 6 iterations, block length N = 1024 and different décodage SISO itératif et performances ML", Octobre
code rate. 1998.
From the above figure, it is found that the BER in the
case of a turbo code of rate R = 1 / 3 (without puncturing)
is better than using R = 1 / 2 (with puncturing), which
exhibits at the same time, better performance than that of
R= 2/ 3. Thus increasing the level of puncturing
introduced a performance degradation of the turbo code.
This is due to the lack of protection of information bits
and lower weight of code words when the parity symbols
are removed periodically.
4. CONCLUSION
In this work we simulated a chain of transmission via a
satellite channel, where the amplifier (TWT) shows non-