Performances des turbo codes parallèles pour un canal satellite non linéaire
PERFORMANCES OF PARALLEL CONCATENATED CODES FOR NON LINEAR SATELLITE CHANNEL Leila Zine, Rachid Amraoui and Rachid Hadj Ameur Zine.email@example.com, firstname.lastname@example.org, email@example.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 iterativeThis work focuses on the elements causing the decoding for error probability BER as compared with thedegradation of a signal transmitted through a nonlinear Viterbi decoding.satellite channel, limited bandwidth. The amplification ofthe satellite often operates near the saturation point. It 2. SYSTEM DESCRIPTIONintroduces the nonlinear distortion amplitude (conversionAM / AM) and phase (conversion AM / PM). This leads to The block diagram of the chain of digital satellitedegradation of performance which are analyzed and transmission adopted by the simulation is given in figureevaluated through computer simulation. This simulation 1.is achieved through modeling of different devices in the Instead of using a simple convolutional code or a singlechain of transmission. Then, the work focuses on block code, it is also possible to combine them and createcorrecting 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 forservices by satellite, the transmission channel is limited in emitted parallel MPSKboth bandwidth and power. To cope with these demands, signal turbo code modulation (PCCC)it is necessary to use the spectrum more efficiently. Andit is also necessary to operate the amplifiers satellites TWTdevices (Traveling Wave Tubes TWT) at the point ofsaturation or near the saturation point for the efficient use received MPSK AWGNof power output. Iterative demodulation signal decodingThese amplifiers introduce two types of distortion on the PCCCoutput signal affecting its amplitude and phase  .This leads to the existence of interference in each satellitechannel. In addition, spread spectrum beyond the channel Figure 1. Model of satellite system transmissionis a source of radio interference between adjacentchannels. Therefore, the quality of transmission isdegraded. When a sequence of symbols dk arrives at the This work focuses on the parallell convolutional encoder, it passes through two parallel steps. The firstconcatenated codes. This new form of concatenation corresponds to the first encoder to upstairs. This step iscombined with iterative decoding has given rise to a new simply the convolutional coding of this sequence. Theclass of error correcting codes: the Turbo-codes, input sequence goes in parallel with the encoder lowerintroduced in 1993 by Claude Berrou and Alain Glavieux after having been interleaved. who first introduced a turbo decoder to transmit dataat less than 1 dB of the Shannon limit with an error rateless than 10-5 .
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 theP : 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 : 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 ( 2fot ) – b(t) sin( 2fot ) – – 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 : (2) Yc=([(t)]expj((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 expj(2fot+i (t)) y(t)=A[m(t)]cos2fot+(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) = 2i / 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,  . is the emitted modulated wave. The output will be corrupted at downlink by the AWGN noise.
Figure 3. Iterative decoding of parallel turbo encoder. 3. RESULTS OF SIMULATIONA comparison of the performance of convolutional codes Figure 5. Quality evaluation of QPSK transmissionwith parallel those of a simple convolutional code for the for 6 iterations, block size N = 1024 and differentBER was performed. At the reception, the signal is constraint lengths.decoded using the iterative decoder. It is expectedtherefore 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 itchannel using a back entrance of 0 dB and performs a plays the role of interleaver length. For this reason wecomparison between cases of transmission of an iterative proposed the simulation of a transmission chain using adecodingandViterbidecoding. turbo-parallel code, QPSK modulation and an interleaverGiven 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 significantevaluate the effect of different parameters such as improvement in bit error rate with increasing length ofconstraint length, length of block interleaving, number of the interleaving.iterations of the decoder and puncturing on theperformance 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 continuouschannel using a drop of input power of 0 dB. We improvement of the BER at each iteration. To illustrateevaluated the effect of the length constraint on the perfectly the dominant role of the number of iterations inperformance of turbo code. For that we have given determining the performance of turbo codes, wevarying values to the constraint length K of encoders simulated the transmission chain for various numbers ofRSCs turbo encoder which is our. iterations ranging from 2 to 6, as shown in figure 7. It is found that the received signal quality improveswith increasing constraint length K. but this increase mustbe controlled, given the complexity decoding. So we cansay that the choice of the length plays a fundamental rolein the design of a turbo code.
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 ispossible to verify that the higher the number of iterations,  K.Konstantinides, K.Yao, "Modelling andthe 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  S.Benedetto, E.Biglieri,"Nonlinear equalization ofturbo 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.  R.Chaggara, " les modulations à phase continue pourThe 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.  C.Berou and A. Glavieux, " Near optimum error correcting coding and decoding: turbo code. IEEE Transactions on Communications, 44, October 1996.  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.  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.  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 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 thecase of a turbo code of rate R = 1 / 3 (without puncturing)is better than using R = 1 / 2 (with puncturing), whichexhibits at the same time, better performance than that ofR= 2/ 3. Thus increasing the level of puncturingintroduced a performance degradation of the turbo code.This is due to the lack of protection of information bitsand lower weight of code words when the parity symbolsare removed periodically. 4. CONCLUSIONIn this work we simulated a chain of transmission via asatellite channel, where the amplifier (TWT) shows non-