EFFECT OF THE INTERLEAVER TYPES ON THE PERFORMANCE OF THE PARALLEL CONCATENATION CONVOLUTIONAL CODES

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 12 No: 03 25 EFFECT OF THE INTERLEAVER TYPES ON THE PERFORMANCE OF THE PARALLEL CONCATENATION CONVOLUTIONAL CODES YahyaJasimHarbi M.Sc. Electronics and communications College of Engineering Electrical Engineering Department University of Kufa -Iraq yahyajasim@gmail.com Abstract-- In this paper, we study the performance of turbo codes with different types of interleaver. Various issues related to the code performance are investigated. These include the effect of the interleaver length, the interaction between the interleaver and the number of decoding iterations, and the effect of interchanging the interleaver between input and output. Simulation results show that some types of the interleavers can be very competitive to random interleaver for different frame lengths. Keywords-- Interleavers, PCCCs, Frame size, Iterative decoding, Bit error rate 1. INTRODUCTION: In a digital transmission system, error control is achieved by the use of a channel encoder at the transmitter and a corresponding decoder at the receiver. The aim is to ensure that the received information is as close as possible to the transmitted information. A well-known result from Information Theory is that a randomly chosen code of sufficiently large block length is capable of approaching channel capacity. However, the optimal decoding complexity increases exponentially with large block lengthup to a point where decoding becomes physically unrealizable. Turbo code (TC) is the name given to parallel concatenation with interleaving [1,2,4,6]. Simplified schematics of the turboencoder and decoder are shown in Fig.1. There are two convolutional encoders in parallel, which are usually taken tobe identical. Information bits are interleaved before being fed to the second encoder. The codeword in a turbo codeconsists of a frame of input bits (x 0 ) followed by the parity check bits from the first encoder (x 1 ) then the parity bits fromthe second encoder (x 2 ). Each of the M constituent encoders presents a parity sequence (xi) at its output.padding is used to append the proper sequence of bits in order to force all the encoders at theend of the frame to the all-zero state. The decoder works in an iterative way. The first decoder will decode the sequence and pass the hard decision togetherwith a reliability estimate of this decision to the next decoder after proper interleaving. The second decoder will utilizethe reliability estimates produced by the first encoder, and thus will have extra information for decoding. After a certainnumber of iterations are executed, a hard decision is made and the estimated sequence is delivered to the user. Severaldecoding algorithms have been proposed. If the Turbo code consists of more components, it is just a matter ofinserting the relevant de-interleaver decoder interleaver blocks. Note that thefinal decoder in the chain also has a hard-decision block associated with it to outputthe decoded bits. Successive iterations will use the extrinsic information from this iterationas a priori

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 12 No: 03 26 information. Extrinsic information is that information generated by thedecoders of this iteration, and is computed by removing the a priori information anddirect channel information from the iteration s a posteriori information. It is essentialthat only extrinsic information is passed between decoders and between iterations forcorrect operation of the Turbodecoder. Information source Fig.1.Basic turbo encoder structure Received Sequence DEMUX Pading Interleaver Decoder 1 Enc. 1 Enc. 2 Fig.2. Basic turbo decoder structure The interleaver plays a very importantpart in the construction of good Turbo codes. There are valid indications asto what makes a good x 0 x 1 x 2 De-interleaver Interleaver Decoder 2 Puncturing & P/S MUX De-interleaver To the channel x 2 x 1 x 0 Estimated Sequence interleaver; unfortunately, however, there is no comprehensiveexplanation or computable quantification of the effects of interleaver choice on the resultantturbo code [2,3,7]. Increasing the number of iterations (to some extent) reduces the significantly. This conclusion was based on the uniform and random interleavers. We examine this conclusion formatrix interleavers.first, we emphasize that there is a mutual benefit between the interleaver and the iterative decoder. A goodinterleaver is not advantageous without sufficient number of iterations, and, on the other hand, increasing the iterationsdoes not do much without good interleaving. 2. Results and Discussion The increase in size of the input frame size has an impact on theinterleaver size. When size of the interleaver increases it adds to thecomplexity of the design. It increases latency and the powerconsumption. For many applications such as speech transmissionrequires coding with shortframe length is desirable since it givesexcellent results with turbo coding having short- frame length.from the plot it is clear that random, helical and Berrou-Glavieux interleavers with long frame length (FS=1024) gives better performance at low number of iterations and Berrou-Glavieux interleaver gives better performance at high number of iterations (5 iterations) whereas for helical interleaver with short frame length system (FS=100) gives best results for Turbo codes at different Impact of various Frame/Interleaver size FS= 100,1024 on the performance of Turbo codes for (1-5) iterations and number of terminated frame errors =5 for AWGN Channel, for log-map-decoder for AWGN Channel are shown by the following figures3,4,5,6,7,8,9,10,11,12,13,14. Show how the performance oftheturbo code depends on the frame length (FS) and the interleaver type that used in the encoder. Itis observed from the simulation results that as interleaverframe/size increases SNR also increases but decreases andattained more error

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 12 No: 03 27 floor, thus Turbo code exhibit a betterperformance when frame length increasescomparing with other work [11]. Fig.3. Impact of Frame/Interleaver size FS=100 on AWGN Channel for log-map-decoder using random iterations. iterations. Fig.5. Impact of Frame/Interleaver size FS=100 on AWGN Channel for log-map-decoder using rectangular interleaver type, Where performance has not improved significantly with increasing the Fig.4. Impact of Frame/Interleaver size FS=1024 on AWGN Channel for log-map-decoder using random Fig.6. Impact of Frame/Interleaver size FS=1024 on AWGN Channel for log-map-decoder using rectangular interleaver type, Where performance has improved significantly with increasing the

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 12 No: 03 28 Fig.7. Impact of Frame/Interleaver size FS=100 on AWGN Channel for log-map-decoder using Barrelshifting interleaver type, Where performance has not improved significantly with increasing the 10-6 Fig.9. Impact of Frame/Interleaver size FS=100 on AWGN Channel for log-map-decoder using helical iterations (low number of iteration). Fig.8. Impact of Frame/Interleaver size FS=1024 on AWGN Channel for log-map-decoder using Barrelshifting interleaver type, Where performance has not improved significantly with increasing the Fig.10. Impact of Frame/Interleaver size FS=1024 on the performance of Turbo codes for (1-5) iterations and number of terminated frame errors=5 for AWGN Channel for log-map-decoder using helical interleaver type, Where performance has improved significantly with increasing the number of iterations (low number of iteration).

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 12 No: 03 29 Fig.11. Impact of Frame/Interleaver size FS=64 on AWGN Channel for log-map-decoder using Berrou- Glavieux interleaver type, Where performance has improved significantly with increasing the number of iterations (low number of iteration). Fig.13. Impact of Frame/Interleaver size FS=100 on AWGN Channel for log-map-decoder using square iterations. 10-6 Fig.12. Impact of Frame/Interleaver size FS=1024 on the performance of Turbo codes for (1-5) iterations and number of terminated frame errors=5 for AWGN Channel for log-map-decoder using Berrou-Glavieux interleaver type, Where performance has improved significantly with increasing the 10-6 Fig.14. Impact of Frame/Interleaver size FS=1024 on the performance of Turbo codes for (1-5) iterations and number of terminated frame errors=5 for AWGN Channel for log-map-decoder using square interleaver type, Where performance has improved significantly with increasing the number of iterations.

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 12 No: 03 30 3. CONCLUSIONS In this paper some of the building blocks of turbo codes, and thebasics of turbo codes have been described. Some of the recent developmentsof turbo codes have been introduced. Especially differentmethods of interleaving have been discussed. The reason for the focuson interleaving is that interleavers have a large influence on thefree distance. When the free distance of a turbo code increases, theerror floor performance improves. Interleavers can be divided into "random" and deterministic interleavers.mainly, deterministic interleavers have been discussed. A deterministicinterleaver is a permutation of an arranged manner. Thiscan make the analyses of the interleaver simpler. The result of a small turbo product code has been given. The interleaverwas replaced by a more general permutation and the resultsinvestigated. These codes were simulated in an AWGNenvironmentunder different signal to noise ratios. The graphs of theseexperiments showed that the original interleaver had the best performance and used the least iteration to estimate the correctcodewords. These experiments were only performed on small and long codes,and therefore the permutation possibilities are limited. From the plot it is clear that random, helical and Berrou-Glavieux interleavers with long frame length (FS=1024) gives better performance at low number of iterations and Berrou-Glavieux interleaver gives better performance at high number of iterations (5 iterations) whereas for helical interleaver with short frame length system (FS=100) gives best results for Turbo codes at different As a further work, by using additional interleaver, that may be improvement the performance of turbo code system and may be reducing the number of iteration and then that makes the computation much easier and the operation of the hardware system much faster. 4. REFERENCES: [1] C. Berrou, A. Glavieux, and P. Thitimasjshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes," in IEEE Transactions oncommunications, 44 (1996), pp. 1261 1271. [2] Maan A. Kousa, " Performance of Turbo Codes with matrix interleaver," The Arabian Journal for Science and Engineering, Volume 28, Number 2B, October 2003, pp. 211 220. [3] RavindraM.Deshmukh, and Dr. S.A..Ladhake, "Optimum Interleaver Design For Turbo Codes," International Journal of Computer Science and Applications Vol. 2, No. 1, April / May 2009, pp. 51 55. [4] YahyaJasimHarbi, "Performance Evaluation Of Turbo Code Encoding and Decoding," Al- Qadisiya Journal for Engineering Sciences, 2011 Volume 4-No.2,pp.112-121. [5] HalvorUtby, "A Survey on Turbo Codes and Recent Development," Master thesis, University of Bergen, Department of Informatics, December 4, 2006. [6] H. H. ABBAS, Simulation of Turbo-Encoder- Decoder Performance. Ph.D. thesis, Baghdad University, Oct. 2001. [7] M. C. Valenti, Iterative Detection and Decoding for Wireless Communications, Ph.D. thesis, Virginia Polytechnic Institute and State University, July 8, 1999. [8] S. Benedetto and G. Montorsi, "Generalized concatenated codes with interleavers," in Proc., Int. Symp.on Turbo Codes and Related Topics, (Brest, France), pp. 32-9, Sept. 1997. [9] J. Cheng, Iterative Decoding, Ph. D, Thesis, California Institute of Technology, Pasadena California, 1997.

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 12 No: 03 31 [10] S. A. Barbulescu, Iterative Decoding of Turbo Codes and Other Concatenated Codes, Univ. of South Australia, Feb. 1996. [11] Prof M. SrinivasaRao, Dr P. Rajesh Kumar, K. Anitha, and AddankiSrinu"Modified Maximum A Posteriori Algorithm For Iterative Decoding of Turbo codes" International Journal of Engineering Science and Technology (IJEST), Vol. 3 No. 8 August 2011.