1. A Novel technique for Improving the Performance of Turbo Codes using Orthogonal signalling, Repetition and Puncturing by Narushan Pillay Supervisor: Prof. HongJun Xu

2. Slide 2 © CSIR 2006 www.csir.co.za Breakdown of Presentation Structure of a new scheme Repeat-Punctured Superorthogonal Convolutional Turbo Code (RPSCTC) Encoder Procedure of Encoding – Parallel Concatenated Superorthogonal Recursive Convolutional Constituent Codes Structure of the RPSCTC Decoder Procedure for Decoding utilizing the MAP algorithm Importance of Interleaving and its effects

3. Slide 3 © CSIR 2006 www.csir.co.za Breakdown of Presentation A variation of the scheme – Dual-Repeat-Punctured Turbo Code (DRPSCTC) Performance Evaluation for RPSCTC using transfer function bounding techniques Simulation Results and Bounds for AWGN and Rayleigh Fading Channels – RPSCTC, DRPSCTC versus an existing scheme Superorthogonal Convolutional Turbo Codes (SCTC)

4. Slide 4 © CSIR 2006 www.csir.co.za Encoding Structure of RPSCTC Structure that of a Parallel Concatenated Code (PCC) Two constituent codes, two parity sequences Separated by repeat and interleaver structures Puncturing mechanism to control the code rate Figure 1. Low-level Encoding structure of RPSCTC

5. Slide 5 © CSIR 2006 www.csir.co.za Procedure of Encoding for RPSCTC More detailed structure of the RPSCTC encoder Identical constituent Superorthogonal Recursive Convolutional encoders Figure 2. Detailed structure of encoder

6. Slide 6 © CSIR 2006 www.csir.co.za Structure of RPSCTC Decoder Two constituent Maximum a-posteriori (MAP) decoders Mutual exchange of soft extrinsic information Cooperative network Figure 3. Structure of the Decoder

7. Slide 7 © CSIR 2006 www.csir.co.za Procedure for Decoding for RPSCTC The MAP algorithm Somewhat like the Viterbi algorithm but trellis traversed in two directions. Figure 4. The MAP algorithm

8. Slide 8 © CSIR 2006 www.csir.co.za Procedure for Decoding for RPSCTC Starting with the log-likelihood ratio (LLR) With the likelihood ratios defined by …………….........……………..(1) …………….........……………..(2) …………….........……………..(3)

9. Slide 9 © CSIR 2006 www.csir.co.za Procedure for Decoding for RPSCTC Extrinsic information from decoder 1 given by Extrinsic information from decoder 2 given by ……………...………..(4) ……………..….…….…..(5)

10. Slide 10 © CSIR 2006 www.csir.co.za Interleaving Conventional turbo coding frame length set equal to interleaver size. Increase in frame length – performance increase Limit on frame length: Transmission delay Decoding delay Hardware delay Use repeat block prior to interleaving Frame length constant – larger interleaver size – better performance Figure 5. Effect of Interleaving

11. Slide 11 © CSIR 2006 www.csir.co.za Interleaving Figure 6. Effect of Interleaving Repeat ‘L’ block allows for the use of a larger interleaver. Spectral thinning Weight one sequence – weight two sequence – high weight turbo codeword.

12. Slide 12 © CSIR 2006 www.csir.co.za Interleaving Weight two sequence – weight four sequence – still yields a high weight turbo codeword.

13. Slide 13 © CSIR 2006 www.csir.co.za Performance Evaluation of RPSCTC Obtain the state transition matrix from state diagram using equation (6) Transfer function can be expressed as equation (7): ……………..…..(6) …………….........……..(7)

14. Slide 14 © CSIR 2006 www.csir.co.za Performance Evaluation of RPSCTC Since the transfer function is defined by equation (8), and, …………….........………..(8) ……………...........…………..(9)

15. Slide 15 © CSIR 2006 www.csir.co.za Performance Evaluation of RPSCTC Then the probability of producing a codeword fragment of weight d given a random input sequence of weight i is given by equation (10) for component encoder 1 and equation (11) for component encoder 2. ………..........(10) ……………..............……..(11)

16. Slide 16 © CSIR 2006 www.csir.co.za Performance Evaluation of RPSCTC Equation (12) is used to achieve the union bound where, for an AWGN channel. ……..(12) ……………...........……..(13)

17. Slide 17 © CSIR 2006 www.csir.co.za Performance Evaluation of RPSCTC and p 2 (d) is given by (14) for side-information (SI) or equation (15) for no side-information (NSI) for a Rayleigh fading channel, where and ……………………..….….(14) ……………....…....(15) …….……...…...(16)

18. Slide 18 © CSIR 2006 www.csir.co.za Another scheme Figure 7. DRPSCTC Encoder Structure of the Dual-Repeat-Punctured Turbo Code (DRPSCTC) encoder Dual repetition prior to encoding Puncturing at both output branches

19. Slide 19 © CSIR 2006 www.csir.co.za Another scheme Decoder for DRPSCTC Slightly greater complexity Better performance Figure 8. DRPSCTC Decoder

20. Slide 20 © CSIR 2006 www.csir.co.za Simulation Results and Bounds Figure 9. SCTC and RPSCTC simulation m=2, m=4 for the AWGN channel

21. Slide 21 © CSIR 2006 www.csir.co.za Simulation Results and Bounds Figure 10. RPSCTC simulation m=2, m=4 in the AWGN channel

22. Slide 22 © CSIR 2006 www.csir.co.za Simulation Results and Bounds Figure 11. SCTC, RPSCTC vs DRPSCTC m=4 AWGN channel q =1,2 for component encoders for DRPSCTC

23. Slide 23 © CSIR 2006 www.csir.co.za Simulation Results and Bounds Figure 12. SCTC,RPSCTC, DRPSCTC distance spectrum N=100, R=1/15

24. Slide 24 © CSIR 2006 www.csir.co.za Simulation Results and Bounds Figure 13. SCTC and RPSCTC simulation m=2, m=4 flat Rayleigh fading channel