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Improving the Performance of Turbo Codes by Repetition and Puncturing

Improving the Performance of Turbo Codes by Repetition and Puncturing

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Improving the Performance of Turbo Codes by Repetition and Puncturing

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  1. Improving the Performance ofTurbo Codes byRepetition and Puncturing Youhan Kim March 4, 2005

  2. Outline • Conventional Turbo Codes • Motivation • Proposed Turbo Coding Scheme • Codeword Distance Spectrum • Iterative Decoder Structure • Simulation Results • Conclusions

  3. Turbo Codes • Parallel Concatenated Convolutional Code • Pseudo-random interleaver between RSC1 and RSC2 • Reduce the chance of both RSC1 and RSC2 generating low weight parity sequences at the same time  Codeword distance spectrum thinning Turbo Code Encoder

  4. Turbo Codes • Near channel capacity performance achieved when very large interleaver is used • Near ML performance can be achieved usingiterative decoder as well

  5. Interleaver Size • Conventional Turbo code • Interleaver gain • Performance enhanced as interleaver size increases • Interleaver size = Frame length  Require very large frame size for good performance • Limit on frame length due to • Transmission delay • Decoding delay • Hardware complexity  Unsuitable for • Short frames • Applicationsrequiringvery low error rate Interleaver gain

  6. Motivation • Why limit ourselves to the case ofinterleaver size = frame length? • Design turbo codes withinterleaver size > frame length • For short frames,  Large interleaver gain even with short transmission delay • For large frames,  Achieve very low error rate • Reuse existing encoder/decoder hardware available for conventional turbo codes

  7. Repeat-Puncture Turbo Code(RPTC) • Repeateach bit L times prior to interleaving • Interleaver size = L x Frame length • Puncture RSC2 parity sequence tocontrol code rate • Asymmetry between CC1 and CC2

  8. Benefits of Repeating • Greater interleaver gain • Low weight parity sequences generated byweight 2 input sequences dominate the performance of turbo codes [Benedetto96, Divsalar96]

  9. Benefits of Repeating • RPTC: RSC2 encodes sequence of weight 2L • In the case of weight 1 input sequence with L=2

  10. Puncturing Pattern • Puncture RSC2 parity sequence to control code rate • Simple puncturing pattern • Transmit the first n bits out of every L bits • E.g.) L=4, n=2 • Easy to compute codeword distance spectrum

  11. Performance Analysis • Transition matrix approach for Turbo codes with puncturing [Kousa02] • Transition matrix for RSC • Encoder state transition over 2 input bits

  12. Performance Analysis (2) • Assume both RSC encoders start and end in the all-zero state • Component code 1 • Encoder state transition of CC1 over entire frame • Conditional weight enumerating function

  13. Performance Analysis (3) • Component code 2 • Period transition matrix • Only first n bits out of L bits are transmitted • Encoder state transition of CC2 over entire frame • Conditional weight enumerating function

  14. Performance Analysis (4) • Assuming uniform interleaver, • Conditional weight enumerating function of RPTC • Union bound on FER

  15. Codeword Distance Spectrum of RPTC • Uniform Interleaver • Code rate = 1/3 (n=1) • RSC polynomial: (1+D2)/(1+D+D2)

  16. Codeword Distance Spectrum of RPTC • More than 10 fold decrease in Adfor L=2

  17. Union Bound • Uniform interleaver • Code rate = 1/3 (n=1) • N=128

  18. Iterative Decoder: Factor Graph

  19. Simulation Parameters • RSC polynomial: (1+D2)/(1+D+D2) • Code rate = 1/3 (n=1) • Max. 40 iterations • Non-fading channel

  20. Performance with Uniform Intlv. • SNR gain at FER = 10-3 • N=256: 1.0 dB • N=1024: 1.5 dB • N=8192: 1.9 dB • SNR gain at BER = 10-5 • N=256: 0.7 dB • N=1024: 0.6 dB

  21. Performance with Prime Intlv. • Note: Prime interleaver is optimized for conventional Turbo codes

  22. Price for Improvement • Increase in encoder and decoder complexity • Memory • Computational requirement • Hardware complexity • Many systems support multiple frame lengths • Short frames may use larger interleaver structures already available at the transmitter/receiver Memory requirement not a problem

  23. Conclusions • Repeat-Puncture Turbo Code • Use simple repetition and puncturing • Repeater: Interleaver size > Frame length • Puncturer: No loss in code rate • Improved codeword distance spectrum • Iterative decoding • Superior performance than conventional turbo codesfor moderate to high SNRs • Suitable for • Improving the performance of short frames in systems supporting multiple frame lengths • Applications requiring very low error rate

  24. Thank you!