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NEWCOM, Department 1-SPW1 meeting ENSEA , April 28th, 2005

Design and Performance of Rate Compatible-SCCC Alexandre Graell i Amat †‡ , Guido Montorsi ‡ , Francesca Vatta* † Universitat Pompeu Fabra. Barcelona, Spain ‡ Politecnico di Torino. Torino, Italy * Universit à di Trieste. Trieste, Italy. NEWCOM, Department 1-SPW1 meeting

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NEWCOM, Department 1-SPW1 meeting ENSEA , April 28th, 2005

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  1. Design and Performance of Rate Compatible-SCCCAlexandre Graell i Amat†‡, Guido Montorsi‡, Francesca Vatta*†Universitat Pompeu Fabra. Barcelona, Spain‡ Politecnico di Torino. Torino, Italy* Università di Trieste. Trieste, Italy NEWCOM, Department 1-SPW1 meeting ENSEA, April 28th, 2005

  2. Motivations • Standard SCCC for high-rates: Outer Encoder Inner Encoder P Politecnico di Torino – Universitat Pompeu Fabra

  3. Motivations • Standard SCCC for high-rates: High-rate Encoder Inner Encoder P • If the interleaver size is fixed different information block sizes for different rates • For very high rates, the increasing value of the outer code rate causes an interleaver gain penalty error floor Politecnico di Torino – Universitat Pompeu Fabra

  4. Motivations • Standard Rate-compatible SCCC: • Rate-compatibility restricts puncturing to the inner encoder • In general, the rate of the inner encoder is restricted to be Ri  1the overall code rate is at mostRo Outer Encoder Inner Encoder P Pi Politecnico di Torino – Universitat Pompeu Fabra

  5. A new class of SCCC RC-SCCC • The inner code may be punctured beyond the unitary rate RSCCC may be greater than the outer code rate • Puncturing is split between systematic and parity bits: MUX u Psi Outer Encoder Inner Encoder Po P Ppi rs: systematic permeability rp: parity permeability Politecnico di Torino – Universitat Pompeu Fabra

  6. C’’o C’o Outer Encoder Po P Psi MUX C’i Inner Encoder Ppi A new class of SCCC • Performance depend on puncturing patterns Po,Psi,Ppi rsand rp should be properly selected • We propose design criteria of this new class of SCCC by deriving the upper bounds to the error probability Politecnico di Torino – Universitat Pompeu Fabra

  7. Upper bounds to the error probability • We obtain: • The dominant contribution to the error probability for (asymptotic with N) is the largest exponent of N, aM. Politecnico di Torino – Universitat Pompeu Fabra

  8. Upper bounds to the error probability • For recursive inner encoder: and • h(aM): weight associated to the highest exponent of N Politecnico di Torino – Universitat Pompeu Fabra

  9. Upper bounds to the error probability • We obtain: • do’f: free distance of C’o • do’’(do’f): minimum weight of C’’o code sequences corresponding to a C’o code sequence of weight do’f • di’f,eff: effective free distance of C’i • h(3)m: minimum weight of C’i sequences generated by weight 3 input sequences Politecnico di Torino – Universitat Pompeu Fabra

  10. C’’o C’o Outer Encoder Po P Psi MUX C’i Inner Encoder Ppi Upper bounds to the error probability • do’f: free distance of C’o • do’’(do’f): minimum weight of C’’o code sequences corresponding to a C’o code sequence of weight do’f • di’f,eff: effective free distance of C’i • h(3)m: minimum weight of C’i sequences generated by weight 3 input sequences Politecnico di Torino – Universitat Pompeu Fabra

  11. Upper bounds to the error probability • We obtain: • do’f: free distance of C’o • do’’(do’f): minimum weight of C’’o code sequences corresponding to a C’o code sequence of weight do’f • di’f,eff: effective free distance of C’i • h(3)m: minimum weight of C’i sequences generated by weight 3 input sequences Politecnico di Torino – Universitat Pompeu Fabra

  12. Upper Bound to the error probability • Then, Pb(e) (asymptotic with respect to N): • For large Eb/N0 BER performance is given by: do’f even do’f odd Politecnico di Torino – Universitat Pompeu Fabra

  13. Upper Bound to the error probability • Design considerations: • Po should be chosen to optimize C’o distance spectrum • Psi and Ppi should be chosen so that h(am ) and hm are maximized • Ppi must be optimized to yield the best C’i IOWEF • Psi must be selected to optimize do’’(do’f ) Psi turns out to be interleaver dependent Politecnico di Torino – Universitat Pompeu Fabra

  14. Rate-compatible SCCC • We designed well-performing rate-compatible SCCC following the aforementioned considerations • Psi to optimize do’’(do’f ) • Ppi to optimize Ci’ IOWEF • We used a searching algorithm that works incrementally, fulfilling the rate-compatible restriction, so that the punctured positions for a given outer rate are also punctured for all higher rates. Politecnico di Torino – Universitat Pompeu Fabra

  15. The SCCC Scheme MUX u Psi Rate-1/2 4 state Rate-1/2 4 state Fix punct. P Ppi constituent codes outer code puncturing do’f=3 do’f=4 Politecnico di Torino – Universitat Pompeu Fabra

  16. rp =2/30 rp =4/30 rp =6/30 rp =8/30 rp =10/30 Performance Bounds Bounds of Rate-2/3 SCCC for several rp N=200. Po,1 Politecnico di Torino – Universitat Pompeu Fabra

  17. rp =2/30 rp =4/30 rp =6/30 rp =8/30 rp =10/30 Performance Bounds Bounds of Rate-2/3 SCCC for several rp N=200. Po,2 Politecnico di Torino – Universitat Pompeu Fabra

  18. rp=2/30. Simulation rp =2/30. Bound rp =4/30. Simulation rp =4/30. Bound rp =8/30. Simulation rp =8/30. Bound rp =10/30. Simulation rp =10/30. Bound Simulation Results Performance of Rate-2/3 SCCC for several rp N=200. Po,1 Politecnico di Torino – Universitat Pompeu Fabra

  19. rp=2/30. Simulation rp =2/30. Bound rp =4/30. Simulation rp =4/30. Bound rp =8/30. Simulation rp =8/30. Bound UMTS PCCC SCCC (VTC’01) Simulation Results Performance of Rate-2/3 SCCC for several rp N=2000. Po,1 Politecnico di Torino – Universitat Pompeu Fabra

  20. rp =4/222. Simulation rp =4/222. Bound rp =10/222. Simulation rp =10/222. Bound rp =16/222. Simulation rp =16/222. Bound UMTS PCCC Simulation Results Performance of Rate-9/10 SCCC for several rp N=2000. Po,1 Politecnico di Torino – Universitat Pompeu Fabra

  21. 22/222 20/222 18/222 16/222 14/222 12/222 10/222 8/222 6/222 4/222 2/222 rp Simulation Results Performance versus rp for several Eb/N0 . R=9/10. N=2000. Po,1 Politecnico di Torino – Universitat Pompeu Fabra

  22. SCCC (10 it.) PCCC (8 it.) LDPC (50 it.) Simulation Results FER Performance comparison. N=428 Politecnico di Torino – Universitat Pompeu Fabra

  23. Conclusions • Derived lower bound to the error probability of a new class of SCCC • Derived suitable design guidelines • Derived optimal Rate-compatible SCCC families • The proposed scheme offers good performance for low to moderate block lengths in a large range of rates • The interleaver gain for low rates is kept also in the case of heavy puncturing • This code structure has been proposed as a candidate coding scheme for ESA MHOMS Politecnico di Torino – Universitat Pompeu Fabra

  24. Open Problems • Convergence analysis EXIT charts and Density Evolution Techniques are difficult to apply • We are open to cooperations with other groups!!! Politecnico di Torino – Universitat Pompeu Fabra

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