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Turbo codes for short and medium block length: the state of the art

Turbo codes for short and medium block length: the state of the art. Department 1 Paris, June 25, 2004. Claude Berrou, Catherine Douillard GET-ENST Bretagne/PRACOM/CNRS 2658, Brest, France. Application. turbo code. termination. polynomials. rates. CCSDS. binary, 16-state. tail bits.

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Turbo codes for short and medium block length: the state of the art

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  1. Turbo codes for short and medium block length: the state of the art Department 1 Paris, June 25, 2004 Claude Berrou, Catherine Douillard GET-ENST Bretagne/PRACOM/CNRS 2658, Brest, France

  2. Application turbo code termination polynomials rates CCSDS binary, 16-state tail bits 23, 33, 25, 37 1/6, 1/4, 1/3, 1/2 3G binary, 8-state tail bits 13, 15, 17 1/4, 1/3, 1/2 DVB-RCS duo-binary, 8-state circular 15, 13 1/3 up to 6/7 DVB-RCT duo-binary, 8-state circular 15, 13 1/2, 3/4 Inmarsat (M4) binary, 16-state no 23, 35 1/2 Eutelsat (Skyplex) duo-binary, 8-state circular 15, 13 4/5, 6/7 Current known applications of convolutional TCs Others: Echostar (Broadcom), 802.16, …

  3. The TCs used in practice

  4. Main progress in turbo coding/decoding since 1993 • Max-Log-MAP and Max*-Log-MAP algorithms • Sliding window • Duo-binary turbo codes • Circular (tail-biting) encoding • Permutations • Computation or estimation of Minimum Hamming distances (MHDs) • Stopping criterion • Bit-interleaved turbo coded modulation • …

  5. Typical performance Gaussian, Max-Log-MAP algorithm, 8 iterations, 4 or 5 bit-quantization

  6. Classical TC and LDPC R=1/3 R=5/6 R=9/10 Gaussian, 424 bits (53 bytes) (reference: ESA MHOMS project) TC is 16-state

  7. About the Rayleigh channel Duo-binary 8-state TC

  8. The ways we are investigating to reach FERs  10-9 • adopt 16-state duo-binary TCs and try to increase the MHD by 25%,by improving permutations • keep 8-state duo-binary TCs and try to increase the MHD by 100%,by introducing a clever 3rd dimension Example

  9. Adding a rate-1 third dimension Combining parallel and (double) serial concatenation 1-   1- Pre-existing turbo encoder • Patch: • a parallel to serial (P/S) multiplexer • permutation ' • rate-1 post-encoder

  10. Adding the rate-1 third dimension (to duo-binary TC) 1-   1- Pre-existing turbo encoder • Patch: • a parallel to serial (P/S) multiplexer • permutation ' • rate-1 post-encoder

  11. Simulation results (8-state DVB-RCS TC + patch) Max-Log-MAP component algorithm, 5 and 8 iterations

  12. Conclusions • not much left to gain in convergence • MHDs to be increased reasonably • also, practical limits to be determined (Rayleigh) • about complexity, latency, …

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