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

Applicationturbo code terminationpolynomialsrates CCSDSbinary, 16-state tail bits23, 33, 25, 37 1/6, 1/4, 1/3, 1/2 3Gbinary, 8-state tail bits13, 15, 171/4, 1/3, 1/2 DVB-RCSduo- binary, 8-state circular15, 131/3 up to 6/7 DVB-RCTduo- binary, 8-state circular15, 131/2, 3/4 Inmarsat (M4)binary, 16-state no23, 351/2 Eutelsat (Skyplex) duo- binary, 8-state circular15, 134/5, 6/7 Current known applications of convolutional TCs Others: Echostar (Broadcom), , …

The TCs used in practice

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 …

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

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

About the Rayleigh channel Duo-binary 8-state TC

The ways we are investigating to reach FERs  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 3 rd dimension Example

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

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

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

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