Turbo Codes

Turbo codes (Berrou et al., 1993) combine two recursive systematic convolutional (RSC) encoders connected by a pseudo-random interleaver Π. Rate 1/3 for rate-1/2 component codes. The decoder uses SISO (Soft-Input Soft-Output) decoding (BCJR algorithm) iteratively: L^(i)(u_k) = L_c · L_ch(u_k) + L_e1^(i) + L_e2^(i) Each decoder passes extrinsic LLRs to the other. After ~8 iterations, performance approaches within 0.5 dB of the Shannon limit. The EXIT chart shows information exchange between decoders converging to the (1,1) corner.