Turbo Decoding of High Performance Error-Correcting Codes via Belief Propagation

摘要

We studied AWGN coding theorems for ensembles of coding systems which are built from fixed convolutional codes interconnected with random interleavers. We call these systems turbo-like codes and they include as special cases both the classical turbo codes and the serial concatenation of interleaved convolutional codes. We offered a general conjecture about the behavior of the ensemble (maximum-likehood decoder) word error probability as the word length approaches infinity. We proved this conjecture for a simple class of rate l/q serially concatenated codes where the outer code is a q-fold repetition code and the inner code is rate 1 convolutional code with transfer function 1/(1+D). We call these codes 'RA' (repeat and accumulate) codes. This was the first rigorous proof of a coding theorem for turbo-like codes.