Illuminating the structure of code and decoder of parallel concatenated recursive systematic (turbo) codes

A coding scheme (turbo codes) was proposed, that achieves almost reliable data communication at signal-to-noise ratios very close to the Shannon-limit. We show that the associated iterative decoder can be formulated in a simpler fashion by passing information from one decoder to the next using log-likelihood ratios as opposed to channel values that need to be normalized. Also no heuristically determined correction parameters are necessary for stable decoding. In addition, we can reduce the average number of iterations needed for the same BER performance by determining when further iterations achieve no more benefit. Furthermore, it seems that the trellis-termination problem appears non-trivial and we give a pragmatic suboptimal solution. We investigate different block sizes and also a hybrid scheme that performs extremely well with less computations. A drawback of the codes has been discovered: the BER curves show a flattening at higher signal-to-noise ratios, this is due to the small minimum distance of the whole code. By analyzing the interleaver used in the encoder we can calculate approximations to the BER at high SNRs. Finally, by careful interleaver manipulation the minimum distance of the code can be increased and the error-coefficient for the remaining small distance events can be further reduced. Furthermore, we have investigated the influence of the interleaver length on the SNR needed to achieve a certain BER. Simulations confirm both the analytical approximation to the BER as well as the method for interleaver design which yields a marked improvement at higher SNR.