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

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Abstract
Recently, a coding scheme (turbo-codes) was proposed, that achieves almost reliable data communication at signal-to-noise ratios very close to the Shannon-limit. In this paper 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. This is in accordance with the MAP derivation of the component decoders. 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; short lengths might be encountered in mobile and personal communications systems (e.g. voice transmission). 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.

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