A multidimensional block coding scheme with iterative decoding

Turbo codes usually use recursive systematic convolutional (RSC) codes. We present a scheme based on block codes. We include an iterative decoding algorithm based on a variation of the Dorsch (1974) algorithm combined with the method of Pyndiah et al. (see Proc. IEEE Globecom´96 Conf., vol.1/3, p.121-25, 1996) for computing the soft decision output. Pyndiah´s method of iterative decoding was limited to only a few decoding tries as each try required the running of an algebraic decoder. Our aim was to increase the number of decoding tries. This was achieved by using a different decoding algorithm based on that of Dorsch. The Dorsch algorithm involves only re-encoding. In its original form it is applicable only to binary codes but we also implement it for codes defined over extensions of GF(2). Such codes have two natural types of interleaver, yielding different performances both in terms of coding delay and bit error rate (BER) for given signal-to-noise ratio (SNR), and we consider both. Our simulations first show the improved performance of our version of the Dorsch algorithm over the standard Chase (1972) algorithm. We then compare our algorithm with that of Pyndiah in the case of the product code formed using the [15,12,4] extended Reed-Solomon code with a total of 4 iterations. In our case, increasing the number of decoding tries increases the complexity of the algorithm only marginally and, with a maximum of 100 decoding tries with the binary interleaver and over a Gaussian (AWGN) channel, we achieve a BER of 10^-5 at the significantly lower SNR of 2.5-2.6 dB. Finally we give the results of simulations for various product codes