| A J-dimensional multiple turbo code consists of the parallel concatenation of J (J > 2) convolutional encoders connected by J - 1 permutors. This dissertation is devoted to the analysis and design of multiple turbo codes. Specifically, we show that low complexity multiple turbo codes have the potential to achieve lower convergence thresholds and larger minimum distances than conventional (J = 2) turbo codes.; The convergence behavior of multiple turbo codes, which is the most important factor that determines the bit error rate (BER) and frame error rate (FER) performance in the low signal-to-noise ratio (SNR) region, is studied using two approaches. First, an analytical approach to determine the transfer characteristics of 2-state convolutional codes is derived. The extrinsic information transfer (EXIT) chart method is then generalized to multiple turbo codes and used to search for low complexity multiple turbo codes with low convergence thresholds.; The performance of a multiple turbo code in the high SNR region is largely affected by its minimum distance. To simplify the minimum distance analysis, the concept of summary distance is extended to J-dimensional (a set of J - 1) permutors and used as a general design metric. Specifically, a sphere packing upper bound on the minimum length-2 summary distance (spread) of J-dimensional permutors is derived. It is also shown that the asymptotic minimum length-2L summary distance, for any integer L ≥ 1, for the class of random J-dimensional permutors is lower bounded by O( NJ-2J-e ), where N is the permutor size and epsilon > 0 can be arbitrarily small. Then, using the technique of expurgating "bad" symbols, we show that the spread of random J-dimensional permutors can achieve the optimum growth rate, i.e., O( NJ-1J ), and that the asymptotic growth rate of the minimum length-2 L summary distance can also be improved.; Two joint permutor construction algorithms are then presented, one for random permutors and another for linear permutors. The success probability of the random construction algorithm is estimated and a modified version of the algorithm is presented that takes the constituent encoder period into account. The second algorithm is designed for a very simple class of permutors---linear permutors. A constructive proof is given showing the existence of J-dimensional linear permutors with optimal spread O( NJ-1J ). (Abstract shortened by UMI.)... |
