Analysis and applications of iterative decoding.

Iterative decoding provides a practical solution for the approaching of the Shannon limit with acceptable complexity. By decoding in an iterative fashion, the decoding complexity is spread over the time domain while the overall optimality is still approached. Ever since the successful application of iterative decoding in turbo codes in 1993, people have been trying to discover the secrets behind iterative decoding. This PhD thesis contains a new, universal method for the analysis of iterative decoding based on cross-entropy. It is proved that the maximum a posteriori probability (MAP) decoding algorithm minimizes the cross-entropy between the a priori and the extrinsic information subject to given coding constraints, and the error correcting ability of each step of decoding can be evaluated with this cross-entropy for a converging turbo decoder. These theoretical results provide a solid ground for analysis of turbo decoding on convergence rate, derivation of Eb/N0 convergence thresholds, evaluation of error performance in the "error floor" region, and design of asymmetric turbo codes. With the new method, thresholds for convergence of turbo decoders can be more strictly predicted compared with using existing EXIT charts or Gaussian approximation method. For performance evaluation in the "error floor" region, the new method provides more detailed information than bounding techniques but is much less time-consuming than direct BER simulations. An asymmetric turbo code designed with the guidance of the new method also exhibits more than 0.1 dB of gain over that guided by the classical bounding technique in both high and low BER regions. Unlike most conventional analysis methods which rely heavily on either Gaussian approximation of distribution of the a priori/extrinsic information or a full knowledge of source bits, or even both, the new method provides analysis in a totally blind fashion. Since hybrid-ARQ is thought to be the mainstream error controlling technology in future high speed wireless communication systems, this PhD thesis also provides some innovative ideas on the applications of iterative decoding in bandwidth efficient hybrid-ARQ systems. Multilevel coded modulation, which is featured with unequal error protection capability, high bandwidth efficiency, and high flexibility, is employed to construct hybrid-ARQ. Multilevel HARQ schemes, including synchronous, asynchronous, and adaptive multilevel HARQ are proposed, and analysed in both theoretical and numerical ways. Significant gains can be observed in comparison with conventional TCM HARQ schemes. However, conventional Chase diversity combining is found to be applicable only to the former two HARQ schemes, but not applicable to the adaptive multilevel HARQ, which however shows best performance in non-combining scenarios, due to its dynamic packet structure. As a solution, multistage iterative combining, which is based on the principles of iterative decoding, is proposed and verified with simulation results