Convergence Analysis and Design of Multiple Concatenated Codes

Doctoral thesis, 2004

The objective of this thesis is to develop a methodology for designing efficient multiple concatenated coding schemes, consisting of two or more constituent codes, concatenated in serial or in parallel. Extrinsic information transfer (EXIT) analysis is found to be a suitable and versatile analysis tool for such codes and thus, the design methodology is based almost entirely on this technique. The performance of multiple concatenated codes (MCCs) in terms of convergence thresholds, decoding complexity required for convergence, and resulting bit-error rate (BER) can be determined from their multi-dimensional EXIT charts. However, multi-dimensional EXIT charts are difficult to visualize, and hence an equivalent two dimensional EXIT chart projection is introduced, yielding a powerful tool for the convergence analysis of MCCs. An exhaustive search for rate-one convolutional codes with memory four or less is performed, resulting in 98 classes of codes with unique EXIT functions. In addition, a search for 8PSK mappings with different performance in terms of BER and mutual information for the individual bits is conducted. Further, optimal puncturing ratios for MCCs in terms of minimizing the convergence threshold are found utilizing the EXIT functions of the constituent codes. Following this approach, additional degrees of freedom for constructing MCCs with low convergence thresholds over a range of code rates are obtained. For an MCC with two constituent codes, decoding is performed by alternately activating the two decoders. With more than two components, the order of activation is no longer obvious. An algorithm that finds the optimal decoder schedule, in terms of minimizing the total decoding complexity required to reach convergence, is proposed. Finally, a method for obtaining unbiased estimates of the symbol energy and the noise variance without knowledge of the transmitted bits is presented.