Performance of turbo codes: The finite length case.

Parallel concatenated convolutional codes, a.k.a. turbo codes, have attracted much attention since their appearance in 1993. Turbo codes are decoded by iterative (turbo) decoders in which a component decoder for each component code exists. Turbo decoders perform quite well with respect to bit and packet error rates. The code structure coupled with the iterative decoding scheme provides performance close to the fundamental communication limits predicted by Shannon with reasonable complexity. In this thesis we investigate the performance of finite length turbo codes. Due to the ad hoc nature of turbo decoding, error rate performance analysis is difficult. In the first part of this thesis, we classify the different characteristics of turbo decoding based on empirical results and analyses available in the literature. This classification helps distinguish two modes of turbo decoding behavior: optimal mode and decoding failures. The performance in the optimal mode is affected by the code structure of a turbo code. The interleaver in turbo code construction makes it difficult to find the code structure for a particular interleaver. In order to overcome this difficulty, we concentrate on special error events of the component convolutional codes. We propose an efficient method to estimate the code structure. By this estimate, an approximation to the error rate performance can be obtained for the optimal mode. Decoding failures occur due to nonoptimal operation of a turbo decoder. Therefore, analysis of iterative decoding is of interest with regard to decoding failures. Iterative decoding analysis methods are available for infinite length turbo codes. By investigating the properties of the component decoders, a probabilistic model is developed for finite lengths. Using this model, we find approximations to probability of decoding failure. Combining the analysis methods for the two modes of a turbo decoder yields an accurate overall approximation to the error rate performance. Numerical results are presented to verify the accuracy of the approximation.PhDApplied SciencesElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123755/2/3096248.pd