Marco Breiling

Analysis and Design of Turbo Code Interleavers

Band 2, Erlanger Berichte aus Informations- und Kommunikationstechnik, Herausgeber: A. Kaup, W. Koch, J. Huber. Shaker Verlag, Aachen, 2002. ISBN 3-8322-0302-8.


The subject of this thesis is the improvement of the power efficiency of Turbo codes by employing designed interleavers. In the first part of the thesis, practical aspects of interleaver design are treated. One chapter presents an algorithm for finding low-weight codewords in a given interleaver. This algorithm is then used to examine a large number of random interleavers in order to draw conclusions about the characteristics of low-weight codewords. These insights are applied in the following chapter to devise a novel interleaver design algorithm, that proves particularly powerful for the case of component encoders with low memory.

The second part of the thesis is subdivided into three chapters, which are devoted to deriving upper bounds on the maximum attainable minimum distance for all possible interleavers of a given length. These bounds are found by following geometric, combinatorial and graph-theoretic approaches. The bounds can be used as benchmarks for designed interleavers, and they provide new insights into the code structure of Turbo codes, which can serve as guidelines for the implementation of improved design strategies. Among the main coding-theoretic results of this thesis, we find that the minimum distance of Turbo codes cannot grow at a rate faster than the logarithm of the codeword length, and that therefore, Turbo codes are asymptotically bad, and there does not exist an error exponent for these codes.