Group structure of turbo codes with application to the interleaver design

This work discusses the group property of the turbo codes when considered as a periodic linear system. It is shown that the interleaving procedure provides a homomorphism between different encoded sequences and thereby breaks the low weight sequences by a factor of at most 1/2^r where r is the constraint length of the code. A method is presented to optimize the structure of the interleaver via a discrete optimization procedure using the Hungarian method (linear sum assignment problem). Numerical results are presented which show a substantial improvement with respect to a random interleaver