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 shows that the interleaving procedure provides a homo-morphism 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 Hungarian method (Linear Sum Assignment Problem). Numerical results are presented which show a substantial improvement with respect to a random interleaver.