Combinatorial analysis of the minimum distance of turbo codes

In this paper, new upper bounds on the maximum attainable minimum Hamming d istance of turbo codes with arbitrary-including the best-interleavers are e stablished using a combinatorial approach. These upper bounds depend on the interleaver length, the code rate, and the scramblers employed in the enco der. Examples of the new bounds for particular turbo codes are given and di scussed. The new bounds are tighter than all existing ones and prove that t he minimum Hamming distance of turbo codes cannot asymptotically grow at a rate more than the third root of the codeword length.