Upper bound on the minimum distance of turbo codes

An upper bound on the minimum distance of turbo codes is derived, which dep ends only on the interleaver length and the component scramblers employed. The derivation of this bound considers exclusively turbo encoder input word s of weight 2, The bound does not only hold for a particular interleaver bu t for all possible interleavers including the best. It is shown that in con trast to general linear binary codes the minimum distance of turbo codes ca nnot grow stronger than the square root of the block length. This implies t hat turbo codes are asymptotically bad. A rigorous proof for the bound is p rovided, which is based on a geometric approach.