Upper bounds on the state complexity of trellis diagrams for turbo codes

Upper bounds on the state complexity of minimal trellises for turbo codes are reported. State complexity depends on a permutation of bit positions, and three specific types of bit orders are considered. One is the standard order. The other two are known to result in a very low complexity when the interleaver in the encoder is a block interleaver. This tendency may be explained on the basis of the fact that the upper bounds for these two types of bit orders will be very small when the interleaver is a block type. Two newly defined interleaver parameters are used here to describe the upper bounds.