A codeword weight lower bound for a class of tail-biting turbo codes

This paper presents an achievable codeword weight lower bound associated with weight-2 input sequences of a class of turbo codes. The class of codes has an interleaver structure that encompasses most practical interleaves used by turbo codes. It partitions the incoming information sequence into blocks of the same size and the interleaver performs intra-block and inter-block permutations. Both pre- and post-permuted blocks are individually tail-biting encoded. Following [4], we refer to the codeword associated with a weight-2 input sequence as a weight-2 error event. We apply a special permutation function that incorporates the separate encoding concept to derive a lower bound of the weight-2 error event. This lower bound reveals that (i) a larger component code period gives better distance for the weight-2 error events, and (ii) separate encoding results in improved distance if the block length is suitably chosen and is large enough.