Performance analysis of the odd-even uniform interleaver for turbo codes

Abstract

Interleaver design has been an intense research area since the invention of turbo codes, both from theoretical and technological perspectives, still receiving the attention of engineers. This work is a theoretical treatment on the subject of interleaver design, bringing into focus the odd-even constraint. Odd-even interleavers constrain information symbols at odd (even) positions to remain at odd (even) positions after interleaving. Having been adopted in a range of operational communication standards as parts of turbo codes on the one hand, and having raised scepticism about their gain in the literature of turbo trellis-coded modulation on the other hand, these interleavers have motivated the present article. Concretely, the authors perform a bit-error analysis of turbo-code ensembles generated by the odd-even uniform interleaver, following the union-bound approach by Benedetto et al. for the analysis of the uniform interleaver. They find that the odd-even constraint does not affect the interleaver gain of uniform-interleaver ensembles; rather, it triggers a redistribution of multiplicities that leads to slightly worse performance mainly in the error-floor region. The authors' findings are corroborated by bit-error-rate simulations.