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

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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.