Comparison of iterative decoder performance with union bounds for short frame turbo codes

We consider short frame turbo-codes, suitable for delay-sensitive services such as conversational speech, or for encoding single ATM cells. We compare the uniform interleaver bound of Benedetto and Montorsi, and a union bound obtained by estimating the weight distribution due to the actual pseudo-random interleaver, with the simulated BER using an iterative decoder. We show that the uniform interleaver bound is significantly pessimistic at high SNR, where the random interleaver union bound is quite close. However, at lower SNR the BER exceeds the union bound, showing that it does not achieve ML decoding. We also consider half rate turbo-codes formed by puncturing various proportions of the data and parity sequences, and adapt the uniform interleaver bounds for these codes. We show that while the union bounds predict better performance for datapunctured codes, in practice they perform better only at high SNR and for limited proportions of data puncturing. Acknowledgements This work has been performed with the support of the U.K. Rngineering and Physical Sciences Research Council It has also been submitted to Les Annales des Telecommunications for possible publication Comparison of iterative decoder performance with union bounds for short frame turbo-codes A. G. Burr and G. P. White, Dept. of Electronics, University of York, U.K.