New performance bounds for turbo codes

Abstract

We derive a new upper bound on the word and bit error probabilities of turbo codes with maximum likelihood decoding by using the Gallager bound instead of the standard union bound. Since the derivation of the bound for a given interleaver is intractable, we assume "uniform interleaving " as in the standard union bound applied to turbo codes. The result is a generalization of the transfer function bounds and remains useful for a wider range of signal to noise ratios, particularly for some range below the channel cut-off rate. Previously, for signal to noise ratios below the cut-off rate, the performance of turbo codes could only be predicted through simulation. We illustrate the usefulness of the new bound via some examples. We also discuss the possibility of extending the derived upper bound to some other codes.