New performance bounds for turbo codes

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. Since the derivation of the bound for a given interleaver is intractable, we assume uniform interleaving as in the derivation of the standard union bound for turbo codes [1], [2], The result is a generalization of the transfer function bound and remains useful for a wider range of signal-to-noise ratios, particularly for some range below the channel cutoff rate. The new bound is also applicable to other linear codes.