Draft of 11 Jan 2001 12 : 17 p . m . Coding Theorems for Turbo Code Ensembles ∗

This paper is devoted to a Shannon-theoretic study of turbo codes. We prove that ensembles of parallel and serial turbo codes are “good” in the following sense. For a turbo code ensemble defined by a fixed set of component codes (subject only to mild necessary restrictions), there exists a positive number γ0 such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than γ0, the average maximum-likelihood decoder error probability approaches zero, at least as fast as n−β , where β is the “interleaver gain” exponent defined by Benedetto et al. in 1996.