The geometry of turbo-decoding dynamics

The spectacular performance offered by turbo codes sparked intense interest in them. A considerable amount of research has simplified, formalized, and extended the ideas inherent in the original turbo code construction. Nevertheless, the nature of the relatively simple ad hoc turbo-decoding algorithm has remained something of a mystery. We present a geometric interpretation of the turbo-decoding algorithm. The geometric perspective clearly indicates the relationship between turbo-decoding and maximum-likelihood decoding. Analysis of the geometry leads to new results concerning existence of fixed points, conditions for uniqueness, conditions for stability, and proximity to maximum-likelihood decoding.