Convergence analysis of turbo-decoding of product codes

Geometric interpretation of turbo-decoding has founded an analytical basis, and provided tools for the analysis of this algorithm. Based on this geometric framework, we extend the analytical results for turbo-decoding of product codes, and show how analysis tools can be practically adopted for this case. Specifically, we investigate the algorithm's stability and its convergence rate. We present new results concerning the structure and properties of stability matrices of the algorithm, and develop upper bounds on the algorithm's convergence rate. We prove that for any 2 × 2 (information bits) product codes, there is a unique and stable fixed point. For the general case, we present sufficient conditions for stability. The interpretation of these conditions provides an insight to the behavior of the decoding algorithm.