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