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. In this paper, we focus on turbo decoding of product codes, and based on the geometric framework, we extend the analytical results and show how analysis tools can be practically adapted 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. Simulation results, which support and extend the theoretical analysis, are presented for Hamming [(7, 4, 3)]² and Golay [(24, 12, 8)]² product codes.