Products of Random Matrices in Iterative (Turbo) Decoding

Abstract:
From an implementation as well as theoretical point of view it is a fundamental property of the symbol-by-symbol MAP decoding algorithm, that the dependence of the decoder output on the decoder inputs decays with distance in the code trellis. By using results from the theory of products of random matrices we present a general prove of this property and show that the rate of decay is exponentially with distance along the trellis. Furthermore, we examine how the rate of decay depends on the channel parameter and the a priori information, and how it evolves during the iterative decoding process. Finally, we comment on possible practical implications.