A refined information geometric interpretation of turbo decoding

Many previous attempts at analyzing the convergence behavior of turbo and iterative decoding, such as EXIT style analysis (ten Brink, S., 2001) and density evolution (El Gamal, H. and Hammons, A.R., Jr, 2001), ultimately appeal to results which become valid only when the block length grows rather large, while still other attempts, such as connections to factor graphs (Kshischang, F.R. et al., 2001) and belief propagation (McEliece, R.J., 1998), have been largely unsuccessful at showing convergence due to loops in the turbo coding graph. The paper presents an information geometric interpretation which, built on the results of M. Moher and T. A. Gulliver (IEEE Trans. Inform. Theory, vol.4, p.3097-104, 1998), S. Ikeda et al. (IEEE Trans. Inform. Theory, vol.50, p.1097-114, 2004), and T. Richardson (IEEE Trans. Inform. Theory, vol.46, p.9-23, 2000), allows us to relate the quantities of interest in the turbo decoder. Using it, we point out a measure which is key in studying convergence.