Since the turbo code was proposed early in 90’s, it is known that the turbo code gives a practical and powerful method for error correction. The properties of the code have been investigated intensively mainly through experiments. Although those results strongly support the high ability of the turbo code, there is no satisfactory theoretical results. In this paper, we elucidate the idea of turbo code through information geometrical viewpoint. From our study, we obtained the stability condition, characteristics of the equilibrium, convergence property, and approximation ability. Recently it is pointed out that another error correcting code, the Gallager code has the similar structure with the turbo code. Also Bethe approximation in statistical physics, and belief propagation for Bayesian net with loops have very good similarities with the turbo code. Therefore, we believe our results will give a new perspective for these family of iterative methods.