Positivity of direct image and Kodaira dimension

 
Let $f: X\rightarrow Y$ be a fibration between two projective manifolds. The Iitaka's conjecture states that the Kodaira dimension of $X$ is larger than the sum of the Kodaira dimension of $X$ and the Kodaira dimension of the generic fiber. By using some deep results in mixed Hodge theory, Kollar proved that the Iitaka's conjecture is true if the generic fiber is of general type. By using some recent analytic methods, we give an alternative proof (without using Hodge theory ) of Kollar's result. We can also generalise it easily to the log canonical model case