It is well-known that the Hodge to de Rham spectral sequence of a smooth projective variety over C degenerates at E_1. The degeneration has two different proofs: i) the classical Hodge-theoretic method; ii) the mod p method. The second method was first given by Deligne-Illusie. The key ingredient of the proof of Deligne-Illusie was their decomposition theorem based on an explicit construction. Professor Mao Sheng and I generalize Deline-Illusie's explicit construction to the Higgs sheaves case, and then obtain our decomposition theorem. As an application, we give a mod p proof of the E_1-degeneration theorem of Cattani-Kaplan-Schmid and Kashiwara-Kawai.