Arthur "Big Boy" Crudup (August 24, 1905 – March 28, 1974) was an American Delta blues ‎singer, songwriter and guitarist. He is best known outside blues circles for writing songs such as ‎‎"That's All Right" (1946), "My Baby Left Me" and "So Glad You're Mine", later covered by Elvis ‎Presley and dozens of other artists.‎

http://en.wikipedia.org/wiki/Arthur_Crudup