To me, literacy is the ability to manipulate the fundamental aspects of some "thing" to clearly demonstrate or communicate a desired idea to others. Literacy allows fluid interaction with others due to effective and efficient reactions. As such, literacy requires understanding and the ability to transfer understanding to others.
Culture is the result of the interaction of ideas, beliefs, experiences, and physical objects. Thus, culture exists as long as interaction occurs amongst the four divisions of culture.
Alternatively, one can view culture as the knowledge of humanity and its expressions. From this knowledge, we develop seemingly innate social protocol that is in a state of constant refinement; it exists, but it lacks definition. To acquire definition, one must become literate.