Was literacy rate in Roman Empire of I - IV century really higher than that of Byzantine Empire e.g. in years 600 - 1204?

I am talking about general literacy rate among all of the inhabitants of Roman Empire. Certainly a big portion of Roman citizens in antiquity could read but they were ( before Aurelius ) only a small part of Empire's society. Let's also not forget about slaves who constituted to10 - 15% of Empire's population.

It doesn't matter to me what language could people write and read, as long as they could do it well.

EDIT: By "well" I mean they could read a book.