The title pretty much says it all, but I am particularly interested in the case where the number of input and output symbols are equal and the transition matrix defining the DMC is nondegenerate. I am only interested in constructive/concrete examples, not (e.g.) a pointer to Shannon's channel coding theorem.
Well, first as constructive as it could get, capacity is only achieved asymptotically. That being said, you can take a look at several families of codes:
I am not sure if this is what you were looking for.