You are correct, a notice for unpaid rent is for exactly what it is, back rent. If you received a notice to pay back rent that is due as well as rent that will be due, then statutorily the notice you received is defective.Although the notice you received is seemingly stautorily defective, your receipt of it is not illegal per se. In any event, I suggest that you try and get caught up with your overdue rent owed your landlord and stay current.