You're just not sending the database - you're sending whether or not it's the database. If you can only send a binary "is the database or is not the database" then 0 and 1 is indeed fully losslessly compressed information. If that's really what you want, then that's how you would do it. Full, perfect, lossless compression reduces your data down to only that information not shared between the sender and the receiver. Sending either 1 or 0 is, in fact, exactly what you want to do if the receiver already knows the contents of the database. Compression asks the question "what is the smallest amount of data I have to receive for the person on the other side to reconstruct the original data?" If the answer is "1 bit" then that's a perfectly valid message - the only information the receiver is missing is a single bit.