I read this strange science fiction romance story long ago when I was twelve. I need help remembering what it was called.

The story goes like this:

Premise: The crew of a starship is divided into two batches. While one batch runs the ship, the other batch is cryogenically frozen. After a point they switch over and so on. The two batches have never seen each other, nor are they allowed to communicate in any way. Before each switchover, the cleaners make sure they have removed everything that belongs to the previous batch, to prevent any kind of communication taking place by accident or otherwise.

Plot: The main character of the story wakes up from his freezing period, and goes to his sleeping quarters. He goes in the bathroom, and suddenly finds a pair of earrings there. He realizes that this belongs to someone from the other batch, and that he shares his room with a woman. Before going back to the freezing room again, he writes her a note and hides it in the tap. When he wakes up again he finds a note waiting for him in the tap, from that woman. Throughout the rest of the story they keep passing notes to each other, even though they never actually see each other. [this is as far as I remember, I forgot what happens at the end]

Has anyone come across this story?