I read this story fairly recently, but I read a lot of time travel SF last year so it may be an older story. (I've searched my ebooks and can't find it.)
An odd telescope, or perhaps a normal telescope looking at an odd star, finds that the result of viewing the star depends on the future somehow. E.g., if there were to be an occultation of the star tomorrow, then when you look today at the same time your view will be blank.
Therefore by preparing occultations today, we can affect what was viewed yesterday, and thus send binary messages into the past.
This was a "description only" sort of story -- there was no dialogue (or very little), just exposition. Most of the story dwelled on how the society was affected by knowing what was going to happen. And whether you could trust the messages you got from the future.
I thought it was Greg Egan but I've searched his bibliography and can't find it there.