In this story, faster than light communication exists but every message is preceded by a long tone. An operator uses his free time to investigate the tone, discovering it's comprised of every transmission ever made. Both sides agree to keep this secret, allowing the illusion of free will in a predestined universe.
This is Beep, by James Blish, a short story that was later expanded into a novel called The Quincunx of Time.
A summary provided by an external reviewer gives the basic outline:
‘Beep’ is driven by two ideas: firstly, the universe is remorselessly deterministic; secondly, FTL communication is possible and, in fact, all such communication occurs simultaneously...
A journalist goes to the government and tells them they’ve got a leak. As proof she tells them she knows about their top secret ansible device. The government track the leak to an old man who runs a consultancy. They spy on him but can’t discover any evidence. Time passes. It turns out the old man is the journalist in disguise (?). She has a copy of the ansible too because a distant relative left it to her in their will (??). Her price for revealing all her secrets is to join the security agency and marry the boss (?!?).
Wikipedia's summary of the novel version provides some more specifics:
Capt. Robin Weinbaum of Earth Security submits to a request for an interview from Dana Lje, a video commentator, mostly because she can and has made his life difficult with her reporting of Security lapses, especially in a recent case involving the Government of Erskine, another planetary system. Ms. Lje reveals that she has received a communication from an outfit calling itself "Interstellar Information Ltd." about an incident in a star system so far away that even by a faster-than-light ship, no message could return from it in less than two months. The incident in fact is due to take place in the next few days. The communication also alleges that there is a new device aboard the ship, and gives the name of the device.
When Weinbaum hears the name—the Dirac communicator—he is forced to believe that Interstellar Information have access to information even he doesn't have. He brings in Dr. Thor Wald to explain the Dirac device to Dana Lje. She agrees to play along with Interstellar and its owner, J. Shelby Stevens, to let Security find out how the company gets its information...
Weinbaum uses the Dirac device to communicate with his agents, even though he suspects the communications may not be secure. Each audiovisual message is preceded by a loud beep and burst of visual static, which is so annoying that Weinbaum orders it edited from the tapes he reviews...
The explanation he gets is this: the beep that he found so annoying represents all the messages ever sent, or that ever will be sent, using the Dirac device. With proper techniques, it is possible to extract any message, whether it be recent, or far in the future.