How does Star Trek faster than light communication work?

In TNG 'Where No One Has Gone Before', the Enterprise is sent hurtling through space past countless galaxies, when the Traveller “upgrades” the ships propulsion. Though the ship is thousands of light years travel away (at warp 9.9), they mention any communication would take 51 years to reach Starfleet.

That means they have communication faster than their maximum warp speed.

How much faster is this communication? I thought warp 9.9 was the Star Trek speed limit?

Answer

Faster-than-light subspace communication is explained in detail in the official Star Trek: The Next Generation Technical Manual, by Michael Okuda and Rick Sternbach, who were the principal production designers for TNG.

From Section 8.5 on the "Subspace Communications Network" (click to enlarge):

In particular, under ideal circumstances, subspace communications travel at Warp 9.9997, which is

"...about sixty times faster than the fastest starship..."

according to the Manual.

With that part out of the way...

According to the Manual, Warp 9.9 (Enterprise D's top speed) is 3053 times the speed of light. If subspace communications achieve roughly 60 times this speed, that means that these transmissions travel at approximately 183,180 times the speed of light. Hence, a subspace communication will cover a distance of roughly 183,000 light years in a year.

On the other hand, in the episode we hear:

PICARD: Data, what distance have we travelled?

DATA: 2,700,000 light years.

But 2,700,000 divided by 183,000 is only about 14.75. In other words, it should only take about 15 years for the communication to reach Starfleet, rather than 51!

Of course, the Manual says that Warp 9.9997 is achieved under "ideal galactic conditions". In could be that Data factored in some non-ideal conditions, such as the lack of subspace relay points outside of the galaxy and the Galactic Barrier.