How would an extrasolar spaceship communicate with Earth?

Given modern technology, what kind of bandwidth could you expect for communication with an extrasolar spaceship? For example, is HD video possible? Is it safe to assume it would vary by distance? Or is that just the power requirements?

I'm actually hoping for low bandwidth where it takes a long time to communicate simple textual data. Part of the plot involves a mystery that can't be fully realized until the probe gets back to Earth.

As a note, power shouldn't be a concern, though, if it helps lower the bandwidth, power can be restricted. I don't care what kind of technology is used to communicate, radio waves or something else, though it should be something we have the ability to create today.

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How would an extrasolar spaceship communicate with Earth?

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