HD Radio:

It works like regular analog radio except HD radio's signal is a collection of compressed digital and analog signals with text containing the song titles, station ID and other data that your modern digital car radio would display which is received by your antenna. HD radio receivers also are designed to remove pop, hiss, and other types of static for the purposes of being as clean as possible when it is reaches your receiver. It will reach your receiver at more or less CD Quality (48khz) and is due to rise.
Also HD radio allows for the transmission of surround sound sub-channels which a regular analog transmission could not support.

So in a sense, High Definition Audio does exist in radio as the audio quality is increased through digital signals by reducing noise and allowance for more information to be transmitted like surround sound sub-channels and text.

There's a lot more to it but that's the summary.