Radio Data System (RDS) is used to send information with radio broadcasts, which can help with tuning in to a channel, or display text on the radio's display, such as information about the currently broadcasted program, or the weather. RDS only works on FM radio.
RDS supplies the radio with a few functions that are very helpful:

Program Identification (PI)
PI is used for storing the country from which is broadcasted, the type of program (local, national), and which radiostation it is. Every broadcasted show has a unique PI code. If the frequency at which the show is broadcasted suddenly changes, it is unnecessary to look up the new frequency because the receiver will do it for you.

Program Service (PS)
PS supplies information (8 characters long) about the broadcasted show, such as what kind of music they play, or if it's a local channel, the name of the city.

Alternative Frequencies (AF)
AF gives information about the frequencies at which the same program is broadcasted. This information is used by the RDS receiver to change stations when the signal gets too weak.

Traffic Program (TP) / Traffic Announcement (TA)
TP is the code that tells the receiver if the station broadcasts traffic information. The TA code is transmitted at the time the traffic information is broadcasted. When turned on, the radio will automatically turn up the volume when traffic information is supplied.

Just a note about Programme Service (PS)
This is used to transmit the station name, and can be up to 8 characters long. The purpose of this so the listener can find out what they're listening to, without needing to know the frequency. If the station is stored as a preset, the name is stored along with it.
(For this reason, the RDS Forum has issued guidelines against dynamic PS messages - ie, flashing the station slogan one word at a time is not recommended in case "BEST" gets stored in the radio as part of "TODAY'S BEST MUSIC".)

Other RDS features:

Programme Type (PTY)
Each programme broadcast carries with it a type, such as News, Current Affairs, Information, Sport or Education. See the full list.
These types let you see at a glance what kind of programming is currently being transmitted, and some sets let you scan the airwaves for a particular type of program - for example, hit a button to tune to the next Classical Music station.

Radio Text (RT)
This allows stations to send short messages about the current programme. It's a 32 or 64 character text string, and generally only home recievers will display it.

Enhanced Other Networks (EON)
This is used frequently by the BBC in the UK. If a listener was tuned to Radio 1, and a travel bulletin starts on a local BBC station, the radio will retune for the duration of the update. The transmitter can send Traffic, News and Weather flags, which the reciever can look out for.
This isn't always a perfect system - someone from BBC Radio Scotland explained to me that to send out a traffic flag, they press a button in the studio, which sends a signal to London, which tells the UK transmitter network that there's a traffic update, thereby introducing a staggering delay.

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