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Even the replacement and most modern remotes (with an LED at the tip that you have to point at the device) use pretty cool tech.
Usually to send data you want a data channel and a clock channel. When the clock changes say from high to low you read the next bit in the data channel. With one LED to send info you need to combine them.
For transmission that's easy. You make the low to high change at a fixed frequency. For the high to low change if it's a zero you make the high to low change 1/3 the way through the cycle. For a 1 you make the change 2/3 the way through the cycle.
On the receiver you you sync up a signal at the same frequency rising with the start of the transmission at a 1/2 on 1/2 off. You look at the data when the reference falls 1/2 the way through the cycle.
If a zero was sent the line had fallen at the 1/3 and it is a zero. If a one was sent the line doesn't drop until 2/3 and it's a one.
The trick is how do you get a signal at the same frequency and in synch. You compare the transmission frequency revived to the frequency of a voltage controlled oscillator. If it's slower you up the voltage and increase the frequency if it's faster you lower the voltage and lower the frequency.
You similarly use a phase detector to determine if they are in phase slightly boosting the frequency until they are in sync.
This system is called a phased lock loop (pll). All this so you don't have to getup to change the channel. The same sort of system is used for reading data from the magnetic disk on a hard drive.