Rate-distortion theory: minimum bits to represent data within distortion D

How many bits do we need to perfectly copy a song?

Imagine you want to send a song to a friend, but you have limited data storage. How can you send it without losing too much quality?

It's like trying to copy a painting. You want to keep the colors and shapes as true to the original as possible, but you can't use the exact same amount of paint. The goal is to use just enough paint to get close to the original painting.

Example

If the original song is 5 MB and you can only send 2 MB, you need to find the best way to reduce the size while keeping the song sounding good.

Remember this

The key insight is finding the balance between how much data you use (rate) and how much quality you lose (distortion).

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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