What are Reed-Solomon codes? What even is a “code” in this context??? That’s the question I kept asking myself.

I had no idea what “coding theory” was… yet I kept coming across those “RS codes”. So I decided to dig in.

Let’s start with a high level overview before going deeper. I’ll try to keep things simple and avoid copy-pasting the same definitions you see everywhere.

From now on, I’ll mostly use “RS” as shorthand for Reed-Solomon codes, because typing it out every time is tiring 😁

The big picture

What are RS codes?

Forget about the word “code” for a second, it can be confusing.

RS is essentially a way to correct errors when transmitting data. That’s it. Simple.

Practical Applications

RS codes are everywhere:

• QR codes: error correction in scanning
• CDs and DVDs: recovering scratched data
• Space communication: handling signal errors from deep space
• Your hard drive: data redundancy in storage systems

A common example: QR codes. When you scan a QR code, RS helps ensure the data is correctly interpreted. That’s why, even if the image has a small scratch, you can still retrieve the data through error correction.

How do they work?

By adding redundancy to the data.

The core idea is to expand the data being sent, making it more resilient to errors. If some parts of the transmission get corrupted, the extra information helps reconstruct the original message. So yes, the data will be bigger but at least it will be correctly transmitted.

Going back to our QR code example, the image consists of many black and white squares. Imagine you have a QR code ready to scan, and you count 400 squares in total.

The reality is that your camera doesn’t actually need all 400 squares to understand the data. It might only require 300 (for example). The extra squares are there to compensate for potential data loss, such as a damaged or partially obstructed image.