Reed Solomon codes are cool
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Reed Solomon codes are cool
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Re: Reed Solomon codes are cool
#2This post should be titled “Error correcting codes are cool”, as it contains zero bits of information that’s specific to Reed-Solomon codes.
If you’re interested in Reed-Solomon codes (and other error correcting codes), I recommend reading Huffman’s (NB: not the same Huffman as in Huffman codes!) textbook on the subject:
Fundamentals of Error Correcting Codes
https://www.amazon.com/Fundamentals-Error-Correcting-Codes-C...
Re: Reed Solomon codes are cool
#3This post should be titled “Error correcting codes are cool”, as it contains zero bits of information that’s specific to Reed-Solomon codes. If you’re interested in Reed-Solomon codes (and other error correcting codes), I recommend reading Huffman’s (NB: not the same Huffman as in Huffman codes!) textbook on the subject: Fundamentals of Error Correcting Codes https://www.amazon.com/Fundamentals-Error-Correcting-Codes…
Fair comment, I'm new to this subject so wanted to write about what I was reading about, but looking forward to reading about this topic further!
Re: Reed Solomon codes are cool
#4Wow. I love explaining Reed Solomon codes and this didn't do it justice.
The basic concept is that if I give you five points all on the same line, you only need any two of them to reconstruct the line.
Reed Solomon doesn't use lines (it isn't optimal) and the geometry they use isn't the Cartesian plane (this requires infinite precision) - but this is what the codes do!
Just like it requires two points to reconstruct a line, three points are required to reconstruct a simple polynomial (degree 2). Reed Solomon uses "high degree polynomials" which require n+1 points to reconstruct the degree-n polynomial.
The codes take data, make a polynomial out of it, and then send points from the polynomial to the other side, which can interpolate it as soon as enough points are gathered!
All of this looks like impenetrable discretization and matrix operations if you just get a description of the algorithms, which makes it seem a lot less approachable than it is.
Re: Reed Solomon codes are cool
#5Wow. I love explaining Reed Solomon codes and this didn't do it justice. The basic concept is that if I give you five points all on the same line, you only need any two of them to reconstruct the line. Reed Solomon doesn't use lines (it isn't optimal) and the geometry they use isn't the Cartesian plane (this requires infinite precision) - but this is what the codes do! Just like it requires two points to reconstruct…
I'm sure there are simpler ways to explain it, I'm new to the topic, sorry if you didn't like it.
Re: Reed Solomon codes are cool
#6I got excited about erasure codes a while ago and tried my best to give an accessible intro at https://www.akalin.com/intro-erasure-codes (with HN discussion at
https://news.ycombinator.com/item?id=18702843 ).
Glad to see other people getting excited by them too!
Re: Reed Solomon codes are cool
#7Wow. I love explaining Reed Solomon codes and this didn't do it justice. The basic concept is that if I give you five points all on the same line, you only need any two of them to reconstruct the line. Reed Solomon doesn't use lines (it isn't optimal) and the geometry they use isn't the Cartesian plane (this requires infinite precision) - but this is what the codes do! Just like it requires two points to reconstruct…
I'm sure there are simpler ways to explain it, I'm new to the topic, sorry if you didn't like it.
I don't think anything you wrote is wrong!
I have a background in error codes - hamming, and luby and raptor and, and, and. Reed-Solomon is particularly "beautiful" from a mathematics perspective (more so than Raptor) - something I can usually explain to anyone and get them interested.
Re: Reed Solomon codes are cool
#8Wow. I love explaining Reed Solomon codes and this didn't do it justice. The basic concept is that if I give you five points all on the same line, you only need any two of them to reconstruct the line. Reed Solomon doesn't use lines (it isn't optimal) and the geometry they use isn't the Cartesian plane (this requires infinite precision) - but this is what the codes do! Just like it requires two points to reconstruct…
I remember playing a computer game in math class where you were presented with a XY plane and had to "hit" points (really circles, didn't need to be exact) by plotting equations through them. With some trial and error you could make a polynomial go through basically as many as you wanted, it's neat to see this applied to a real problem!
Re: Reed Solomon codes are cool
#9Wow. I love explaining Reed Solomon codes and this didn't do it justice. The basic concept is that if I give you five points all on the same line, you only need any two of them to reconstruct the line. Reed Solomon doesn't use lines (it isn't optimal) and the geometry they use isn't the Cartesian plane (this requires infinite precision) - but this is what the codes do! Just like it requires two points to reconstruct…
I'm sure there are simpler ways to explain it, I'm new to the topic, sorry if you didn't like it.
Well it might not be the most in depth explanation, but your enthusiasm is appreciated, and contagious too.
I'm down the Wikipedia rabbit hole too, now.
Re: Reed Solomon codes are cool
#10This post should be titled “Error correcting codes are cool”, as it contains zero bits of information that’s specific to Reed-Solomon codes. If you’re interested in Reed-Solomon codes (and other error correcting codes), I recommend reading Huffman’s (NB: not the same Huffman as in Huffman codes!) textbook on the subject: Fundamentals of Error Correcting Codes https://www.amazon.com/Fundamentals-Error-Correcting-Codes…
I'd also recommend Error Control Coding by Lin/Costello