Error Correcting Curves

Error Correcting Curves - Numberphile

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9 ай бұрын

Isabel Vogt on error correction, curves, and some big polynomials. Extra footage at: • Eating Curves for Brea...
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Isabel Vogt at Brown University - www.math.brown.edu/ivogt/
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Пікірлер: 391

@major__kong

One of the first uses of Reed-Solomon error correcting codes was to transmit data back from the Voyager spacecraft. Once they got beyond Jupiter, the signal to noise ratio became untenable without error correction.

@ethanbove629

Took a class with Professor Vogt my freshman year of college and absolutely loved it, she’s a fantastic lecturer. So happy to see her on numberphile!

@Furiends

It was a bit glossed over but properly a Reed-Solomon code can correct up to half the redundant bits. So +1 would only detect the error and +2 would correct up to 1 bit. If you have a million bits then the chances of more than one error is really high. So in practice it's somewhere around 1.5x the information rather than 3x the information.

@liama23

I always love the interaction with Brady. He's questions and thoughts are always on point and helpfull.

@jakebrodskype

Note that when you do these manipulations in binary, they get a whole lot easier and faster to process. Reed-Solomon coding is actually one of the earliest and easiest error correction codes to calculate. It was so easy that even in the limited processing of pagers in the 1980s, they could work quite well. But there are more complex error correction codes that can correct longer strings of errors. There are Bose-Chaudhuri-Hocquenghem (BCH) codes, of which Reed-Solomon is a subset, there are "turbo-codes" and there are Low Density Parity Check codes (LPDC). Each of these methods will enable one to get perfect copy closer and closer to the noise floor.

@wChris_

Reed-Solomon Codes are very prominently used for CDs. That way a tiny scratch can be accounted for and doesnt make your data unrecoverable.

@numberphile

Extra footage from this interview over on Numberphile2:

@stephenbenner4353

The “sending it twice” has been the default method of error correction since the invention of the telephone, but it can break down if factors like someone’s accent or a poor connection make the repeat sound similar. For example, “nine” and “one” can sound similar and letters like “B” and “D” can also sound similar, and still sound the same to the hearer upon repeat.

@fissNotHere

Fun fact: Credit card numbers already have error detection so that the scenario described on the start doesn't happen. It's not error

@CharlesVanNoland

Is this Isabel's Numberphile debut? She's awesome!

@davidgillies620

The mathematics of how this is accomplished in real-world applications is very interesting as well. I can't recall if Numberphile has done a lot of videos on finite fields, but they're nicely suited to software and hardware implementations. Nowadays they've largely been replaced by turbocodes although they're still important. The Voyager probes use Reed-Solomon codes, as does the Compact Disc audio standard.

@popio

Isabel Vogt is an amazing teacher. Great video!

@SurfinScientist

Great explanation of Error-Correcting Codes! I never looked at Reed-Solomon codes in this way.

@VasiliyLomovoy

I was always surprised that Jules Verne, in the "In Search of the Castaways (French: Les Enfants du capitaine Grant, lit. 'The Children of Captain Grant')", did not have a letter in a bottle streaked with small print all over the field with the coordinates of the island where the shipwrecked were saved, instead of a long-winded artistic description of the severity of their situation.