h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: The Mathematics Behind Digital-quality Technology - A84330786
Author: Icy North - U225620

This is a very basic introduction to the principles of error-detecting and error-correcting codes. It's a branch of mathematics which has underpinned the digital revolution.

It's a bit dry in places (well, it is maths after all!), but I hope some people will be curious enough to investigate. I find it a fascinating subject.

It expands on a brief discussion of the topic in A533170 - Digital Codes

Comments and suggestions, please

Icy

Good entry on a subject I knew nothing about (being a firm believer in the greatness of analogue tech ).

I think the "quality" in the title may be a little redundant as digital technology is by its very nature digital-quality!

Thanks Mr D.

Yes, I agree about the title

It's a good entry that's easy to follow. I agree with a the need for a snappy title.

The Maths of Digital Music?

Or Digital Maths? Maybe that's too simplistic.

I think it needs music into it..

Recorded music's just the case study I feature. The same branch of maths underpins digital broadcasting too (which I mention at the outset).

Yeah, but illiteration..

>>each complete codeword has an even number of 1s, or, as mathematicians would say, is even parity.<<

I would say, "has even parity".

Matrix multiplication: You can't multiply the tall column with a 3x7 matrix. You probably mean it the other way round (rectangular matrix * column).

I'll go back to my matrices textbook, thanks, TB.

Maybe I was using imperial rather than metric

Fixed, thanks

You're most welcome

Sorry I can't comment longer, busy with RL just now

Oh, and the "has even parity" should be changed in the "Error Correction and Hamming Codes" as well (in the 1. 2. 3. list)

Corrected & links added

Anything else?

Apologies for the huge delay in responding to this thread. As ever Icy, a very creditable effort. Well done, sir.

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Yay!

Thanks all

Glad you enjoyed it too, Sam. Sadly, the mathematics can't explain why the sound on BBC Four always arrives about a tenth of a second after the picture.

>>>Sadly, the mathematics can't explain why the sound on BBC Four always arrives about a tenth of a second after the picture.