[omazurov]

> Larger and larger block sizes are important. LDPC probably is the more practical methodology today, though I admit that I'm ignorant about them. Still cool to see someone try to push Reed Solomon to such an absurdly huge size though.

Multi-dimensional RS codes are an easy way to get to an absurdly huge size for real (granted they stop being MDS). Long term archiving is an obvious application. One-way communication, like in deep space, is another. Though, speed requirements are less demanding there. That one tried to push the envelope for a one-dimensional RS code to those limits is a curiosity. Some techniques may be useful in other practical approaches. It's a pity the code representation had to depart from GF(2^n).

[dragontamer]

> Multi-dimensional RS codes are an easy way to get to an absurdly huge size for real (granted they stop being MDS)

Yeah, that's the traditional way of doing things. CD-ROMs used multi-dimensional RS (the RS(28,24) was just one bit of the inner-code IIRC, which would fit inside another multidimensional RS code).

But since its no longer MDS, the "search space" of non-MDS codes is quite large. So you have the question of "which code has a higher-probability of successfully correcting errors/erasures" ??

LDPC and Turbo codes apparently have better probabilities of fixing errors/erasures, at far lower computational costs. To the point where a fair number of applications seem to prefer Turbo / LDPC codes today over multidimensional codes (built out of RS)

[omazurov]

I'm not talking about CD-ROMs or immediate availability in any form. How would you encode a petabyte (for a starter) with LDPC/Turbo? Not available right away but accumulated over months with no predefined upper limit? Computational cost remains an important factor but other requirements take over.

[dragontamer]

> How would you encode a petabyte (for a starter) with LDPC/Turbo?

I'm fairly certain that particular problem you're asking for is solved by "fountain LDPC codes", and can't be solved by RS by any methodology.

RS is limited to its block size (in this case, 2^20 sized block), which can be "extended" by interleaving the codes (with various kinds of interleaving). But interleaving a petabyte of data is unreasonable for RS.

I admit I'm not hugely studied in practical codes, mostly just got the college-textbook understanding of them.

[omazurov]

I can only repeat my initial statement:

> Multi-dimensional RS codes are an easy way to get to an absurdly huge size for real.

"Multi-dimensional" may mean 3,4,..,10 dimensions. "Absurdly huge" means a petabyte and beyond. "For real" means practical recovery of swaths of lost or damaged data. "Fountain LDPC codes" are essentially one-dimensional. Extending them to the ability of recovering an annihilated data center would make them impractical. Making them multi-dimensional would make them inferior to RS (which is still MDS in every single dimension).

[Bulat_Ziganshin]

There is Leopard codec implementing very similar approach in GF(2^n). AFAIR, it's a bit slower, but overall it looks more useful than FastECC

(OTOH, since we anyway store hashes and other info, we may store there extra overflow bits required for recoding into GF(p). That said, FastECC on practice works like a slightly non-MDS code, but at least there are guarantees how much extra data we need to store)