Science Are there any BLers with a knowledge of higher mathmatics? I have a class of question.

[4DQSAR]

I'm old enough to recall floppy discs. Due to how they work, each 4-bit symbol had to be encoded into a 5-bit symbol due to a simple rule:

-No symbol can have more than two consecutive 0 bits.

There were a number of approaches but broadly they fell into GCR (as explained above) or the brute-force method (MFM) of simply taking each symbol, performing an XOR on all the bits and interleaving the result of the two. So while GCR converted four bits to five, MFM DOUBLED the amount of data stored.

I later learnt that someone had figured out that in fact the hardware worked with three 0 bits in a row and someone came up with what was termed ans 8.3 format i.e. eight bits could be encoded as eleven bits while ensuring no more than three 0 bits occurred in a row.

Now, I had to write down EVERY symbol to check that this was indeed prectical - but isn't their a simple function that would provide for any run-length of any symbol(s) as a limit?

Sorry if I haven't explained this well. I had a C64 and am told it will indeed support 8.3 but I'm uncertain if my longhand method is reliable.

 

[Cheshire_Kat]

In computer science, group coded recording or group code recording (GCR) refers to several distinct but related encoding methods for representing data on magnetic media. The first, used in 6250 bpi magnetic tape since 1973, is an error-correcting code combined with a run-length limited (RLL) encoding scheme, belonging into the group of modulation codes.The others are similar encoding methods used in mainframe hard disks or microcomputer floppy disks until the late 1980s. GCR is a modified form of a NRZI code, but necessarily with a higher transition density.


Read more here:
CGR explained ...

 

[4DQSAR]

Isn't NRZI more to do with how the signal is modulated rather the actual symbol encoding?

 

[Cheshire_Kat]

Isn't NRZI more to do with how the signal is modulated rather the actual symbol encoding?

GCR itself is all about how data is stored on magnetic media; be it tape or disk. GSR is not one single set of methods, but a collection of them.

 

[4DQSAR]

I agree - but it's a class that can include multiple different symbol lengths depending on the exact version.

So it's simply a matter of how does one compute the minimun number of bits needed when a specified number of symbols are excluded (which I did explain). Originally any symbol with more than two consecutive 0 bits, but it was later discovered that the hardware would work with three consecutive 0 bits.

I mentioned 11b.3b which IS a thing, but more generally how does one calculate the number of bits required? 11b.3b is SLIGHTLY more efficient than 5b.4b BUT can one get even closer to the minumun? - for that one needs a bounding algorithm. A general methodology.

Patel, Arvind Motibhai (1988). "5. Signal and Error-Control Coding". In Mee, C. Denis; Daniel, Eric D. (eds.). Magnetic Recording. Vol. II: Computer Data Storage (1st ed.).

By hand is slow and prone to error. So a more GENERAL algorithm is what I'm asking for.