Re: Error rate probability


"Keith A. Lewis" <klewis@xxxxxxxxxxxxxxxx> wrote in message
news:d9siv9$rg8$1@xxxxxxxxxxxxxxxxxxxxxx
> "jan hauben" <jan.hauben@xxxxxxxxxx> writes in article
<dviwe.132562$ej.7213120@xxxxxxxxxxxxxxxxxxxxx> dated Tue, 28 Jun 2005
20:34:17 GMT:
> >in general :
> >one extra bit can detect one fault (like parity-bit)

That one parity bit detects all odd length errors.

>
> True for any size frame.
>
> >two extra bits can correct one fault bit

nope. It takes 4. Basically you have to generate a pointer back to the
single wrong location from the parity bits, (and some of those could have an
error as well)

>
> Certainly for a single bit. But for 2 data bits + 2 check bits, you can
> have 4 different single-bit errors, or no error at all (a 5th case). So
you
> would need more than 2 bits to correct them all.
>
> Let
> N = data bits
> C = check bits
> E = maximum expected errors in (n+c) frame
>
> You need
> sum(choose(N+C,i),i=1..E) <= 2^C
>
> See "Hamming Codes" for more info.
>
> >if a little mistake is acceptable, one can use gray-code
>
> Gray code is useful in circuits where you want only 1 bit to change at a
> time, for whatever reason. I don't understand what use that would be in
> error detection.
>


With Audio and video, you don't have to correct, but just fill in.
Extend a few milliseconds, detect absence or error and just hold the last
value.
Or Average. It is completely different from Data encoding/decoding.

It usually takes an additional 3 to 4 bits to correct another single bit
error.

hamming codes are a great place to start they are perfect codes too.


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