Re: Error rate probability
- From: klewis@xxxxxxxxxxxxxxxx (Keith A. Lewis)
- Date: Tue, 28 Jun 2005 22:28:57 +0000 (UTC)
"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)
True for any size frame.
>two extra bits can correct one fault bit
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.
--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
.
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