Cell Relay Archive

["ronald h. davis" <ronaldd@lucent.com>]

"C. M. Heard/VVNET, Inc." wrote:
> 
> > But, if E(X) = X^5 + X^4 + 1 (burst error of pattern 110001 in 5th byte),
> > then also E/G = X^5 + X^4 + 1 which is 0x31 in value. We may wrongly
> > conclude as per above paragraph that single bit error has occurred at
> > MSB position. Considering the ambiquity discussed, how can one say that
> > G(X) polynomial corrects single bit error properly? The problem lies in
> > accurately classifying whether the error is single bit or multi-bit,
> > leave alone single bit error correction.
> >
> > The probability is higher that i could be missing some important point.
> > I would appreciate if anyone resolves the above issue for me.
> 
> Actually you have raised a very intelligent question.  As you have correctly
> concluded, the particular error pattern in your example results in an
> uncorrectible error.  No matter what you use -- whether it is used for
> error correction or just for error detection -- there will always exist
> such patterns.  The practical engineering question is whether the
> probability of an undetected error is acceptably small.
> 

crc is fundamentally a probability game: you look for circumstances in
which the probability of taking the wrong answer is small.  for
instance, take the case given above in which a single bit error and a
3 bit error produce the same residual.  if the bit error rate on the
facility is 10^-7, then the probability of the former is 10^-7 while
the probability of the latter is 10^-21.  so the likelihood that the
0x39 residual would be produced from the 3 bit error pattern something
like 1 in 10^14.

however, there are numerous other bit error patterns that produce the
same result; in fact any bit error pattern which is a multiple of the
generator polynomial is undetectable.  according to i.432 the
likelihood of receiving a cell with an undetectable error in the cell
header for a ber of 10^-7 is around 10^-18.  of course, the higher the
ber, the more likely that a header error will not be detected.

so the moral of the story is, i think, that the atm hec is pretty
reliable to correct the right errors and to detect the errors that
are present in the cell header.

-- 
  __  ______  __  / __/ |       lucent technologies, naperville il, usa
_/ (_(_) / (_(_/_/_(_/  .       ronald.h.davis@lucent.com
author of "atm for public networks" published by mcgraw-hill
     http://www.amazon.com/exec/obidos/ASIN/0071344764