Posted by David Surowski (129.130.6.100) on September 28, 2000 at 18:35:57:
WARNING:
This query is purely mathematical and not of much
practical value, involving the Bit Error Rates of the
Hamming Codes. For a precise statement of the question,
as well as some background, you can download the article
from my web page; see
www.math.ksu.edu/~dbski/schedule#seminar
(it's the article BER and the Hamming Codes). In a word,
I seek the EXACT derivation of the BER for the Hamming
Codes. In an earlier dialog with Michele Elie in Italy,
he referred me to the result of J. van Lint (Lecture
Notes in Mathematics, vol. 201, Springer-Verlag, New
York, 1973, pp. 25--26). However, van Lint computes the
POST-DECISION BER and not the MESSAGE BER. That is, van
Lint's calculation gives the expected number of CODEBIT
errors rather than the average number of MESSAGEBIT
errors. However, I have strong evidence that reveals
that these two results are the same (underscoring the
VERY SPECIAL NATURE of the Hamming codes). (In
particular, a little bit of combinatorial analysis shows
that the second-order terms (in the BSC crossover
probability p) are the SAME.)
Any comments apropos the above would be received with
immense delight.
David Surowski
Department of Mathematics
Kansas State University
dbski@math.ksu.edu