cm.bell-labs.com
Shannon channel capacity in a simple way.
In a bandwidth of X Hz one can transfer 2*X symbols
per second, that is change state, from this to that,
2*X times per second. (doing 1,0,1,0,1,0 produces
the X Hz max freq signal, if 2kbps it gives a 1kHz tone)
That was Nyquist.
(unluckily the filter for this optimum has an infinite
delay from input to output, so nobody yet knows if it has
been implementad commercially, although announced
rollouts, etc has been made, 2.4Mbps on a pinhead,etc)
Shannon capacity if some bits are kind of wrong:
- assume a way of detecting correct data, wrong data
- assume a telepathic, polite way of asking for a retransmit
(Duh??)
example: one error in 100, at 100bits per second.
after 99 bits the next will be wrong, telepathic message,
that bit arrives once again.
First approximization capacity is 99 bits per second
(actually 100 bits in 1.01 second, but close enough as 99)
But once in 100 error bits that second bit will also be
wrong, capacity will actually be somewhat less, once in 100x100 bits, 98.99 (kind of 1/100 + 1/10,000...)
etc,etc..
Interesting conclusion, half of all bits are wrong, left
as an excercise, exam on practical daytrading..
More interesting, all bits are upside down..
=======
Another learning experience.. error rates and information..
This one telecom student got a summer job with the local
weather station and soon calculated that during summers
- on the average one day in 100 were rainy (0.01, 1%)
(works only where the summer is longer than 100 days)
- the weather reports were wrong two days in 100 (0.02,2%)
(but still got some rainy days correct)
Smart as he was he improved the error rate from 2% to 1%
by preprinting "the sun will shine tomorrow" for the
whole summer and went to the beach.
What was the amount of information in his forcasts??
Ilmarinen (the weather man)
P.S. Shannon capacity is actually about transfering
information, one need that coding-compressing thing, like
"please repeat that animated advertisement you already
have cached in memory". (the buggy else statement and
error handling is more interesting, but in Greenspan
Fortran pointers cannot be used, so programs usually work,
do not need boom and bust reboots, new versions for
another new set bugs) |
