[Discuss-gnuradio] information theory -- follow up (off topic)

[Brian_Whitaker]

Apologies, but I felt compelled to post this... it took me a bit to find it.
>From Simon Haykin's Comm Systems Text, he describes the result of one of
Shannon's key theories, dubbed "The Shannon Limit."

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The information capacity of a continuous channel of bandwidth B Hertz,
perturbed by additive white Gaussian noise of power spectral density No/2
and limited in bandwidth to B, is given by:

C = B log(base2) (1 + P/(NoB) ), 

with C in bits/second, where P is the average transmitted power.

The information capcity theorem is one of the most remarkable results of
information theory for, in a single formula, it highlights most vividly the
interplay among three key system parameters: channel bandwidth, average
transmitted power (or, equivalently received signal power), and noise power
spectral density at the channel output.

  The theorem implies that, for given average transmitted power P and
channel bandwidth B, we can trnasmit information at the rate C bits per
second as defined [above], with arbitrarily small probabllity of error by
employing sufficiently complex encoding schemes. It is not possible to
transmit at a rate higher than C bits per second by any encoding system
without a definite probability of error. Hence, the channel capacity theorem
defines the fundamental limit on the rate of error-free transmission for a
power-limited, band-limited Gaussian channel...
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You can have infinate capacity with any of the following:  infinate signal
power,  complete absense of noise (either of which give you infinate SNR),
or infinite BW.

====================================================
Brian Whitaker, Applications Engineer
Maxim Integrated Products, Sunnyvale CA
address@hidden
v: +01.408.530.6098  or +01.408.331.4127,  f: +01.408.331.1239
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