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elite
Guest
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 Posted:
Mon Dec 26, 2005 5:15 pm Post subject:
shannon capacity limit |
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Base on shannon capacity limit,what are the possibility of transmittin
information when the signal is lower than the noise?
thks for any help that is being provided for the above question. |
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Steve Underwood
Guest
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| Posted:
Mon Dec 26, 2005 5:15 pm Post subject:
Re: shannon capacity limit |
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elite wrote:
| Quote: | Base on shannon capacity limit,what are the possibility of transmitting
information when the signal is lower than the noise?
thks for any help that is being provided for the above question.
|
Why not plug the numbers into the channel capacity equation, and see?
Steve |
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IM
Guest
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| Posted:
Tue Dec 27, 2005 9:15 am Post subject:
Re: shannon capacity limit |
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Hello:
Spread Spectrum. |
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James (Sungjin) Kim
Guest
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| Posted:
Tue Dec 27, 2005 9:15 am Post subject:
Re: shannon capacity limit |
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Steve Underwood wrote:
| Quote: | elite wrote:
Base on shannon capacity limit,what are the possibility of transmitting
information when the signal is lower than the noise?
thks for any help that is being provided for the above question.
Why not plug the numbers into the channel capacity equation, and see?
Steve
|
In that case where the signal power is lower than the noise power,
shannon capacity is represented as
C = log2( 1 + SNR)
where SNR = P_s / P_n < 1. This means that up to SNR is 0, there is a
way to transmit the information of which the transmission rate is less
than C. To understand the shannon capacity formula, we must remind that
the frame size is infinitely large and the coding scheme is a random
coding. Note that if we use a better coding scheme, e.g., LDPC or turbo
coding, than the random coding which shannon used, we achive close to
shannon capacity with even shorter frame size.
- James Gold |
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robert bristow-johnson
Guest
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| Posted:
Wed Dec 28, 2005 9:15 am Post subject:
Re: shannon capacity limit |
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elite wrote:
| Quote: | Base on shannon capacity limit,what are the possibility of transmitting
information when the signal is lower than the noise?
|
you know those beautiful photos of Jupiter, Saturn, Uranus, and Neptune
that Voyager 1 & 2 were sent from a 20 watt transmitter (with a pretty
good beam antenna) over billions of kilometers of distance (run the
inverse-square law on that one!) and both space and our atmosphere are
known to be pretty noisy. i think the S/N ratio was many dBs below 0.
yet we got them beautiful photos. (it might have taken days to receive
and decode the data.)
even if S/N << 1, as long as it's > 0, there is some channel capacity.
you might need a helluva lot of redundancy to encode the weak signal to
get through all that noise (and redundancy takes *time*), but you can
do it.
beside "Spread Spectrum" (as was mentioned), also look up "Reed-Soloman
Coding". (speeling not gauranteeded.)
| Quote: | thks for any help that is being provided for the above question.
|
FWIW.
r b-j |
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Jerry Avins
Guest
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| Posted:
Wed Dec 28, 2005 5:15 pm Post subject:
Re: shannon capacity limit |
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robert bristow-johnson wrote:
| Quote: | ... (speeling not gauranteeded.)
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Shouldn't that be "spieling"?
Jerry
--
Engineering is the art of making what you want from things you can get.
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Randy Yates
Guest
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| Posted:
Wed Dec 28, 2005 5:16 pm Post subject:
Re: shannon capacity limit |
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"James (Sungjin) Kim" <jamessungjin.kim@gmail.com> writes:
| Quote: | Steve Underwood wrote:
elite wrote:
Base on shannon capacity limit,what are the possibility of transmitting
information when the signal is lower than the noise?
thks for any help that is being provided for the above question.
Why not plug the numbers into the channel capacity equation, and see?
Steve
In that case where the signal power is lower than the noise power,
shannon capacity is represented as
C = log2( 1 + SNR)
where SNR = P_s / P_n < 1. This means that up to SNR is 0, there is a
way to transmit the information of which the transmission rate is less
than C.
|
This is also known as the "channel coding theorem": "All rates below
capacity C are achievable."
--
% Randy Yates % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC % and kiss her interface,
%%% 919-577-9882 % til then, I'll leave her alone."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr |
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James G.
Guest
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| Posted:
Wed Dec 28, 2005 5:16 pm Post subject:
Re: shannon capacity limit |
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━verb (spieled, spieling) 1. to talk endlessly or glibly.
So, I think *spelling* hasn't be guaranteed in his text.
Futhermore, he wanted to point out "Reed-Solomon coding".
-James Gold. |
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James G.
Guest
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| Posted:
Wed Dec 28, 2005 5:16 pm Post subject:
Re: shannon capacity limit |
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| FWIW ?? |
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Randy Yates
Guest
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| Posted:
Wed Dec 28, 2005 5:16 pm Post subject:
Re: shannon capacity limit |
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"James G." <JamesSungjin.Kim@gmail.com> writes:
For What It's Worth.
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr |
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Jerry Avins
Guest
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| Posted:
Wed Dec 28, 2005 11:29 pm Post subject:
Re: shannon capacity limit |
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James G. wrote:
| Quote: | ━verb (spieled, spieling) 1. to talk endlessly or glibly.
So, I think *spelling* hasn't be guaranteed in his text.
Futhermore, he wanted to point out "Reed-Solomon coding".
|
Yes. He was having fun, and I succumbed to the urge to join in. Note
also his "gauranteeded.".
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ |
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Vladimir Vassilevsky
Guest
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| Posted:
Thu Dec 29, 2005 1:16 am Post subject:
Re: shannon capacity limit |
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robert bristow-johnson wrote:
| Quote: | you know those beautiful photos of Jupiter, Saturn, Uranus, and Neptune
that Voyager 1 & 2 were sent from a 20 watt transmitter (with a pretty
good beam antenna) over billions of kilometers of distance (run the
inverse-square law on that one!) and both space and our atmosphere are
known to be pretty noisy. i think the S/N ratio was many dBs below 0.
yet we got them beautiful photos. (it might have taken days to receive
and decode the data.)
|
The Shannon formula deals with E/No ratio (energy per bit of useful
information divided by noise specral density), which is much more
informative parameter then SNR. For Voyager missions the E/No threshold
was somewhere around 3dB, i.e. much higher then the noise.
| Quote: | beside "Spread Spectrum" (as was mentioned), also look up "Reed-Soloman
Coding". (speeling not gauranteeded.)
|
Shannon formula relates to the useful information only. The redundancy
of the SS and/or RS is a different story.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com |
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