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.
shannon capacity limit
Started by ●December 26, 2005
Reply by ●December 26, 20052005-12-26
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
Reply by ●December 27, 20052005-12-27
Reply by ●December 27, 20052005-12-27
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. 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
Reply by ●December 28, 20052005-12-28
elite wrote:> 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.)> thks for any help that is being provided for the above question.FWIW. r b-j
Reply by ●December 28, 20052005-12-28
robert bristow-johnson wrote:> ... (speeling not gauranteeded.)Shouldn't that be "spieling"? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●December 28, 20052005-12-28
"James (Sungjin) Kim" <jamessungjin.kim@gmail.com> writes:> 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
Reply by ●December 28, 20052005-12-28
=E2=94=81verb (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.
Reply by ●December 28, 20052005-12-28
Reply by ●December 28, 20052005-12-28
"James G." <JamesSungjin.Kim@gmail.com> writes:> FWIW ??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
