Jon Harris wrote: (snip)> I also remembering seeing a bunch of noise about 56K modems being able to exceed > the Shannon theoretical channel limit a few years back, including I think a > thread here on comp.dsp. But upon closer examination, I think there were some > assumptions that Shannon made that didn't apply to the modem scenario (the noise > being white and Gaussian maybe?).Well, they are pretty special in the way they use the line. The answer (ISP) side must be an ISDN line. That is, there can only be one ADC/DAC between you and the ISP. The modem can synchronously decode the signal, learning where the sample points are. That is something I don't believe Shannon assumes. Though the question might be more applicable to Nyquist. While he seems to have the credit for the sampling frequency, the problem he was working on was getting digital signals through an analog channel, just as the modems are doing. -- glen
An intriguing story about undersampling
Started by ●June 5, 2005
Reply by ●June 6, 20052005-06-06
Reply by ●June 6, 20052005-06-06
On Mon, 06 Jun 2005 14:25:41 -0700, glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote:>Jon Harris wrote: > >(snip) > >> I also remembering seeing a bunch of noise about 56K modems being able to exceed >> the Shannon theoretical channel limit a few years back, including I think a >> thread here on comp.dsp. But upon closer examination, I think there were some >> assumptions that Shannon made that didn't apply to the modem scenario (the noise >> being white and Gaussian maybe?). > >Well, they are pretty special in the way they use the line. > >The answer (ISP) side must be an ISDN line. That is, there can only be >one ADC/DAC between you and the ISP. The modem can synchronously decode >the signal, learning where the sample points are. That is something I >don't believe Shannon assumes.Actually Shannon does assume perfect synchronization; anything without perfect synchronization realizes degradation. That degradation gets piled into "implementation loss" in many cases. The 56k spec just better utilizes the system to minimize impariments that would cause degradation. They're still consistent with capacity analysis wrt Shannon's work.>Though the question might be more applicable to Nyquist. While he seems >to have the credit for the sampling frequency, the problem he was >working on was getting digital signals through an analog channel, just >as the modems are doing.Few comm systems do otherwise. ;) Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
Reply by ●June 6, 20052005-06-06
glen herrmannsfeldt wrote:> Jon Harris wrote: > > (snip) > >> I also remembering seeing a bunch of noise about 56K modems being able >> to exceed >> the Shannon theoretical channel limit a few years back, including I >> think a >> thread here on comp.dsp. But upon closer examination, I think there >> were some >> assumptions that Shannon made that didn't apply to the modem scenario >> (the noise >> being white and Gaussian maybe?). > > > Well, they are pretty special in the way they use the line. > > The answer (ISP) side must be an ISDN line. That is, there can only be > one ADC/DAC between you and the ISP. The modem can synchronously decode > the signal, learning where the sample points are. That is something I > don't believe Shannon assumes.The whole system is outside the realm of Shannon's assumptions. An analog encoding of a digital signal, reassembles as bits at the central office, and transmitted thereafter digitally.> Though the question might be more applicable to Nyquist. While he seems > to have the credit for the sampling frequency, the problem he was > working on was getting digital signals through an analog channel, just > as the modems are doing.Aren't all wire lines analog? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●June 6, 20052005-06-06
Richard Owlett wrote:> Jerry Avins wrote: > >> [snip] The lucid science articles in, Astounding Science Fiction ... >> >> ... I could only answer "ASF". (The same mag that touted the >> Hieronymus machine) > > > and timoline [sp????] ie "slow glass" > > But I thought that was _Analog_ in Campbell era.Thiotimoline, from "The Endochronic Properties of Resublimated Thiotimoline" by Isaac Asomov. The name changed from "Astounding" to "Analog" while I was a frequent reader. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●June 6, 20052005-06-06
Jon Harris wrote:>"Jerry Avins" <jya@ieee.org> wrote in message >news:ys2dnSRg3ph4MjnfRVn-gw@rcn.net... > > >>Jon Harris wrote: >> >> >>>"Eric Jacobsen" <eric.jacobsen@ieee.org> wrote in message >>>news:hh69a1puu2ndmu2i724iphvbj9tgpbb5ct@4ax.com... >>> >>> >>> >>>>On 6 Jun 2005 02:38:56 -0700, "Andor" <an2or@mailcircuit.com> wrote: >>>> >>>> >>>> >>>> >>>>>What has been challenged in Information Theory in the last few years? >>>>> >>>>>(Genuine interest) >>>>> >>>>> >>>>It's not so much a challenge as a clarification of the limitations of >>>>Shannon's analysis. Shannon's capacity analysis was for a single >>>>use with a single user, and Multiple User Detection techniques and >>>>MIMO have both driven an expansion of Shannon's analysis to include >>>>multiple uses in the same channel. The results do differ from the >>>>single use case. >>>> >>>> >>>I also remembering seeing a bunch of noise about 56K modems being able to >>> >>> >exceed > > >>>the Shannon theoretical channel limit a few years back, including I think a >>>thread here on comp.dsp. But upon closer examination, I think there were >>> >>> >some > > >>>assumptions that Shannon made that didn't apply to the modem scenario (the >>> >>> >noise > > >>>being white and Gaussian maybe?). >>> >>> >>Basically, channel capacity depends not only on bandwidth, but also on >>SNR. With a high enough resolution, you can encode the entire Library of >>Alexandria in the length of short piece of Invar. When the line gets a >>wee bit noisy, those 56K modems slow down. >> >> > >Yes, that is the essence of Shannon's theorem. The modem article claimed to >exceed the "Shannon capacity" of a phone line, IIRC. Upon closer examination, >it didn't. > >Upon extremely superficial examination it didn't. None of those claims about exceeding Shannon capacity bothered to explain why the author thought it did. What the system does potentially exceed is the FCC (and I think other country's) power limits. The modems are capable of a little more than 56k, but are articially capped to a lower rate to stay within the maximum power requirements. Regards, Steve Regards, Steve
Reply by ●June 7, 20052005-06-07
Jerry Avins wrote:> glen herrmannsfeldt wrote:(snip about 56k modems)>> Well, they are pretty special in the way they use the line.>> The answer (ISP) side must be an ISDN line. That is, there can only >> be one ADC/DAC between you and the ISP. The modem can synchronously >> decode the signal, learning where the sample points are.>> That is something I don't believe Shannon assumes.> The whole system is outside the realm of Shannon's assumptions. An > analog encoding of a digital signal, reassembles as bits at the central > office, and transmitted thereafter digitally.I believe the current standards are 33.6k uplink, though I don't know that is a requirement of the technology.>> Though the question might be more applicable to Nyquist. While he seems >> to have the credit for the sampling frequency, the problem he was >> working on was getting digital signals through an analog channel, just >> as the modems are doing.> Aren't all wire lines analog?Well, yes. As well as I remember it, Nyquist was trying to find out how fast he could get telegraph pulses through a coaxial cable. If you consider the cable a low pass filter, he found the limit to the rate they could go through and be separated at the other end. Though it reminds me of the discussion claiming that either ADSL or cable modems aren't really modems because it is a digital signal. They really are, because it really is modulated. Even ethernet uses synchronous phase modulation, also known as Manchester coding, but to some people the word modulation is important. -- glen
Reply by ●June 7, 20052005-06-07
glen herrmannsfeldt wrote:> Jerry Avins wrote:...>> Aren't all wire lines analog? > > > Well, yes. As well as I remember it, Nyquist was trying to find out how > fast he could get telegraph pulses through a coaxial cable. If you > consider the cable a low pass filter, he found the limit to the rate > they could go through and be separated at the other end.... He was continuing a line of inquiry begun by Michael Pupin much earlier. Pupin explained rather well why the first "successful" transatlantic cable needed several minutes per bit. He elucidated phase velocity and dispersion, and why they mattered. Until the cable was laid, nobody even thought about it. http://www.geocities.com/neveyaakov/electro_science/pupin.html Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●June 7, 20052005-06-07
Jerry Avins wrote: (snip)> He was continuing a line of inquiry begun by Michael Pupin much earlier. > Pupin explained rather well why the first "successful" transatlantic > cable needed several minutes per bit. He elucidated phase velocity and > dispersion, and why they mattered. Until the cable was laid, nobody even > thought about it. > http://www.geocities.com/neveyaakov/electro_science/pupin.htmlThere was a story not so long ago about the design of the GPS system almost not considering general relativity. In the end they made support for it optional, but it quickly was determined that it needed to be on. -- glen
Reply by ●June 7, 20052005-06-07
"Jerry Avins" <jya@ieee.org> wrote in message news:86GdnUq6PeRicjnfRVn-vQ@rcn.net...> Aren't all wire lines analog? >Aren't all computers analog?
Reply by ●June 7, 20052005-06-07
John E. Hadstate wrote:> "Jerry Avins" <jya@ieee.org> wrote in message > news:86GdnUq6PeRicjnfRVn-vQ@rcn.net... > > >>Aren't all wire lines analog? >> > > > Aren't all computers analog?Why do you keep pretending to be superficial? Anything to be contrary? Digital computers are digital; that's what makes them digital computers. They use digital circuits which are in turn made -- tadaa! -- from analog components. Your silly claim would have it that ships are made not of steel, but of ore. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
