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How can digital be more spectrum efficient than analog ?

I'm using standard definitions, you are not.

...

Here is a chart for your edification:

Table 8.2 Error Rate of a Binary Transmission System Versus Signal-to-rms- Noise Ratio

Error Rate S/N (dB) Error Rate S/N (dB) 10^-2 13.5 10^-7 20.3 10^-3 16.0 10^-8 21.0 10^-4 17.5 10^-9 21.6 10^-5 18.7 10^-10 22.0 10^-6 19.6 10^-11 22.2

By comparison, the worst SNR allowed for a POTS telephone line is 24 dB (which would cause most customers to scream bloody murder). That is 2 dB *higher* than the 22 dB which produces a vanishingly small error rate on a binary digital system.

The above chart is from page 361 of "Telecommunications System Engineering" Third Edition, Roger L. Freeman, 1996.

It is summed up by Freeman with this statement,

"In a purely binary transmission system, if a 20-dB signal-to-noise ratio is maintained, the system operates nearly error free."

And we might note that various different modulation schemes are even better than that. PSK for example would have numbers approximately 3 dB better, allowing a 10^-3 bit error rate with only a 13 dB SNR... which is a useful error rate unattainable at that SNR with an analog system.

Please look up a few definitions. Here is a web site that has a dictionary of standard terms, which is quite useful.

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A few that are relevant:

digital transmission system: A transmission system in which (a) all circuits carry digital signals and (b) the signals are combined into one or more serial bit streams that include all framing and supervisory signals. Note: A-D/D-A conversion, if required, is accomplished external to the system.

analog transmission: Transmission of a continuously varying signal as opposed to transmission of a discretely varying signal.

A digital system is one that carries digital (discretely varying) signals. An analog system does *not*.

But just to be sure we understand what "digital" is in regard to data or signals,

digital data: 1. Data represented by discrete values or conditions, as opposed to analog data. (188) 2. Discrete representations of quantized values of variables, e.g. , the representation of numbers by digits, perhaps with special characters and the "space" character.

analog data: Data represented by a physical quantity that is considered to be continuously variable and has a magnitude directly proportional to the data or to a suitable function of the data.

analog signal: 1. A signal that has a continuous nature rather than a pulsed or discrete nature. Note: Electrical or physical analogies, such as continuously varying voltages, frequencies, or phases, may be used as analog signals. 2. A nominally continuous electrical signal that varies in some direct correlation with another signal impressed on a transducer. Note: For example, an analog signal may vary in frequency, phase, or amplitude in response to changes in physical phenomena, such as sound, light, heat, position, or pressure.

Claiming there is no noise in a digital system, or that something applies to digital "modulation technique" as opposed to a digital "system" is indicative of not understanding what a digital system is by definition.

As I've pointed out in another article, Shannon's 1948 paper "A Mathematical Theory of Communication" has a section on digital channels with noise. On page 19, Part II begins with this:

"PART II: THE DISCRETE CHANNEL WITH NOISE

  1. REPRESENTATION OF A NOISY DISCRETE CHANNEL

We now consider the case where the signal is perturbed by noise during transmission or at one or the other of the terminals. This means that the received signal is not necessarily the same as that sent out by the transmitter. Two cases may be distinguished. If a particular transmitted signal always produces the same received signal, i.e., the received signal is a definite function of the transmitted signal, then the effect may be called distortion. If this function has an inverse -- no two transmitted signals producing the same received signal -- distortion may be corrected, at least in principle, by merely performing the inverse functional operation on the received signal.

I've always liked that paragraph because it defines the distinction between distortion and noise pedantically, but it also clearly indicates the concept of noise in a digital system.

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson
Loading thread data ...

Quoting Shannon to him seems to have scared him off... oh well.

I did want to know what he meant by "forward-error-correction bits" though...

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson

Niether do weasel words... but you found some.

A pointless statement, which is not correct anyway:

digital signal (DS): A signal in which discrete steps are used to represent information. Note 1: In a digital signal, the discrete steps may be further characterized by signal elements, such as significant conditions, significant instants, and transitions. Note 2: Digital signals contain m-ary significant conditions.

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The data is digital, the channel is digital, and it is a digitial transmission system is in use.

Which is why all fiber systems are digital, not analog, and provide the vast majority of the bandwidth being used for data communications these days????

Which is to ask, why are you posting such goofy statements?

And since his point was to negate it, but his statement didn't...

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson

I wouldn't push the analogy too hard. Mismatched impedance sends power back toward the source How would that be accounted for?

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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Reply to
Jerry Avins

An intelligent discussion of the topic must either be general, of use carefully defined and agreed-upon terms. I think we've covered the generalities, and defining terms like "receiver-side fidelity" so that they are not specific to a particular subset of applications isn't worth doing for now. We basically have no disagreement. Why work hard to write down what we agree about?

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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Reply to
Jerry Avins

...

You don't indicate the bandwidth occupied by the respective signals or their relative average powers. A complete accounting for the difference must account for those aspects.

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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Reply to
Jerry Avins

That's one classification of the system. It has no bearing on the actual nature of the signal itself. You would have me believe that fiber systems use digital photons as opposed to analog ones.

A frequency in the near-infrared is 400,000,000,000,000 Hz. The number of carrier cycles per bit that fiber systems use would hardly be considered efficient on wire lines. To rephrase, fiber crawls when it's judged by the throughput its bandwidth /could/ allow.

You don't get it so it's goofy? Come now!

...

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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Reply to
Jerry Avins

We don't need a "complete accounting" to demonstrate the point, which is that the above quoted statement was not correct. I didn't indicate the data rate either... Yawn.

Of course all of that can be done, but it is then more difficult to see the correlation, which *I* certainly did not want to hide.

Since you brought it up though, here is another little chart. (Generated from data that is available from a number of sources, but always as graphs that I cannot reproduce with simple ASCII text.)

Bit Error Rate Energy per bit / Spectral Noise Density, dB

PSK DBPSK 8-PSK

1e-02 4.0 5.6 6.2 1e-03 6.7 6.8 8.8 1e-04 8.3 9.2 10.9 1e-05 9.6 10.2 12.0 1e-06 10.5 11.1 12.9 1e-07 11.3 11.9 13.5

Satisfied?

If not, I would suggest more research. I'm sure that you can find an easy to understand tutorial on the net. Or you can visit virtually any decent library and find a copy of one or more editions of Freeman's book that I've cited.

Incidentally, the claim that my comment about "above a minimum SNR, digital systems are essentially error free" equates to "with non-zero noise and an information rate greater than zero implies infinite bandwidth" is bogus in terms of Eb/No, where clearly a greater than -1.6 dB Eb/No can produce low error rates without infinite bandwidth.

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson

That is *the* way that systems are classified.

Well, if *you* want to use only *your* definitions, how do

*you* plan on communicating with the rest of the world?

It's a *digital system*, no matter what *you* want to call it.

Yawn.

Your own definition, again?

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson

You'd seem more open minded if you were less open mouthed. If a signal occupies greater bandwidth, of course it can perform better in the presence of noise. A fair comparison of noise performance demands that bandwidth and power be controlled for. I'm sure you know that. Are you being deliberately obtuse?

Without it, there is no way to see the correlation.

No. Those are all digital systems by your criterion. How do they compare to analog systems that use the same level of resources? You need to open your mind to what's actually written, instead of filtering it through your preconceptions.

You said "essentially zero", not "zero". That gives you a pass.

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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Reply to
Jerry Avins

I'd say neither digital or analog is perfect. With analog one is pretty limited in the imperfections: low bandwidth for example. Or if better SNR is required the use of FM modulation. And (pre/de)emphasis: incresing some part of the frequency spectrum in level that you want to have with less noise, and decreasing the level (and noise) on eception.

Digital allows much more clever ways to do something similar: adjust the signal to the channel, i.e. make it 'white' and void of redundancy. JPEG and MPEG are examples here.

Thomas

Reply to
Zak

News to me. I thought that all electromagnetic signals were composed of integer numbers of photons. The only analog portion might be the probability that your system saw a photon when one was or wasn't there.

IMHO. YMMV.

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rhn A.T nicholson d.0.t C-o-M
Reply to
Ron N.

Why are *you* being obtuse?

This was not a "fair comparison of noise performance" between two systems. The point is that for whatever bandwidth is required for a given bit rate, the indicated SNR will produce an essentially error free channel. And no analog channel will do so at that SNR. There is no claim that resource uses are or are not equal, only that digital systems can function at lower SNR levels. And that *has* been demonstrated.

The implied meaning claimed above, that you support, is not correct.

Perhaps /your/ mind should be open, and something else closed?

In fact the discussion in Freeman's book from which that table came does *not* mention bandwidth or power at all; and for exactly the same reason that I didn't. In the section where he discussion digital microwave link design requirements he does go into detail. As noted below, that can be expressed as Eb/No in dB.

You need to accept that the point has been demonstrated in several ways now, whether you want to accept it or not.

If *you* think you can document that analog systems have better performance at those SNR values, be my guest to demonstrate it with the same kind of data from equally reputable sources.

But in reality what you will find is that virtually all long distance fiber optic links use digital, and that analog is used only on relatively short links, which is simply because fiber has a relatively high SNR.

You will also find that most telecommunication over satellite has also move from analog to digital, for the same reason. Power is a premium quantity on a satellite, and to obtain the same performance a digital system can use less power than an analog system. Actually, that also provides a nice example for your desired "fair comparison of noise performance" between two systems too, because in either case the transponder on the satellite is the same (and provides *precisely* the same bandwidth regardless of whether a digital or an analog signal is being sent. Typically a C-Band digital signal requires about 10 dB less transmit power than an analog signal using the same transponder (and with a C/N of only about 10 dB incidentally).

That is why virtually all satellite services, which originally began with various FDM and SCPC analog carrier systems have in recent years moved to digital.

Yes, Sherlock, I said that to begin with and you are just now noticing what it actually is that you are arguing about?

Who is being open minded, or not?????

--
Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson

Jerry's statemen is wrong, but it may surprise you to find that your interpretation isn't any more correct than his!

A signal is something that conveys information. If the information is discrete by its nature (states, levels, etc) then the signal is a "digital signal". If the information is continuous by its nature, the signal is analog.

Hence whether there is or is not an integer number of photons, electrons, or whatever... it is the *information* *to* *be*

*conveyed* that determines if it is analog or digital.

(I also usually like to point out that while "discete" is sufficient to define "digital", I personally prefer to be a little redundant and define it as "discrete values from a finite set".)

Whatever, if you have an analog system using photons, and not enough photons happen along to provide what you detect as a continuous change in signal... your system is still analog, but it has a low signal-to-noise ratio! :-)

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson

Well, the "too cheap to meter" was the slogan of the nuclear power industry in the 50's& 60's...

But it's damn near the case now on data modula the construction costs [lost 2 bankruptcies ago, likely]

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A host is a host from coast to coast.................wb8foz@nrk.com
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Reply to
David Lesher

...

You /still/ aren't reading what I write. I don't claim that analog systems perform better than digital. I I did -- and do-- claim that you haven't demonstrated otherwise. Of course a howitzer can shoot further than a .22. So what?

Sure. With fiber, bandwidth practically does grow on trees.

...

These exchanges are growing tedious; you answer only what you assume I write.

Jerry

--
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
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Reply to
Jerry Avins

But you cannot refute the examples and descriptions, with impeccable references, that I have cited which *clearly* demonstrate what I had said. Can you explain why everything from the PSTN to satellite TV and now broadcast FM has moved to digital? Is it because digital systems *don't* perform better?

And while you ignore the examples, and deny the obvious, you make inaccurate statements like these:

"A digital system useful where SNR is very low has a very low threshold and very low throughput."

Did I mention that a digital TV signal using a C band transponder needs a 10 dB signal to noise ratio typically, while an analog signal on the same transponder requires 25 dB?

"All electromagnetic signals are analog."

Not the sort of comment to instill confidence that you know what digital and analog systems are, much less when digital is better...

This will be my last reply unless *you* can be responsive.

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson

"Efficiency" is a two edged sword. If you want to apply efficiency to some existing technology you have to make allowances. If you want to implement something ssssoooo efficient that nobody can use it, you are on your own. If you know any "old-timers" in radio amateurs club ask them when 100Hz accurate Morse code became popular, it was when TX-RX equipment advanced to this kind of accuracy. So IT is about transfering info, and as much as possible on existing channels and in this context digitasation of info is "efficient".

Have fun

Stanislaw Slack user from Ulladulla.

Reply to
Stanislaw Flatto

Do you really not know? If you don't, then I'd suggest you've got a lot of studying left to do before you should claim that you understand how to compare the capacities of analog and digital systems.

Honestly, it's pretty rich to quote Shannon and then claim that you don't know what "forward-error-correction bits" has to do with it.

I have to say that this has been an interesting exchange, and it's unfortunate that I'm coming in so late in the dialogue as I'd really like to have pointed out the dozens of errors you've made along the way. If it's any consolation there has been some incorrect information posted by others as well, but you seem to be quite insistant that you know the answers. By my reading of your posts, you don't.

Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions.

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Reply to
Eric Jacobsen

Since he didn't say what he meant, *nobody* has any idea... that includes you.

Mind reading class?

Except that is *not* what I said.

There were not even dozens of statements, much less dozens of errors.

So, you pop in and say everyone else was wrong, that you know all the answers... but do not provide even one of them...

Who knows, maybe you do know. But...

Not much of a post Eric.

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Floyd L. Davidson            
Ukpeagvik (Barrow, Alaska)                         floyd@apaflo.com
Reply to
Floyd L. Davidson

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