FPGA Central

Eric Jacobsen wrote in
http://groups.google.com/group/comp....369177d865440e :


> On Sat, 17 May 2008 15:55:02 -0700, "Green Xenon [Radium]"
> <[email protected]> wrote:


>> Let's say I am using QAM and want a baud-rate of only
>> 1-symbol-per-second but I want there to be 1-billion-bits-per-symbol.
>> How many phases do I need?
>


> You can do it with one if you have log2(1B) amplitudes. Two if you
> have log2(1B)/2, four with log2(1B)/4, amplitudes, etc., etc. With
> QAM you can encode information in both the phase and the amplitude.


If I have log2(1B) phases, I need only one amplitude. Right?

If so, then -- just out of curiosity -- could such a technique enable 1
Gbps speeds on dial-up internet?

On May 18, 2:01 pm, "Green Xenon [Radium]" <gluceg...@excite.com>
wrote:
> Eric Jacobsen wrote inhttp://groups.google.com/group/comp.dsp/msg/dc369177d865440e:
>
> > On Sat, 17 May 2008 15:55:02 -0700, "Green Xenon [Radium]"
>
> > <gluceg...@excite.com> wrote:
>
> >> Let's say I am using QAM and want a baud-rate of only
> >> 1-symbol-per-second but I want there to be 1-billion-bits-per-symbol.
> >> How many phases do I need?
> >
>
> > You can do it with one if you have log2(1B) amplitudes. Two if you
> > have log2(1B)/2, four with log2(1B)/4, amplitudes, etc., etc. With
> > QAM you can encode information in both the phase and the amplitude.
>
> If I have log2(1B) phases, I need only one amplitude. Right?
>
> If so, then -- just out of curiosity -- could such a technique enable 1
> Gbps speeds on dial-up internet?

If it could, then it would have already been done. Google for "Shannon
capacity theorem". They've pretty much squeezed all that can be
squeezed out of a 3-kHz channel on a copper telephone line. I assume
what you're suggesting is log2(1B)-PSK.

Jason

[email protected] wrote:
> On May 18, 2:01 pm, "Green Xenon [Radium]" <gluceg...@excite.com>
> wrote:
>> Eric Jacobsen wrote inhttp://groups.google.com/group/comp.dsp/msg/dc369177d865440e:
>>
>> > On Sat, 17 May 2008 15:55:02 -0700, "Green Xenon [Radium]"
>>
>> > <gluceg...@excite.com> wrote:
>>
>> >> Let's say I am using QAM and want a baud-rate of only
>> >> 1-symbol-per-second but I want there to be 1-billion-bits-per-symbol.
>> >> How many phases do I need?
>> >
>>
>> > You can do it with one if you have log2(1B) amplitudes. Two if you
>> > have log2(1B)/2, four with log2(1B)/4, amplitudes, etc., etc. With
>> > QAM you can encode information in both the phase and the amplitude.
>>
>> If I have log2(1B) phases, I need only one amplitude. Right?
>>
>> If so, then -- just out of curiosity -- could such a technique enable 1
>> Gbps speeds on dial-up internet?
>
> If it could, then it would have already been done. Google for "Shannon
> capacity theorem". They've pretty much squeezed all that can be
> squeezed out of a 3-kHz channel on a copper telephone line.


> I assume
> what you're suggesting is log2(1B)-PSK.


What's that and why the '-' sign before the 'PSK'?

Also, does QAM require that there be changes in the peak-to-peak
amplitude of the signal? Or can the peak-to-peak amplitude remain
constant while the phases determine the signals?

If I want 1-symbol-per-second with 1-billion-bits-per-symbol, can I use
QAM with a constant peak-to-peak amplitude but with log2(1B) phases?

You need to include the effects of noise, or your line of thinking won'
make sense.
Regards,
Steve

On Sun, 18 May 2008 13:17:44 -0700, "Green Xenon [Radium]"
<[email protected]> wrote:

>[email protected] wrote:
>> On May 18, 2:01 pm, "Green Xenon [Radium]" <gluceg...@excite.com>
>> wrote:
>>> Eric Jacobsen wrote inhttp://groups.google.com/group/comp.dsp/msg/dc369177d865440e:
>>>
>>> > On Sat, 17 May 2008 15:55:02 -0700, "Green Xenon [Radium]"
>>>
>>> > <gluceg...@excite.com> wrote:
>>>
>>> >> Let's say I am using QAM and want a baud-rate of only
>>> >> 1-symbol-per-second but I want there to be 1-billion-bits-per-symbol.
>>> >> How many phases do I need?
>>> >
>>>
>>> > You can do it with one if you have log2(1B) amplitudes. Two if you
>>> > have log2(1B)/2, four with log2(1B)/4, amplitudes, etc., etc. With
>>> > QAM you can encode information in both the phase and the amplitude.
>>>
>>> If I have log2(1B) phases, I need only one amplitude. Right?
>>>
>>> If so, then -- just out of curiosity -- could such a technique enable 1
>>> Gbps speeds on dial-up internet?
>>
>> If it could, then it would have already been done. Google for "Shannon
>> capacity theorem". They've pretty much squeezed all that can be
>> squeezed out of a 3-kHz channel on a copper telephone line.
>
>
>> I assume
>> what you're suggesting is log2(1B)-PSK.
>
>
>What's that and why the '-' sign before the 'PSK'?
>
>Also, does QAM require that there be changes in the peak-to-peak
>amplitude of the signal? Or can the peak-to-peak amplitude remain
>constant while the phases determine the signals?

In name, QAM suggests that there is amplitude modulation. If only
phase is modulated then it's PSK.

>If I want 1-symbol-per-second with 1-billion-bits-per-symbol, can I use
>QAM with a constant peak-to-peak amplitude but with log2(1B) phases?

Actually, I think it's 2^1B phases. That was my mistake previously
to say log2(1B). e.g., 8-PSK transmits three bits per symbol by
using 8 distinct phases. 2^3 = 8.

Conceptually what you're suggesting is okay, i.e., to use 2^1B phases
to get 1B bits/symbol. Clearly one needs an immense SNR and phase
precision to do this, though, so it's about as practical as my
single-clock-cycle FFT algorithm for any N. It's theoretically
sound, but I don't think it could be built or survive a practical
channel.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php

Eric Jacobsen wrote:
> On Sun, 18 May 2008 13:17:44 -0700, "Green Xenon [Radium]"
> <[email protected]> wrote:
(snip)

>>If I want 1-symbol-per-second with 1-billion-bits-per-symbol, can I use
>>QAM with a constant peak-to-peak amplitude but with log2(1B) phases?

> Actually, I think it's 2^1B phases. That was my mistake previously
> to say log2(1B). e.g., 8-PSK transmits three bits per symbol by
> using 8 distinct phases. 2^3 = 8.

If you don't run into thermal noise, you will run into zero-point
motion, that is, quantum noise. Even at absolute zero there is
still vibration creating noise.

-- glen