On 11/8/2013 3:50 PM, Tim Wescott wrote:


> There is noise, and there is distortion that requires equalization.  So I
> can't just have an infinitely finely-spaced PWM.
>
> I had been hoping that there was some developed application, and one
> person mentioned something -- so I'll pursue that and see what I can see.

With DC balance requirement and minimum transitions, symbol could be a 
period of square wave with variable phase from 0 to Pi (excluding 
endpoints). Gray coded data is obvious choice.
Frequency of the square wave is another degree of freedom; however there 
should be integer relationship between possible frequencies. Otherwise 
the receiver would be very complex and inefficient.

This frequency + phase modulation is probably as efficient as it could 
be. Sync and equalization shouldn't be a problem.


Vladimir Vassilevsky
DSP and Mixed Signal Designs
www.abvolt.com

On 08/11/13 21:50, Tim Wescott wrote:
> On Fri, 08 Nov 2013 13:03:34 -0600, mnentwig wrote:
>
>> Hi,
>>
>> maybe the original problem statement needs more detail.
>> Otherwise, the amount of information in a single transition (or two if
>> you need to establish a timing reference) approximates infinity, when
>> the distance between the transitions ("symbol length") isn't bounded.
>>
>> Assume the detectable time resolution is 1 (similar to discrete
>> amplitude levels in a conventional system, i.e. QAM). Then I can encode
>> 8 bits if the max. symbol length is 256, 16 bits for 65536 max. duration
>> etc.
>
> I'm not at liberty to detail the whole channel, so I'm trying to just
> shine a light on the relevant parts.
>
> There is noise, and there is distortion that requires equalization.  So I
> can't just have an infinitely finely-spaced PWM.
>
> I had been hoping that there was some developed application, and one
> person mentioned something -- so I'll pursue that and see what I can see.

You may need to be very pragmatic about the degree to
which you pursue perfection and the degree to which
you accept non-ideal performance.

I suspect that without a background in transmissions
through non-ideal channels, you might make some
elementary mistakes. It is one of those areas that can
take decades to understand and a large engineering
resource to implement. Seriously consider picking
off-the-shelf "components" and re-purposing them.

On Fri, 08 Nov 2013 13:03:34 -0600, mnentwig wrote:

> Hi,
> 
> maybe the original problem statement needs more detail.
> Otherwise, the amount of information in a single transition (or two if
> you need to establish a timing reference) approximates infinity, when
> the distance between the transitions ("symbol length") isn't bounded.
> 
> Assume the detectable time resolution is 1 (similar to discrete
> amplitude levels in a conventional system, i.e. QAM). Then I can encode
> 8 bits if the max. symbol length is 256, 16 bits for 65536 max. duration
> etc.

I'm not at liberty to detail the whole channel, so I'm trying to just 
shine a light on the relevant parts.

There is noise, and there is distortion that requires equalization.  So I 
can't just have an infinitely finely-spaced PWM.

I had been hoping that there was some developed application, and one 
person mentioned something -- so I'll pursue that and see what I can see.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Hi,

maybe the original problem statement needs more detail.
Otherwise, the amount of information in a single transition (or two if you
need to establish a timing reference) approximates infinity, when the
distance between the transitions ("symbol length") isn't bounded.

Assume the detectable time resolution is 1 (similar to discrete amplitude
levels in a conventional system, i.e. QAM). Then I can encode 8 bits if the
max. symbol length is 256, 16 bits for 65536 max. duration etc.



	 

_____________________________		
Posted through www.DSPRelated.com

Welcome to information theory.  Elegant subject, but the tools available for computing and designing signals are very limited.  You are probing around and while that's fine, you can get vastly different answers as you add more and more constraints.  

What many have suggested is to work in the differential domain.  In discrete time, let indicators denote the locations of transitions.  What is the minimum number of indicators to encode B bits?  Why, it is 1.  Define x to be the indicator vector of length 2^B.  Then for any B bits, you can encode with only one indicator, and thus mapping back from differential domain you get only one transition.  However, this is basically a pulse-position modulation scheme with HUUUUUUUUGE alphabet size.  Of course performance is poor.  

However, you should know that there are domains where such schemes are used, in particular in systems with significant nonlinearities, detector constraints, or electro-mechanical constraints.  Look up "Combinatorial PPM" as a keyword to find some interesting ideas. 

You described a transmitter that can send bilevel signal, but you haven't said anything about the propagation channel, noise, receiver constraints.  So we can all continue to conjecture, and try to fish further constraints out of you, or you can describe the entire system and help us help you. 

So, what it is that you are trying to do again? 

Julius 


On Friday, November 8, 2013 11:45:51 AM UTC-5, Tim Wescott wrote:
> 
> Ignoring DC balance for the moment:
> 
> 
> 
> If I separate a time period into 10 slots and allow two transitions, then 
> 
> I can encode 36 different possibilities, or about 5 bits with two 
> 
> transitions.  I pay heavily in terms of how well I can receive in a noisy 
> 
> environment, but I gain greatly in terms of how many bits I can encode 
> 
> per transition.
> 
> 
> 
> If I separate a time period into 21 slots and allow four transitions, 
> 
> then I can encode 4845 different possibilities, for 12 bits with just 
> 
> four transitions.
> 
> 
> 
> Trying to achieve DC balance then complicates things, and I'm obviously 
> 
> far more noise sensitive than if I just transmit binary.
> 
> 
> 
> There's lots of avenues to pursue, most of which are dead ends, which is 
> 
> why I was hoping to find someone who'd already been there and done that.
> 
> 
> 
> -- 
> 
> Tim Wescott
> 
> Control system and signal processing consulting
> 
> www.wescottdesign.com

On Fri, 08 Nov 2013 08:17:44 -0800, makolber wrote:

>> With the current equipment that I have to work with I cannot use the
>> entire >bandwidth available to me, because I cannot exercise the
>> modulator to its >fullest. -- Tim Wescott Wescott Design Services
>> http://www.wescottdesign.com
> 
> I must not understand the question because the answer seems to be
> trival...
> 
> encode a 1 as 1  and encode a 0 as -1
> 
> doesn't that yield the least amount of transistions?
> 
> If you want no DC component then xor your data with a PRBS stream before
> encoding?
> 
> I must be missing something in your question.
> 
> Mark

Ignoring DC balance for the moment:

If I separate a time period into 10 slots and allow two transitions, then 
I can encode 36 different possibilities, or about 5 bits with two 
transitions.  I pay heavily in terms of how well I can receive in a noisy 
environment, but I gain greatly in terms of how many bits I can encode 
per transition.

If I separate a time period into 21 slots and allow four transitions, 
then I can encode 4845 different possibilities, for 12 bits with just 
four transitions.

Trying to achieve DC balance then complicates things, and I'm obviously 
far more noise sensitive than if I just transmit binary.

There's lots of avenues to pursue, most of which are dead ends, which is 
why I was hoping to find someone who'd already been there and done that.

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

> With the current equipment that I have to work with I cannot use the entire >bandwidth available to me, because I cannot exercise the modulator to its >fullest. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com

I must not understand the question because the answer seems to be trival...

encode a 1 as 1  and encode a 0 as -1

doesn't that yield the least amount of transistions?

If you want no DC component then xor your data with a PRBS stream before encoding?

I must be missing something in your question.

Mark

On Thu, 07 Nov 2013 22:01:13 +0000, Eric Jacobsen wrote:

> On Thu, 07 Nov 2013 15:05:37 -0600, Tim Wescott
> <tim@seemywebsite.really> wrote:
> 
>>On Thu, 07 Nov 2013 18:59:13 +0000, Tom Gardner wrote:
>>
>>> On 07/11/13 17:35, Tim Wescott wrote:
>>>> If wishes were horses, then after writing this I'd have one hell of a
>>>> feed bill:
>>>>
>>>> Say that I have a modulator that can transmit bi-valued information
>>>> -- let it be -1 and 1 for the sake of argument.
>>>>
>>>> I can transition from one state to the other any time that I want,
>>>> but each transition carries a cost -- so I want to design a
>>>> modulation scheme that maximizes the amount of information that's
>>>> carried for a given average frequency of transition.
>>>>
>>>> The signal that is so modulated is transmitted through a noisy
>>>> channel,
>>>> so I'd like something that does a good job of packing the transmitted
>>>> energy into the received symbols.
>>>>
>>>> While I'm wishing, something that insures DC balance, or better and
>>>> has a distinct guaranteed average zero over some (fairly long) period
>>>> of time would be best.
>>>>
>>>> And finally, something that ends up with nice orthogonal symbols at
>>>> the receiving end, and that isn't too arcanely difficult to
>>>> synchronize to would, of course, be nice.
>>>>
>>>> Any thoughts?  I was trying to decide if there's some M-ary version
>>>> of MSK that could be squared up and used, but somehow I don't think
>>>> that's going to work.
>>>>
>>>> Thanks in advance.  I think I need to call the feed store.
>>> 
>>> Maybe I'm missing something, but if you add inter-symbol interference
>>> to the AGWN, don't you have exactly the channel that the cellular
>>> phone RF engineers deal with? The latest standards get very close to
>>> the Shannon limit - certainly closer than any amateur is likely to
>>> dream up.
>>
>>That's a good thought.  I don't think they have the same constraint that
>>I do -- they'll be more concerned about bandwidth in an environment
>>where an actual transition is otherwise 'free', where I'm more concerned
>>about limiting the actual transitions between the two states.
>>
>>But I'll take a look...
> 
> I'm still kinda confused about your requirements.   What is the original
> information that you're trying to modulate?   A bit stream? Are the bits
> arriving at a regular rate?

It's more like measurements are taken at a rate that's constrained by the 
data rate.

> IIRC you have the 2nd edition of Sklar's text, so maybe it's different,
> but in the 1st edition Chapt. 7 is about Modulation and Coding
> Trade-Offs, and Figure 7.6 shows an example of a bandwidth-efficiency
> plane.    This sort of thing allows you to pick your SNR (Eb/No) vs
> spectral efficiency (bits/s/Hz) tradeoff spot and see what common
> modulation type is near there, or pick a modulation type and see what
> you can get out of it.    He also shows the Shannon limit and Capacity
> boundary on the same plot, which you know you can't go beyond.

Yes, I understand that it's usual to think in terms of bandwidth when 
you're trying to communicate through a given channel.  In my case I'm 
stuck with an unusual modulator which cannot have lots of transitions.

> If the bits are arriving regularly the modulation type should be able to
> be selected reasonably easily, assuming your medium is an electrical or
> EM thingie as opposed to glass or water or acoustic waves or something.

It's an "or something".  If it was EM, I would have given the client your 
name and regretfully washed my hands of the opportunity.
 
>  From there it's probably a coding scheme that might allow you to
> minimize the transitions, but that's going in the opposite direction
> from usual in that transitions are typically needed in the demod to
> maintain synchronization, especially at low SNR, and for a number of
> other reasons (high entropy in comm is usually high efficiency, reducing
> entropy usually carries some cost).

I understand that, and keep smacking into that while tussling with it 
intuitively.  I had hoped that someone may have actually had some 
experience with it, and had some formal tradeoffs worked out.

> Any, not sure I understand the constraints correctly of fully, but
> thought I'd throw that out.

Just think in terms that the transition itself costs more than any 
increase in bandwidth caused by lots of transitions.  With the current 
equipment that I have to work with I cannot use the entire bandwidth 
available to me, because I cannot exercise the modulator to its fullest.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

On 11/7/13 1:37 PM, Tim Wescott wrote:
> On Thu, 07 Nov 2013 15:28:44 -0600, Vladimir Vassilevsky wrote:
>
>> On 11/7/2013 11:35 AM, Tim Wescott wrote:
>>
>>> Say that I have a modulator that can transmit bi-valued information --
>>> let it be -1 and 1 for the sake of argument.
>>>
>>> I can transition from one state to the other any time that I want, but
>>> each transition carries a cost -- so I want to design a modulation
>>> scheme that maximizes the amount of information that's carried for a
>>> given average frequency of transition.
>>
>>> While I'm wishing, something that insures DC balance,
>>
>> Something like PWM(x) pulse followed by PWM(-x) pulse?
>>
>> Vladimir Vassilevsky DSP and Mixed Signal Designs www.abvolt.com
>
> Well, that insures the DC balance but spends those precious transitions
> pretty freely.
>

i dunno.  can you have 0 as a state?

so a binary 1 is encoded as   ... 0 0 1 0 -1 0 0 0 ...

and a binary 0 is encoded as  ... 0 0 -1 0 1 0 0 0 ...

overlap and add.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On 07/11/13 21:05, Tim Wescott wrote:
> On Thu, 07 Nov 2013 18:59:13 +0000, Tom Gardner wrote:
>
>> On 07/11/13 17:35, Tim Wescott wrote:
>>> If wishes were horses, then after writing this I'd have one hell of a
>>> feed bill:
>>>
>>> Say that I have a modulator that can transmit bi-valued information --
>>> let it be -1 and 1 for the sake of argument.
>>>
>>> I can transition from one state to the other any time that I want, but
>>> each transition carries a cost -- so I want to design a modulation
>>> scheme that maximizes the amount of information that's carried for a
>>> given average frequency of transition.
>>>
>>> The signal that is so modulated is transmitted through a noisy channel,
>>> so I'd like something that does a good job of packing the transmitted
>>> energy into the received symbols.
>>>
>>> While I'm wishing, something that insures DC balance, or better and has
>>> a distinct guaranteed average zero over some (fairly long) period of
>>> time would be best.
>>>
>>> And finally, something that ends up with nice orthogonal symbols at the
>>> receiving end, and that isn't too arcanely difficult to synchronize to
>>> would, of course, be nice.
>>>
>>> Any thoughts?  I was trying to decide if there's some M-ary version of
>>> MSK that could be squared up and used, but somehow I don't think that's
>>> going to work.
>>>
>>> Thanks in advance.  I think I need to call the feed store.
>>
>> Maybe I'm missing something, but if you add inter-symbol interference to
>> the AGWN, don't you have exactly the channel that the cellular phone RF
>> engineers deal with? The latest standards get very close to the Shannon
>> limit - certainly closer than any amateur is likely to dream up.
>
> That's a good thought.  I don't think they have the same constraint that
> I do -- they'll be more concerned about bandwidth in an environment where
> an actual transition is otherwise 'free', where I'm more concerned about
> limiting the actual transitions between the two states.

They are *extremely* concerned about bandwidth, and
have layers upon layers of techniques to minimise the
bandwidth.

The primary metric of quality of their systems is
"bits/s per MHz per km2". The MHz and km2 are fixed,
so the Shannon limit dictates the max aggregate
bits/s i.e. the max income.