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. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Getting the most information in a limited number of transitions
Started by ●November 7, 2013
Reply by ●November 7, 20132013-11-07
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.
Reply by ●November 7, 20132013-11-07
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... -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●November 7, 20132013-11-07
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
Reply by ●November 7, 20132013-11-07
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.comWell, that insures the DC balance but spends those precious transitions pretty freely. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●November 7, 20132013-11-07
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? 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. 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. 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). Any, not sure I understand the constraints correctly of fully, but thought I'd throw that out. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●November 7, 20132013-11-07
On 11/7/2013 3:37 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? >> > Well, that insures the DC balance but spends those precious transitions > pretty freely.??? PWM is designed to have minimum transitions per X amount of bits.
Reply by ●November 7, 20132013-11-07
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.
Reply by ●November 7, 20132013-11-07
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."
Reply by ●November 8, 20132013-11-08
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
