and we right don't that everyone one um we pen uh and and this is a uh and so what we found since six agrees in T i okay so uh i first give you have a a a a brief background about uh these things rise detection in the um but a go problem and were looking at and then uh a power about the resulting a a message on feedback architecture in which are things as a a a a a lot to send two messages to the fusion center and then we tell about a uh the are P but i've that to the so called a message own configuration base where or since as is only a lot to say uh one in the message to the fusion center then will conclude sound a uh remote okay case for red a uh or would be of a these things wise detection basically we we have a multi sensors yeah use of them making a a it's all measurement and then you are there's a fusion center and all the six things as a was saying a quantized version of the measurements to the fusion center so so in um in in a and you know applications are what we talk about these are uh and that what we use it for about a wireless network so there's always a a a a a a cat that's is a you can on the channel between the sensor and the fusion center so that's why uh a is um a common to in that the quantization function has to match the measurement to a finite alphabet although though this is not really uh require you know problem setup uh but that's for for this and for these cars and C we were assume these are uh this this title quantization where you are mapping being to a finite of rubber and not we looking at use a binary hypotheses are testing problem way by a the sensors thing each since a a a the sense the measurements are coming from a to a a a a different hypotheses so we know that the line these solutions and the fusion center use uh trying to make a final decision based on the quantized measurements from the sensors oh oh oh which is the correct hypotheses so the the main uh a problem to solve in this case is trying to find the optimal strategy okay all these quantization function that were minimize on eric crack criteria so uh in this will would be a uh just comes into and looking at a that area a probably T it's so want to minimize the basing in error probability and this a sound has basically been studied you know over the last and to us by menu of those by in things the be our research but out of many different uh formulation may different things they and consider in these uh these enjoyed detection uh a can use that we assume that the measurements okay all observations of sensors are independent a a a a given a can use an on a you do hypotheses so this is because many because um he becomes a and B a problem you if we don't have are independent assumption in the general case or i i must at that a a i'm the some special case of when you have call a call we the measurements but and is on special these solutions you would do you you why able to find you are optimal solutions so the main problem that the will do at ease are can see the uh the pro the question of are having feed that in these are these things i think detection architecture so uh by feed that we are going to define in of or right of age noise things uh so that if but i one to being at is basically were um um are all sensors have information about some all or other things as messages so uh in them i just in the nodes uh a go kind all the most people are a way that people around as in feed that you are in these kind example where you have sensors us sending uh in a and ties measurements to a fusion center a fusion center is coming up reading the every decision and then is but cost everything back to the few all the things those and the sensors were saying a second message making use of these on reservation as so is that's wrong information that i now games right from of use and centre a a to and the second message before before was saying a a back to the fusion center so this this would be a um a a a a a a not to do the kind of feedback there a a on this thing uh about will be looking at a so now and in to this is that we call a two message some configuration oh we also do at uh some one mess X about these eating configuration it don't but the that thing to note you use that the message messages are not independent anymore because um now the second message is going to depend on ah information that a actually you is that car really some of the things of measurements of with you a and we want to and so close of how to design all these are quantization function singer know optimal away K where the optimal a i in the there's use would do that okay so yeah so this key the problem that people that we want solve is to to of find all these are team uh on use and functions to minimize or error a probably the a we know that using a a likelihood ratio quantizers is i use the a team in to do so not surprise hearing C's as you some by uh a king and a fast knee ninety six so they provide a uh so call P uh as and by an optimal solutions whereby if you fix uh the the quantization functions all file all the other things thus okay except for the one are interested in you fix all the rising day you you can uh find the optimal quantizer for that particular things that uh you want to optimize okay and you can can do this iterative the so is by a side of process and to fine two uh to will find the optimal solution to compose of a the solution a at the end they about unfortunately there's not close once a reason in uh we don't really know why use the uh performance uh the ads actual performance uh uh and then to good performance of the uh the or um put particular architecture okay so all these word depend on numerical michael computation uh so that is not a price okay so even but we out feed that we we know that find a a a uh these optimal quantizers is that they've got problem K uh you do we even if we assume that the sensors are making i i'd observations okay it turns out that a a the a D much as was okay so but we we know that all the cup uh since as to be using that you racial quantizers so base you want to find a too much wrestle okay oh oh ah a oh of these are likelihood ratio quantizers and that's wrestles kind can be different okay you well you use of a basically you to find stress soon use of a a system a couple you questions and can sound this so can be a different even five we've i idea some sense so um the if you want to find a a the optimal solution i so i missed the problem right in uh i intractable tractable and uh use difficult got to compare the performance of a with a if you have it down here you have no feed that was the difference in in the performance or even one compatible performance across different kinds of a on that were architectures okay so that's why that's the it this motivation for looking at these also quite a respondent okay so what we you one to do is on you still trying to find a the a team was we use and we want to a fine i strategies disease that uh that mean all these these errors buildings an egg you want to use or want to find uh a team uh strategy is to minimize these error exponent of maximise the F so we value all these error exponent can so that a a power configuration we all feed that we we see that the um a team error exponent is given by a uh finding the quantizer the that a a a minus the such an a an over here okay and and this so we so we see that is actually a team of for all the things is to use the same quantizer a K two uh to quantized a measurement before is saying send you back to the fusion center okay so now look as as a if we use we use the same kind of or how are we going to uh a that these uh a problem of that we a how the the i don't have a spend and then D for from the case of these parallel configuration ralph so the first a a that's so are looking at use the uh to two its architecture which are already uh this a brief these us now also so um i didn't well is happening here is the first message saying by use things the okay so we is the oh okay is quantized by some quantization function and the that do we sent to the fusion center so now i it was an a is gonna car it a feed that message so this can be a of and no if that message a which can see some of V are sending a feedback that two things are K so what you need to do we you you only need to take all the measurements uh or the messages from the all the other things as use some cell function to from the message and feed that to since okay maybe has sense K already we he's all measurements we we or we know like a so we doesn't need you don't need to consider that inside is on feedback comes and uh the second that is is going to be for use things that can using a old measurement okay so these nice alone doesn't change that may only one single measurement each sensor and also also based on the as strong information that the fusion center has provided to form a second message before passing me back to a some something and finally a fusion center of make a final decision based on all the message it was all the first message as a sell like the second message a to make the final decision so that are two types of it that that we can do get the first one is the so for three that way by you there's a you don't want eyes any of the information the fusion center doesn't compress any other information you has so we sense of for every information back to the or the sensors uh use no light uh a a a a a a a it because up because um in in in actual a because he's using you won't be able to i be doing to do that because we we are doing use a where increasing the number of things as like so this is that sometimes them as a character okay that go set up and then map in that case is when you have a re should the feed that where you are use of your are um feedback information is as you compress okay to some find for but in don't in here is that we are assumed that a fusion center is gonna retain all these values or the values of the first messages okay used used retaining that okay a a compressed person so that is the the first result that we have all the um to to message architecture and turns out that as you the average spend that under the for feed that case is is send S are at every S more under the restricted that case and better than not the same as the error and and the the parallel configuration we that so the how that that is an our as known are talking about yeah is uh when we do at the is saying so actually a lot to send a a a a a message is as you or you can do not be says having a a a a that message about of it the power the number of be so we the original you can string of quantization functions to we have any uh i have a for the size of a diesel down have the power configuration were be a a it to send a message of of of a but size of two D okay so it lot these results is that a that is oh you you so not useful we we are talking about a exponent um that we is a big and in to give a uh maybe a i can try they spend these no when we first did is the result i also the hidden facts bet that feedback back as you doesn't uh improve the error exponent but you know as we've moves the results way a set oh i i have some intuitive explanation for that so uh in this case of what is happening these are all the feed that you know a finite when you have find that number things as your feed that can improve your error exponent and no sorry can improve your detection performance uh uh is that in to a of of the the power configuration soon use not increasing in sporting city fast so we were talking about about uh a rose bone were talking about uh yeah how to here a a as should with the the every race on the king sporting you fast well we see is the feed that improvement he's no in uh use now at the saying this point is a scale where the as the main every self so that's i so even though when you doing the for see that you are not going and to get any a uh it's true a gain in terms of error experiment so in terms of the proof so uh and just going go through a a few a a few steps of the proof so the first thing to know use that we know that the full feedback cases of is going to be better than of the received that case right in the from that case of a feeding back the fruit phonation okay so in this case you can the for feedback case you are able to see me the the received a that case a ease of the things by T uh a in the the for information in compressing then and then a that the receipt a feedback is a is a is a better than the the parallel configuration because of in this case we can just know the feedback that can achieve the same performance so that we will do need to so be in this case is that the from feed that a a a a can not go for and as well as a parallel configuration and the the way to go about doing these Z uh using a lot so uh that a real the last deviation so we had from the trend that by we have a a little about that depends on um this low moment generating function i so i is the second and they're be for the lot more more joint thing to my function so to well we need to do is uh as actually the the means that used to trying to a these on the value of these directive the where and we have i the observations disease as you quite easy you do not when when our observations are no longer a i D because a and the second message is as recall rate that with each other okay so that that would be the this is the main problem down here that we need to about so if we do that is known in generating function seems about the do talking about a a likelihood ratio yours alright these are lot and renting in and has this phone is a convex curve that goes uh take the value is you i'm during one uh well we have these uh this uh this result that says that if i E do at the a is just planning on this curve or a of is gonna change when the the number of nodes increases okay you would get sampling shopper uh what happens he's if i do that uh fixed once low on the curve okay and i do at the second if at the point that that has no that's not T then these a second derivative can not increase uh a starting point not really okay so the a that's that's he's actually uh you in not in there then um applying james and in quality at um a a a a in is and uh cases in a by trying to all uh the second directly the first and second or these with their are quantizer portions i of the uh all of a wide a function that you know trying to copy okay so once so we have that the and once you can buy the secondary T if and then you see that uh these this funds this square a function will were go to zero if you take the a we have a angle a on both sides okay and you are left with these thing and and in are we need to find a a a a lower by of for these are uh moments renting function which can be easy D down okay is not to do got here and in the there is uh the is uh a lot of and in function can be shown to be ah to be the little bottle by these are i respond and from the parallel configuration okay so one a a a a week one thought of that some and that we were making use that the fusion center a readings the for the information the message so as the first set of messages so i can see if you has only limited memory and can only a a a a reading of compressible version oh of these are a them at macy's message was and ten out that this is as you a got problem K uh so that the top how in night to use a all tax approach that uh because it is a matter of types of you need to assume find a of about observations i didn't a good no quantization function so one okay to to to so like in this case is uh the feed that also doesn't help we a to open problem that in the more general uh scenario with the these uh how does a few that contribute to the error spend then a so you know that to kind of try to gain some insight into that problem than we do a a really the problem the so i one i six are architecture way by now we have we do but the sensors into two to good of things as so the first goal was so as is uh things the first message uh to the fusion center and fusion center fixed back these are compressed i don't the for information or compressed version to the second most things sensors okay ooh in this case if you you will uh the architecture use actually equivalent to a to this kind of that so a i that so that's why is a call you are uh daisy chain architecture okay where you you have a first the the i so as we at which can be compressed or or you and then before use been fact that to the a a second group most things are they so that didn't we can see that two types of it that the for that okay where you there's no loss in the information that is been fact that you know the risk a feedback case and again we have to a uh you know go T which is uh in media so that in the full of feedback case the for three that every and then has to be at you have at least ask us as the we that one okay but in this case we need to compare we've the tree configuration so in this case if we don't have any you back to the second group a basically are getting a three okay so uh a reason that thing to do is to compare these we've the i or ten minutes three so okay a again if we have a feed that the actually the error S one a same as the parallel but E if we if we have we should that feed that in this case one just doing didn't happens use that you receipt of feed that is she the you worse than your parallel configuration okay okay use a by the by your tree error exponents so in some cases this the receipt a feed that have one and can be the same as a three N in some cases which we can uh find uh put to good example do so that the received a feed that use um i actually were saying the street K so that have a smaller than you this case and that for the received the feedback is has a given by these uh this expression suppression what here if you do that these one B C's actually um is happening here is the first school are so as is going to use the same quantization function come mad and then at the at the first stage the fusion center is con compared the ah the receive are likelihood ratio we've that's that's T okay before you saying um before you compress the all the the a a first group of information i i first group model of a sense this so green into a really decisions you are one so in this case if a the second row things the received a zero fun of use think that is going to use a different quantization as compact use uh receiving a one okay but in in either case the second be is going also going to use the same quantization function okay the which depends on the feedback message oh there so i in this case under the uh is sounds we also provide some special conditions we by a receipt of feed that i read or use the same as all tree at right one then okay so in conclusion that that a S messages this is uh uh we had that binary hypothesis testing no by i mean the decentralized binary hypothesis testing problem and we so that she that in the two configurations that we talk about uh does not improve the error exponent but that's because uh the fusion center has access to a full information that is available a a lot of can get from these it's seems memory she right uh the performance gain due to feed that may not so i you're increasing the communication cost when you're are you're do have feedback that we see that feed that can as improve on her from in the received that feed that uh well i six a busy chain architecture okay and we provide a characterization for the exponent so that L i if the top of that mean be we've one open problem okay i okay