yes and and one of the lucky you guys will have a full time results position i don't have to teach and uh the first or or is uh for all so that one of my colleagues in the level crossing signal time and both of those that device yeah that's right but use your not and uh this is paper is the side is result of it is it's H T okay the previous papers were speaking about right reasons problem we will be speaking about seven or problem how can you directly obtain the iterative algorithms just like in turbo codes in durable iterative decoding the bic and which will be or from uh maximum likelihood estimation uh this week has been of interest since many years uh that are being and then is is of iterative decoding are being and with the of you six it charge density evolution that has been quite and then is is using factor graph belief propagation interestingly enough very basic understanding of the process was obtained using information geometry and in fact it was a first that and to address this problem and there also so a first that's using an optimization okay how could we obtain an interactive i don't even for performing something close to maximum likelihood using optimization this is exactly what we would be doing so that that that them the is first just so that such so that to do not for T to soon and the that we would be writing a maximum estimate then we would translate it using a very simple to that would be three three in in the a very simple tricks and very simple estimate in such a way that it can be uh the done in terms of optimization then ooh will show that that um using a single approximation we can obtain exactly the algorithm which is used for decoding bic C N but and this approximation will be used some so okay three K and uh uh we gonna use this trick to check there is that of bic and it be is efficient or not so a meaning from a that time to really understand how you could be a the algorithms will get information about the efficiency of the algorithm so that cool so it is the situation which would be sitting we have a convolution and for the information bits here the code words here which are interleaved map to symbols and then sent them to the channel i would not be specifically working with specific interleavers specific but things or whatever everything which is a can in the paper is is valid for a a a a kind of interleaver or any kind of symbol matt and of his see the performance will be different and that it will be seen right okay so in addition to see that will the close here i uh but let us here are vectors okay so because of the thing with vector is a and an individual bits okay the binary messages C and go to do it's interleaved sequence and uh okay there's okay so the maximum likelihood sequence detector is like that it's of use it's very basic uh where and you can either where where maximization or over you the the binary messages or the it works coded bits provide in that you can every combination of the coding bits it's which do not don't to the goal okay this is a a a compact notation for saying i was zero is the indicator function of the quality its value is a one for a code where its value is zero or for a a combination of beach which does not be that belong to the core okay since this is not really easily manipulate it is from the optimization well we use this is very small a which i the been you write the used but which has a can be found that's where so meaning that you can maximise a there on that oh and the value of the probability P here uh so so that the thing the maximum of the argument of this function that are then if it's up for that one is that this probability can be fully factor right meaning it's a product of individual probabilities for each bit okay it's a matter selection and most than than anything at and the second advantage is that this this problem T is continuous so for an optimization problem is much and but not continue okay and you state this problem is on track double why because you have many need in that in the vector and if you want to do a i to compute this quantity for every possible combination you a lot what okay but this is the the first request was to be cushion but the per bit second rate is that in this problem you have to kind of information one information is coming from the channel a because you you a measurement coming composed of the the information is coming from the fact that you are looking for can i did this is a of information and and is probably but as so okay in this for but here we just fact i is it in that and L we take care of one of the information Q with take care of the all their information okay and instead of working with the probabilities is for the front that was what will be working on a big margin meaning we will have a and variables instead of to to the uh obviously maybe we we of go very far using exactly this procedure we can but to here in this process here we do not have any kind of approximation we have no the bit margin as appear and this equation here is exactly equivalent to the previous one this an approximation with have in this talk is this one the bit much or and a of the product i we pose but the product of be marginal okay so so that the previous equation is replaced that this one okay obviously seems to be a coarse approximation it happens that if you choose directly the interleaver or if you choose to the mapping it's that the too bad approximation okay okay but the coding now uh is that of a think is tractable because the computation of the marginal destructible okay this is struck but this is computed well this is computed vol and uh now we have a is a a problem which is a different for each bit so we change the problem now but they do the criterion here the bands i'm K depends on the location of a so that the average original problem is replaced by a by you distribute the optimization strategy and the only the problem seven of and cost function okay this criterion yeah is relevant for the mac for the cliff be okay and you it is shown that if you do that for the K B the solution must be something like that meaning that if you have a solution to the prime that mean from one of the set of information i'm of a V coming from the other a set of information but must agree for the maximization a which should here would be for a whether this it will be you you zero or one okay so they have to agree on be to make of this bit okay so i and that in this process context the that that a mediation of oh C case must provide an agreement between the code or estimate and them D mapping estimate the for the beacon position K but and that is that are independent optimization the musicians maybe you could do not agree implicitly for the estimates of the other okay so and you will see in in the next few slides that the track collaborative them used in decoding of the S C N is is exactly the solution all this kind of problem okay so that i to know that i can't time is that i i only derived bic and decoding and algorithm it to to use C M decoding a one using the single approximation for a maximum you not well in need building a my it up working more on that meaning that if one not a little lower of the group it if you if you if you will take the um of of these criteria now you are just not you can not have inconsistency consistency between the estimate of the base for the values case okay so if i think has to a in some way meeting that yeah the if you taken by this quantity will be an indication of the agreement between the coder and the demapper for the sequence okay if you work individually and that it's the most agree but if you were on the one sequence the kind of three and thus there is absolutely no where and this is for of here if you do not have any kind of the error the as as you made provided by these criterion would be exactly the maximum likelihood so this is true in the paper okay so that's given in words what is written here in equation okay now this is outlined here only that's the we must come back to the individual criteria C K if you just minimise these the individual criteria you just fine that this completely here is is it did not there this be to here is something which may be look strange but it is exactly what is computed by you the C G I E R algorithm okay so would be fixing one of the one set of the want it is and who will go to do that you interactive musician we have a is i mean standing station here we that oh okay pigtails to the to some three use a value and we compute the next completely based on sept solutions this one here for for or computing you and this one here for computing have if you just know that what everything is doing this is but the or classical in the are S E and decoding and this is exactly what is computed but you be C J R are are greater that meaning that channel decoding algorithm it's a a compact notation that you can numerically to check that do this is to it B C J are maybe it's not that when one if you provide to a C procedure i to a probability is that it should be if you compute the probably probabilities of each possible work right product of these quantities quantities kill but of the words which do not we don't to the code and then compute the matching also a which is exactly what is we and here if you do that you have to exactly at in the output of a B C J and it turns out that this quantity is which were they now by matt's me maximizing some criterion are exactly the web keep the in in in uh coding name the extrinsic information and now there is no magic in for graduating in six rather than a are plus to a it is the uh uh true since that as and have group of the mediation procedure so to to i we have an optimization problem which was or to model maximum likelihood we can obtain single first exactly equivalent to maximum because you like to a good detection we have a an approximation which has been obtained by fully factor using this the the probability mass functions then then a so that model algorithm because we had individual uh quantities is which were optimized through a distributed optimization strategy and we can if you know come back to the glue factor in the first the sum of all possible C case we know how a way of evaluating E yeah approximation was good or not because if we write the uh um the the sum of the individual criteria we will not be able to check if the did not for and the decoder where the greeting on on of values which where for for the day so that's provides as a way of evaluating the quality of the solution of the ica and it directly decode okay we have covered just problems which a a in another the paper okay so that's see first okay what is new here nothing but the fact that we thing it may be a B S C and decoding or even but as the fact that we have maybe be a way of checking if there is that is correct on not and you can see here the cost function of the mixture means that of the global maximization first the let's say the bit error rate that number of errors we are known as K and you can see that that's for C T V for maybe you can see that the refuge correlation it can be one okay and as another example i i show you these kind of result we have but duration of sixteen grand by mapping the set partitioning convolutional code this five seven and we are mixing their use E V over and zero from five to twelve db with a uniform distribution so it is a very complex situation if we choose the threshold indeed be equal to minus twenty here okay so the bit error rate for the frames above the threshold which are assume to the uh who because they are are you are trying to maximise the functions are above a threshold it that's okay you see that above the threshold the bit error rate it quite stable but if if you change the the threshold for of frames and of the fresh you have a much higher bit error right okay i it would be a is your here um okay one here okay but we are close to that and but that's a page yeah of three G T frames well i there would be correct is very small and and what is as is the probability of first i'll a meaning that the point that not per cent ish of sequences which are to been rejected because build a because the right below of the threshold but that work correct okay but this is the basis of the work okay okay that me summarise what we obtain iterative decoding obtained from maximum likelihood we we had no specific assumption about the book things that we you a mapping or whatever the is obviously will impact the performance the in by the quality of the upper be here approximation which has been made in the in this where we obtain clearly a that we should provide a extrinsic information between both lot rather than a was probably is and we have a a we have a common just a do which has been a set it okay could be know that we do use a go and uh uh we have a the process for a evaluating the efficiency of the result uh because of this and that is and it's likely we not sure that simulations are running to check that that B most of the as we have in this kind of course G are not you good approximation but most of them are out you to conventional to local minima uh which is okay makes sense but we have to prove that and it work current yeah and a ticket and that do you think the some kind of some as is can be applied to to about composition could could you like to to of current position well well is it okay that this applies to any kind a okay it's a toy example bic and here is that for example it applies to so you editions on which you have several four sets of information on the same seem would you have here three sets of information in a a coat on top of the M this would apply also that that's okay it's quite generic a um i you aware of any results from information tree which word um justify your approximation no which i and i can send you your the the psd of the uh not to what was specifically working on information theory from a some geometry up like to these kind of work it's tricky and we could not really justified the approximation