0:00:13yes and and one of the lucky you guys will have a full time results position
0:00:17i don't have to teach
0:00:18and uh
0:00:20the first or or is uh for all so that one of my colleagues
0:00:24in the level crossing signal
0:00:26and both of those that device
0:00:28yeah that's right
0:00:29but use your not
0:00:31and uh
0:00:32this is
0:00:33paper is the side is result of
0:00:35it is it's
0:00:36H T
0:00:43the previous papers were speaking about right
0:00:47we will be speaking about seven or problem
0:00:50how can you
0:00:52directly obtain
0:00:54the iterative algorithms just like in turbo codes in
0:00:59iterative decoding the bic and which will be or
0:01:03from uh maximum likelihood
0:01:08this week
0:01:09has been
0:01:10of interest
0:01:11since many years
0:01:13uh that are being and then is is of iterative decoding are being
0:01:17and with the
0:01:18of you six it charge density evolution
0:01:21that has been quite and then is is using factor graph belief propagation
0:01:27interestingly enough
0:01:29basic understanding of the process was obtained using information geometry and in fact it was a first that and to
0:01:36address this problem
0:01:38and there also so a first that's using an optimization
0:01:42okay how could we obtain an interactive i don't even for performing something close to maximum likelihood
0:01:48using optimization
0:01:50this is exactly what we would be doing
0:01:53so that that that them the is first
0:01:55just so that such so that to do not
0:01:57for T
0:01:59to soon
0:02:01the that we would be writing
0:02:04a maximum estimate
0:02:06we would translate it
0:02:08using a very simple to that would be
0:02:10three three
0:02:10in in the a very simple tricks and very simple estimate
0:02:15in such a way that it can be
0:02:17uh the done in terms of optimization
0:02:22ooh will show that that um using a single approximation
0:02:26we can obtain exactly the algorithm which is used for decoding bic C N
0:02:34and this approximation will be used some so okay
0:02:37three K
0:02:38and uh uh we gonna use this trick to check there is that of bic and
0:02:43it be is efficient or not
0:02:46so a meaning
0:02:48from a that time to really understand how you could be a the algorithms will get information about the efficiency
0:02:55of the algorithm
0:02:56so that cool
0:02:59so it is the
0:03:00situation which would be sitting
0:03:02we have a convolution and for the
0:03:04information bits here
0:03:06the code words here which are interleaved
0:03:09map to symbols and then sent them to the channel
0:03:12i would not be
0:03:14specifically working with specific interleavers specific but things or whatever everything
0:03:19which is a can in the paper
0:03:21is is valid for a a a a kind of interleaver or any kind of symbol matt and of his
0:03:25see the performance will be different
0:03:27and that it will be seen right
0:03:30okay so
0:03:31in addition to see that will
0:03:33the close here
0:03:36uh but let us here are vectors
0:03:38okay so because of the thing with vector is a and an individual bits
0:03:44the binary messages C and go to do it's
0:03:46interleaved sequence
0:03:48and uh okay
0:03:53okay so the maximum likelihood sequence detector
0:03:56is like that it's of use
0:03:59it's very basic
0:04:01uh where
0:04:03you can either
0:04:05where where maximization or over
0:04:08you the the binary messages
0:04:12the it works
0:04:14coded bits
0:04:15provide in that you can
0:04:17every combination of the coding bits it's which do not don't to the goal
0:04:21okay this is a a a compact notation for saying
0:04:26i was zero is the indicator function of the quality
0:04:28its value is a one for a code where its value is zero or for a a combination of beach
0:04:33which does not be that belong to the core
0:04:40this is not really easily manipulate it is from the optimization
0:04:44well we use this is very small a
0:04:46which i the been you write the used but which has a can be found that's where
0:04:51so meaning that you can maximise a there on that
0:04:55the value of the probability P here
0:05:00so so that the thing the maximum of the argument of this function
0:05:04that are then if it's up for that
0:05:08is that
0:05:08this probability can be fully factor right meaning it's a product of individual probabilities for each bit
0:05:15okay it's a matter selection and most than than anything at
0:05:19and the second advantage is that this this problem T is
0:05:24so for an optimization problem is much and but not continue
0:05:30and you state this problem is on track double
0:05:33why because you have
0:05:35many need
0:05:36in that in the vector and if you want to do a i
0:05:39to compute
0:05:39this quantity for every possible combination you a lot
0:05:44what okay
0:05:46this is
0:05:47the the first request was to be cushion but the per bit second rate is that
0:05:52in this
0:05:53problem you have to kind of information
0:05:56one information is coming from the channel
0:05:59a because you you a measurement coming composed of the the information is coming from the fact that you are
0:06:05looking for
0:06:06can i did
0:06:07this is a of information
0:06:09and is probably
0:06:12but as so okay in this for but here
0:06:15we just fact i is it
0:06:17in that and L
0:06:18we take care of one of the information
0:06:21Q with take care of the all their information
0:06:27instead of working with
0:06:29the probabilities is for the front that was what will be working on a big margin
0:06:33meaning we will have a and variables
0:06:36instead of to to the uh
0:06:40maybe we we of go very far using exactly this procedure
0:06:44we can but to here
0:06:46in this
0:06:47process here
0:06:49we do not have any kind of approximation we have no
0:06:52the bit margin as appear
0:06:56equation here is exactly equivalent to the previous one
0:07:01this an approximation with have
0:07:03in this talk
0:07:04is this one
0:07:05the bit much or and a of the product
0:07:09i we pose but the product of be marginal
0:07:12okay so so that the previous equation is replaced that this one
0:07:17obviously seems to be a coarse approximation
0:07:20it happens
0:07:22if you choose directly
0:07:24the interleaver or if you choose to the mapping
0:07:27it's that the too bad approximation
0:07:33the coding now uh is that of a think is tractable
0:07:36because the computation of the marginal destructible
0:07:42is struck but this is computed well
0:07:45this is computed vol
0:07:50now we have a
0:07:52is a a problem which is a
0:07:53different for each bit
0:07:55so we change the problem now
0:07:57but they do the criterion here the bands
0:08:01i'm K depends on the location of a
0:08:05so that the average original problem
0:08:07is replaced by a by you distribute the optimization strategy
0:08:12and the only the problem
0:08:14seven of and cost function
0:08:22this criterion
0:08:24is relevant for the mac for the cliff be
0:08:30you it is shown that
0:08:32if you do that for the K B
0:08:34the solution must be something like that meaning that
0:08:38if you
0:08:39have a solution to the prime
0:08:42that mean from one of the set of information i'm of a V coming from the other a set of
0:08:48but must agree for the maximization
0:08:52which should
0:08:52here would be
0:08:54for a whether this it will be
0:08:56you you zero or one
0:08:57okay so they have to agree on be
0:09:00to make of this bit
0:09:04so i and that in this process context the that that a mediation of
0:09:08oh C case
0:09:10must provide an agreement
0:09:13between the code or estimate and them
0:09:15D mapping estimate the for the beacon position K
0:09:21and that is that are independent
0:09:24optimization the musicians
0:09:25maybe you could do not agree implicitly for the estimates of the other
0:09:34and you will see in in the next few slides that
0:09:38the track collaborative them
0:09:40used in decoding of the S C N
0:09:43is is exactly
0:09:45the solution
0:09:46all this kind of problem
0:09:50so that
0:09:52i to know that i can't time is that i i only derived
0:09:56bic and decoding and algorithm it to to use C M decoding a one
0:10:02the single approximation
0:10:04for a maximum you
0:10:08well in need building a my it up working more on that
0:10:11meaning that
0:10:12if one not a little lower of the group it
0:10:16if you if you if you will take
0:10:18the um
0:10:20of of these criteria
0:10:23you are just
0:10:26you can not have inconsistency consistency between the estimate
0:10:29of the base for the values
0:10:32okay so if i think has to a in some way
0:10:41the if you taken by this quantity will be an indication of the agreement
0:10:46between the coder and the demapper for the sequence
0:10:51okay if you work individually and that it's
0:10:53the most agree
0:10:54but if you were on the one sequence
0:10:56the kind of three
0:10:58and thus there is absolutely no where
0:11:00and this is for of here
0:11:02if you do not have any kind of the error
0:11:05as as you made
0:11:07provided by these criterion would be exactly the maximum likelihood
0:11:11so this is true in the paper
0:11:15okay so that's
0:11:16given in words what is written here in equation
0:11:20okay now
0:11:22this is outlined here only
0:11:24that's the we must come back to the individual criteria C K
0:11:29if you just minimise these the individual criteria
0:11:33you just
0:11:37this completely here
0:11:39is is
0:11:40it did not there
0:11:41this be to here is something which may be look strange
0:11:45but it is exactly what is computed by you the C G I E R algorithm
0:11:53would be
0:11:54fixing one of the one set of the want it is and who will go to do that you interactive
0:12:00we have a is i mean standing station here
0:12:03we that
0:12:04oh okay pigtails
0:12:06to the to some
0:12:07three use a value
0:12:10we compute
0:12:11the next completely based on sept solutions
0:12:15this one here
0:12:19for for or computing you and this one here for computing have
0:12:25if you just know that what
0:12:26everything is doing
0:12:28this is
0:12:29but the or
0:12:30classical in the are S E and decoding
0:12:33and this is exactly what is computed but you be C J R are are greater that meaning that channel
0:12:38decoding algorithm
0:12:40it's a
0:12:40a compact notation that you can numerically to check that do this is to it B C J are maybe
0:12:46it's not that when one
0:12:48if you provide to a C procedure
0:12:50i to a probability is that it should be
0:12:53if you compute the probably probabilities of each possible work right
0:12:57product of these quantities quantities
0:13:00but of the words which do not
0:13:02we don't to the code
0:13:03and then compute the matching also a which is exactly what is
0:13:08we and here
0:13:09if you do that
0:13:10you have to exactly at in the output of a B C J
0:13:14and it turns out that
0:13:16this quantity is which were they now by
0:13:19matt's me maximizing some criterion are exactly
0:13:23the web
0:13:24keep the in in in
0:13:26uh coding name the extrinsic information
0:13:30and now there is no magic in
0:13:32for graduating in six rather than a are plus to a it is
0:13:37uh uh true since that
0:13:39as and have group of the mediation procedure
0:13:45to to i
0:13:48we have an optimization problem which was
0:13:51or to model
0:13:52maximum likelihood
0:13:53we can
0:13:55obtain single first exactly equivalent to maximum because you like to a good detection
0:14:00we have a an approximation which has been obtained by fully factor using this
0:14:05the the probability mass functions
0:14:08then then a so that model algorithm because we had individual
0:14:13quantities is which were optimized
0:14:15through a distributed optimization strategy
0:14:19and we can
0:14:21if you know come back to the glue factor in the first the sum of all possible C case we
0:14:26know how a way of evaluating E
0:14:30yeah approximation was good or not
0:14:32because if we write
0:14:34the uh um
0:14:36the the sum of the individual criteria we will not be able to check
0:14:42the did not for and the decoder where the greeting
0:14:46on on of values which where
0:14:49for for the day
0:14:51so that's provides as a way of evaluating the quality of the solution of the ica and it directly decode
0:14:58okay we have covered just problems which
0:15:00a a in another the paper
0:15:03okay so that's
0:15:04see first
0:15:05okay what is new here
0:15:07nothing but
0:15:08the fact that we thing it may be
0:15:10a B S C and decoding or even
0:15:12but as the fact that we have maybe be a way of checking
0:15:16if there is that is correct on not
0:15:19and you can see here
0:15:21the cost function
0:15:22of the mixture means that of the global maximization
0:15:26the let's say the bit error rate that number of errors
0:15:29we are
0:15:30known as K
0:15:32and you can see that that's for C T V for maybe
0:15:35you can see that the refuge correlation
0:15:38it can be one
0:15:42okay and
0:15:44as another example i i
0:15:45show you these kind of result
0:15:47we have
0:15:48but duration of sixteen grand by mapping the set partitioning
0:15:52convolutional code this
0:15:53five seven
0:15:54and we are mixing
0:15:56their use
0:15:57E V over and zero from five to twelve db with a uniform distribution so it is a very complex
0:16:05if we choose
0:16:07the threshold
0:16:08indeed be equal to minus twenty here okay
0:16:12so the bit error rate for the frames above the threshold
0:16:17which are assume
0:16:18to the uh
0:16:21because they are are you are trying to maximise the functions are above a threshold it that's okay
0:16:26you see that
0:16:27above the threshold
0:16:29the bit error rate it
0:16:30quite stable but
0:16:32if if you change the
0:16:34the threshold
0:16:36for of frames and of the fresh
0:16:39you have a much higher bit error right
0:16:41okay i it would be a is your here um okay
0:16:45one here
0:16:48we are close to that
0:16:51but that's a page
0:16:52yeah of three G T frames
0:16:54well i
0:16:55there would be correct
0:16:57is very small
0:16:59and and what is as is the probability of first i'll a meaning that
0:17:02the point that
0:17:03not per cent ish of sequences which are to been rejected because
0:17:08build a because the right below of the threshold
0:17:11but that work correct
0:17:14but this
0:17:16is the basis of the work
0:17:19okay that me summarise
0:17:21what we obtain
0:17:23iterative decoding obtained from maximum likelihood
0:17:26we we had no specific assumption about the book things that we you a mapping or whatever
0:17:33the is obviously will impact the performance
0:17:36the in by the quality of the upper be here approximation which has been made in the in this
0:17:44we obtain
0:17:45clearly a that we should provide a extrinsic information between both
0:17:51rather than
0:17:52a was probably is
0:17:56we have a a we have a common just a do which has been a set it okay could be
0:18:00know that we do use a go
0:18:02and uh uh we have a
0:18:04the process for a
0:18:05evaluating the efficiency of the result
0:18:08uh because of this and that is
0:18:11and it's likely we not sure that
0:18:14simulations are running to check that
0:18:18most of the as we have in this kind of course G are not you good approximation but most of
0:18:24them are out you to conventional to local minima
0:18:28which is
0:18:29okay makes sense but we have to prove that and it
0:18:32work current yeah and a ticket
0:18:34and that
0:18:54do you think the some kind of some as is can be applied to to about composition
0:18:59could could you like to
0:19:00to of current position
0:19:02well well is it okay that this applies to
0:19:05any kind a okay it's a toy example bic and here is that for example it applies to so you
0:19:12on which you have several four sets of information on the same seem
0:19:17would you have here three sets of information in a a coat
0:19:21on top of the M
0:19:22this would apply also
0:19:24that that's
0:19:25okay it's quite generic
0:19:38i you aware of any results from information tree which word um justify your approximation
0:19:46no which i and i can send you your the the psd of the uh not to what was specifically
0:19:52working on information theory
0:19:54from a some geometry up like to these kind of work
0:19:57it's tricky
0:19:58and we could not really justified the approximation