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