**Iddo**** Naiss**

__About me__

My name is Iddo Naiss, and
I am a student in the joint math-ee program in BGU,
now studying for my Masters degree in the fast route from Bs.C.
My advisor is Haim
Permuter

__Our work-The Blahut-Arimoto Algorithm; extantions__

·
The Blahut Arimoto
type algorithms are used for optimizing the directed (or mutual) information,
which is known to have an important role in characterizing the capacity of
various channels and the rate distortion for various sources with distortion.

·
In our work we extend the Blahut
Arimoto Algorithm for estimating the capacity of
feedback channels and the rate distortion for source coding with feed forward,
which are characterized by the optimization problem over the directed
information

·
Our first paper is about maximizing the directed
information in order to estimate the capacity of feedback channels. The paper
is being reviewed by IEEE trans. of info. theory. In
the meanwhile, it was uploaded to arXiv to http://arxiv.org/abs/1012.5071. The slides

·
Our second paper proves that the expression given above
for R(D) is true, and then apply a BA type algorithm
onto this new optimization problem. We also transform this problem to a
geometrical programming maximization one, which is given as follows:

subject to:

This
optimization problem can be solved using a Matlab code(cvx).

·
The paper is being reviewed by IEEE trans. of info. theory. In the meanwhile, it was uploaded to arXiv to http://arxiv.org/abs/1106.0895. The slides

·
Follows is a header *.h code that consists of all
functions and procedures necessary in order to use the extended algorithm

·
In order to illustrate the algorithms performance, we
give 2 *.c codes.

The first is for the feedback channel case
(trapdoor channel with m=3 states and delay d=1)

The second, for rate distortion source coding with feedforward
(an a-symetrical markov
source as a function of the delay for block length n=10)

· Both *.c files has two *.txt output that consists of tables. The first is of the rate, where each line is for a different block length. The other is the same for the distortion. One can use Matlab to plot the data.

·
Here I present the matlab files
for the channel with feedback case. They are less efficient but are easier to
use.

·
In order to illustrate the algorithms performance, we
give a couple of *.m codes.

The first are to built the channel we wish
(trapdoor channel with m=3 states and delay d=1)

The state matrix

the probability

expanding the matrix probability to a higher rank
for future usage

and finally the channel

The last file is for using the codes above