# Investigating Directed Information

## Objective

This research investigates a new measure that arises in information theory
called directed information. Recent advances, including our preliminary results, shows that
directed information arises in communication as the maximum rate that can be transmitted reliably
in channels with feedback. The directed information is multi-letter expression and therefore very
hard to optimize or compute.

Our plan is first of all to find an efficient methodology for optimizing the measure using the
dynamic programming framework and convex optimization tools. As an important by-product of
finding the fundamental limits is finding coding schemes that achieves the limits. Second, we
plan to find new roles for directed information in communication, especially in networks with
bi-directional communication and in data compression with causal conditions. Third, encouraged by
a preliminary work on interpretation of directed information in economics and estimation theory,
we plan to show that directed information has interpretation in additional fields such as
statistical physics. We plan to show that there is duality relation between different fields with
causal constraints. Due to the duality insights and breakthroughs in one problem will lead to new
insights in other problems. Finally, we will apply directed information as a statistical
inference of causal dependence. We will show how to estimate and use the directed information
estimator to measure causal inference between two or more process. In particular, one of the
questions we plan to answer is the influence of industrial activities (e.g. $\text{CO}_2$
volumes) on the global warming.

Our main focus will be to develop a deeper understanding of the mathematical properties of
directed information, a process that is instrumental to each problem. Due to their theoretical
proximity and their interdisciplinary nature, progress in one problem will lead to new insights
in other problems. A common set of mathematical tools developed in

### Call for proposal

ERC-2013-StG
See other projects for this call

### Funding Scheme

ERC-SG - ERC Starting Grant

### Host institution

BEN-GURION UNIVERSITY OF THE NEGEV
.
84105 Beer Sheva
Israel
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 224 600
Principal investigator
Haim Permuter (Dr.)
Daphna Tripto (Ms.)

### Beneficiaries (1)

BEN-GURION UNIVERSITY OF THE NEGEV
Israel
EU contribution
€ 1 224 600