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Feedback and Tow-Way Communication
Systems

Final Report Summary - FDBKCOMM (Feedback and Tow-Way Communication<br/>Systems)

The overall objective of the proposal is to design new coding techniques for communication with feedback and communication through two-way networks. The following specific objectives are aimed at solving open problems, whose solution will yield optimal communication schemes:
1) Find the feedback capacity of single-user channels with memory,
2) Design communication over multiple-user channels with feedback such as Multiple-Access
Channel (MAC),
3) Find robust communication over compound channels with feedback and universal decoding,
4) Find the capacity region of two-way channels, such as the Blackwell-Shannon's Binary Multiplying Channel (BMC).

We have investigated all four goals and used a new measure called directed information that helps solving these problems. Furthermore we have been able to formulate one additional goal that relates investment science with the new measure that we use for feedback capacity. This is an interdisciplinary research that connects communication engineering with economics.

Our main results are the following:
1) Formulating the capacity of single point-to-point channels with feedback
2) Designing new scheme of communication for multiple users based on code-trees
3) Found universal feedback schemes for channels with feedback
4) Developed theory for continuous-time communication with feedback
5) Developed new algorithms for computing the directed information and by this computing bounds of the capacity of channels with feedback

Relevant publication on those topics may be found in:

L. Zhao and H. H. Permuter, "Zero-error feedback capacity via dynamic programming," IEEE Trans. Info. Theory. Vol. 56, pp 2640 - 2650, Jun. 2010.
J. Chen, H. H. Permuter, and T. Weissman "Tighter Bounds on the Capacity of Finite-State
Channels via Markov Set-Chains ," IEEE Trans. Info. Theory. , Vol. 56, pp 3660 - 3691, Aug.
2010.
Y. -H Kim, H. Permuter and T. Weissman, “Directed Information, Causal Estimation, and Communication in Continuous Time,” IEEE Trans. Info. Theory, Vol. 59, pp 1271-1287, 2013
I. Naiss and H. Permuter, “Extension of the Blahut-Arimoto Algorithm for Maximizing Directed Information” IEEE Trans. Info. Theory, Vol. 59, pp 204 -222, 2013
I. Naiss and H. Permuter, “Computable Bounds for Rate Distortion with Feed-Forward for Stationary and Ergodic Sources” IEEE Trans. Info. Theory, Vol. 59, pp 760 -781, 2013.
U. Basher, A. Shirazi and H. Permuter, “Capacity Region of Finite State Multiple-Access Channel with Delayed State Information at the Transmitters” IEEE Trans. Info. Theory Vol. 58, pp 189-206, 2012.


In addition we found a connection between feedback communication and economics through the new measure called the directed information. This work is still in progress and preliminary publication includes
H. Permuter, Y.-H Kim and T. Weissman, “Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing” IEEE Trans. Info. Theory, Vol. 57, pp 3248 -3259, 2011

The project has advanced our understanding of information transmission and to guide us as to how to design better communication systems, in particular wireless systems. Wireless communication is being integrated into all aspects of life, such as personal communication, medical devices, control in industrial manufacturing through automatic sensors and Radio Frequency Identification (RFID), global position satellite (GPS) and the entertainment industry. The communication industry is rapidly growing industry, and new standards with better communication schemes are necessary to accommodate the high demand for client and portable communication with low-energy consuming. Furthermore, we made a significant connection between a new measure from information theory science with investment science where we should that this new measure called directed information characterizes the benefit of causal side information in investments. We develop a unified mathematical theory base on causal conditioning and directed information that can analyze systems with causality constraints.