Attaining Fairness in Communication for Omniscience.

Area of Science:

• Information Theory
• Game Theory
• Communication Systems

Background:

• Multi-terminal compressed sensing and coded cooperative data exchange involve users sharing observations of a random source.
• Omniscience is the state where all users can reconstruct the entire source from shared data.

Purpose of the Study:

• To investigate fairness in achieving omniscience in communication networks.
• To model the problem as a coalitional game and apply game-theoretic solutions for rate allocation.

Main Methods:

• The study models the problem as a coalitional game, identifying the core as the optimal rate region.
• It analyzes two fairness solutions: the Shapley value and the egalitarian solution.
• Polynomial-time approximation for Shapley value and a steepest descent algorithm for the egalitarian solution are proposed.

Main Results:

• The Shapley value is linked to remaining information after sharing common randomness.
• The egalitarian solution aims for an even distribution of rates within the core.
• Both solutions can be computed efficiently and distributively through subgame decomposition.

Conclusions:

• Game-theoretic fairness solutions provide a framework for equitable resource allocation in distributed information systems.
• Efficient algorithms are developed to overcome computational complexity.
• Distributed computation of fairness solutions is feasible, enhancing practical applicability.