On Duality Between Source Coding and Channel Coding in Multi-User Settings

Ziv Goldfeld

Abstract:

Duality between point-to-point channel and source coding problems has been widely studied since it was initially pointed out by Shannon back in 1959. However, the research of duality between multi-user settings has not received much attention and still remains largely obscure. In this work we propose a comprehensive extension of the operational point-to-point duality to the multi-user case. This is done by providing a set of principles according to which a multi-user channel coding problem is transformed into its dual coordination source coding counterpart, and vice versa. These principles encompass a wide variety of models, inter alia, models with side information (SI), cooperation and action. Considering two operationally dual channel and source coding models, its apparent that their capacity and rate-coordination region also admit dual forms. Namely, up to renaming some of the random variables involved, the information terms defining the regions' corner points are identical. This observation is corroborated by solving a diversity of dual pairs of settings and validating that this relation between the obtained regions hold. Amongst the considered settings, several new problems are solved; e.g., the deterministic BC with two-sided decoder cooperation, and the coordination coding problem of two correlated sources with one-sided encoder cooperation and causal\non-causal SI at the decoder. Specific examples of some of the general settings are considered, solved and their optimal rate regions are plotted. The plots reveal an intriguing symmetry between the capacity and the rate-coordination regions of each pair of dual settings. This symmetry is to be further investigated as the duality between multi-user channel and source coding problems is yet to be fully understood.

Biography:

Ziv Goldfeld was born Tashkent, Uzbekistan, in 1984, and immigrated to Israel in 1990. He received his B.Sc. (summa cum laude) degree in Electrical and Computer Engineering from the Ben-Gurion University, Israel, in 2012. He is currently a student in the direct Ph.D. program in that same institution, supervised by Dr. Haim H. Permuter. His research interest include topics in information theory and communication theory. Mr. Goldfeld is a recipient of the Basor Fellowship.