From Gaussian Multiterminal Source Coding to Distributed Karhunen–Loève Transform

Characterizing the rate-distortion region of Gaussian multiterminal source coding is a longstanding open problem in network information theory. In this talk, I will show how to obtain new conclusive results for this problem using nonlinear analysis and convex relaxation techniques. A byproduct of this line of research is an efficient algorithm for determining the optimal distributed Karhunen–Loève transform in the high-resolution regime, which partially settles a question posed by Gastpar, Dragotti, and Vetterli. I will also introduce a generalized version of the Gaussian multiterminal source coding problem where the source-encoder connections can be arbitrary. It will be demonstrated that probabilistic graphical models offer an ideal mathematical language for describing how the performance limit of a generalized Gaussian multiterminal source coding system depends on its topology, and more generally they can serve as the long-sought platform for systematically integrating the existing achievability schemes and converse arguments. The architectural implication of our work for low-latency lossy source coding will also be discussed. This talk is based on joint work with Jia Wang, Farrokh Etezadi, and Ashish Khisti.