Information Theoretic Bounds for Low-Rank Matrix Completion

TL;DR

This paper applies information theory to derive order-wise optimal bounds for low-rank matrix completion, framing it as a communication problem over an erasure channel.

Contribution

It introduces an information theoretic framework for analyzing low-rank matrix completion and establishes fundamental bounds for the problem.

Findings

Order-wise optimal bounds for matrix completion

Reformulation as a communication problem over erasure channels

Achievability and converse arguments used for bounds

Abstract

This paper studies the low-rank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper then uses achievability and converse arguments to present order-wise optimal bounds for the completion problem.