Over the last decade, Approximate Message Passing (AMP) algorithms have become extremely popular in various structured high-dimensional statistical problems. Many of the original ideas of AMP were developed in the physics and engineering literature and have recently been extended for use in computer science and machine learning. In this tutorial the authors give a comprehensive and rigorous introduction to what AMP can offer, as well as to unifying and formalizing the core concepts within the large body of recent work in the area. They lead the reader through the basic concepts of AMP before introducing the concept of low-rank matrix estimation. The authors conclude by covering generalized models. To complete the picture for researchers, proofs, technical remarks and mathematical background are also provided. This tutorial is an in depth introduction to Approximate Message Passing for students and researchers new to the topic.

Developing increasingly computationally-efficient codes for communication and compression has been the major goal of information and coding theory. There have been significant advances towards this goal in the last couple of decades with the emergence of turbo codes, sparse-graph codes, and polar codes. The world has seen faster network speeds and greater storage due to many of these developments. A new class of codes, Sparse Regression Codes (SPARCs), are a promising class of codes for achieving the Shannon limits of a communication channel. This monograph presents a unified and comprehensive overview of sparse regression codes, covering theory, algorithms, and practical implementation aspects. Written by the world's recognized experts in the field it describes the use of SPARCs for efficient communication over AWGN channels, for lossy compression and multi-terminal communication. Researchers and students in modern communication and network systems will find Sparse Regression Codes an essential resource in understanding these new techniques that will have a significant impact on such systems in the years to come.