  Developing computationally-efficient codes that approach the
Shannon-theoretic limits for communication and compression has long been one of
the major goals 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. These codes are designed
primarily for discrete-alphabet channels and sources. For Gaussian channels and
sources, where the alphabet is inherently continuous, Sparse Superposition
Codes or Sparse Regression Codes (SPARCs) are a promising class of codes for
achieving the Shannon limits.
  This survey provides a unified and comprehensive overview of sparse
regression codes, covering theory, algorithms, and practical implementation
aspects. The first part of the monograph focuses on SPARCs for AWGN channel
coding, and the second part on SPARCs for lossy compression (with squared error
distortion criterion). In the third part, SPARCs are used to construct codes
for Gaussian multi-terminal channel and source coding models such as broadcast
channels, multiple-access channels, and source and channel coding with side
information. The survey concludes with a discussion of open problems and
directions for future work.
