Communication Over a Noisy Channel Using High-Dimensional Linear Regression with Gaussian Design

• Activity Number: 321
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Cynthia Rush* and Adam Greig and Ramji Venkataramanan
• Companies: Yale University and University of Cambridge and University of Cambridge
• Keywords: high-dimensional regression ; information theory ; approximate message passing ; machine learning ; Channel coding

Abstract

The use of smart devices and wireless networks is ubiquitous, creating a pressing need for low-complexity communications schemes that reliably deliver high data rates. Using sparse superposition codes, we analyze the task of communicating over a noisy channel through the statistical framework of high-dimensional linear regression with Gaussian design and sparse coefficient vectors. Through this analysis, theoretical bounds on the rate at which information can be communicated across a channel inform us about the minimum sample size necessary for successful support recovery. We propose an approximate message passing decoder for sparse superposition codes over the additive white gaussian noise channel (AWGN). The performance of the decoder is rigorously analyzed and it is shown to asymptotically achieve the AWGN capacity with an appropriate power allocation. New results on the performance of the decoder at finite blocklengths is also presented.