An Improved Analysis of Least Squares Superposition Codes with Bernoulli Dictionary

TL;DR

This paper improves the theoretical analysis of sparse superposition codes with Bernoulli dictionaries for Gaussian channels, providing tighter bounds on error probability using least squares decoding.

Contribution

It presents a simplified and tighter upper bound on block error probability for superposition codes with Bernoulli dictionaries, extending previous Gaussian-based analyses.

Findings

Tighter upper bounds on block error probability

Simplified analysis compared to previous work

Extension of superposition code analysis to Bernoulli dictionaries

Abstract

For the additive white Gaussian noise channel with average power constraint, sparse superposition codes, proposed by Barron and Joseph in 2010, achieve the capacity. While the codewords of the original sparse superposition codes are made with a dictionary matrix drawn from a Gaussian distribution, we consider the case that it is drawn from a Bernoulli distribution. We show an improved upper bound on its block error probability with least squares decoding, which is fairly simplified and tighter bound than our previous result in 2014.