Fourier analysis on the hypercube, the coefficient problem, and applications

In this dissertation, we primarily study some problems that revolve around Fourier analysis. More specifically we focus on the magnitudes of the frequency components. Firstly, we perform a study on the hypercube. It is well known that the Delsarte linear programming bounds provide rich information on the magnitudes of the Fourier coefficients, grouped by Hamming weight. Classically, such information is primarily used to attack coding problems, where the objective is to maximize cardinality of a subset of a metric space subject to a minimum distance constraint. Here, we use it to study anticoding problems, where the objective is to maximize cardinality of a subset of a metric space subject to a maximum distance (diameter) constraint. One motivation for such study is the problem of finding memories that are cheap to update, where the cost of an update is a function of the distance in the metric space.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Ajjanagadde, Ganesh.

Advisor dc:contributor.advisor

• Gregory Wornell and Henry Cohn.

• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/127011

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/127011