Zero-error communication over adder MAC

Adder MAC is a simple noiseless multiple-access channel (MAC), where if users send messages X₁, . . . ,X[subscript h] [epsilon] {0, 1}[superscript n], then the receiver receives Y = X₁ + · · · + X[subscript h] with addition over Z. Communication over the noiseless adder MAC has been studied for more than fifty years. There are two models of particular interest: uniquely decodable code tuples, and B[subscript h]-codes. In spite of the similarities between these two models, lower bounds and upper bounds of the optimal sum rate of uniquely decodable code tuple asymptotically match as number of users goes to infinity, while there is a gap of factor two between lower bounds and upper bounds of the optimal rate of B[subscript h]-codes. The best currently known B[subscript h]-codes for h >/- 3 are constructed using random coding. In this thesis, we study variants of the random coding method and related problems, in hope of achieving B[subscript h]-codes with better rate. Our contribution include the following. 1. We determine the rate achieved by changing the underlying distribution used in random coding. 2. We determine the rate of a list-decoding version of B[subscript h]-codes achieved by the random coding method. 3. We study several related problems about Rényi entropy.

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

2018

Author dc:creator

• Gu, Yuzhou

Advisor dc:contributor.advisor

• Yury Polyanskiy.

• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

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

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/120387

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/120387