Zero-error communication over adder MAC

• Main Author: Gu, Yuzhou
• Other Authors: Yury Polyanskiy.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2019
• Subjects: Electrical Engineering and Computer Science.
• Online Access: http://hdl.handle.net/1721.1/120387

Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018. === This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. === Cataloged from student-submitted PDF version of thesis. === Includes bibliographical references (pages 53-54). === 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. === by Yuzhou Gu. === M. Eng.