Print Email Facebook Twitter The shannon capacity on C(n,k) Title The shannon capacity on C(n,k) Author den Dulk, Timo (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Optimization) Contributor Gijswijt, D.C. (mentor) Fokkink, R.J. (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics Date 2022-07-12 Abstract This thesis focuses on a problem formulated by Claude Shannon named the Shannon capacity. This problem is about information rate per time unit over a noisy channel. The noisy channel is here represented by a graph. We specifically focus on a class of circulant graphs that are denoted by C(n,k) with vertex set z/nz, where all vertices are connected with the k-1 vertices before and after it. We will discuss upper bounds that were found for the Shannon capacity and how C(n,k) behaves with these upper bounds. After that we will focus on multiple ways to calculate lower bounds for the Shannon capacity of $C(n,k)$. For these three search methods will be used. These are exhaustive searching for optimal values, optimal ways to make packagings and solutions created by using a special form. As last the answers will be discussed by combining the upper and lower bounds for C(n,k). From this conclusions are drawn after which some possibilities will be given for further research. Subject Shannon capacityCirculant graphsLovász theta function To reference this document use: http://resolver.tudelft.nl/uuid:54779ec5-79c5-4481-a0fe-46c3aaaa4aab Part of collection Student theses Document type bachelor thesis Rights © 2022 Timo den Dulk Files PDF thesis_Shannon_capacity.pdf 928.14 KB Close viewer /islandora/object/uuid:54779ec5-79c5-4481-a0fe-46c3aaaa4aab/datastream/OBJ/view