Using the First Order Reed-Muller Code for Channels With Unknown Offset

Using the First Order Reed-Muller Code for Channels With Unknown Offset

van Prooijen, Birgit (TU Delft Electrical Engineering, Mathematics and Computer Science)

Weber, J.H. (mentor)
de Groot, J.A.M. (graduation committee)

Delft University of Technology

Applied Mathematics

2022-08-25

While the Minimum Euclidean Distance detection is known to be optimal for channels affected by Gaussian noise, it has been shown that Minimum Pearson Distance detection (MPD) may perform better when the channel is also affected by an unknown offset, though for a good performance some adaptations for classical binary block codes are necessary. It is shown for cosets of first order Reed-Muller codes R(1,m) containing words of weight d/2, where d is the code's distance, that the minimum Pearson distance is always low for m≤4. However, it is possible to find cosets where the minimum Pearson distance is higher for m≥5.

Coding Theory
Reed-Muller
Pearson Distance
Cosets
offset

http://resolver.tudelft.nl/uuid:abd24f75-f90c-49f3-bc2f-614eefdc8197

Student theses

bachelor thesis

© 2022 Birgit van Prooijen