Design of Deterministic Matrices for Compressed Sensing Using Finite Fields

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Abin, Hamidreza | 2016

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49671 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Amini, Arash
Abstract:
The design of deterministic sensing matrices is an important issue in compressive sensing in sparse signal processing. Various designs using finite field structures, combinatorics, and coding theory have been presented. The contribution of this thesis is designing many codes with large minimum distance using algebraic curves. Here, we initially design a algebraic-geometric code over a maximal curve in a Galoi field Fpm Afterwards, we map the code to the field Fp using trace map. This code has a large minimum distance. Using this code, we design a matrix with low coherence. One of the main issues in presented designs is that the number of matrix rows is considered to specific integers near prime powers
Keywords:
Coherence Parameter ; Compressive Sensing ; Finite Field Extension ; Riemann-Rokh Theorem ; Algebraic Curves ; Function Field Codes ; Maximal Curves