Direct methods to solve systems of equations are a building block of any application involving numerical analysis. While the performance characteristics of dense systems are predictable, sparse systems can have large deviations in running time depending on the order in which Gaussian elimination is applied. Finding the order that results in the lowest running time is in general an NP-Hard problem. Nested dissection is a popular divide and conquer heuristic algorithm used by several numerical solvers. At the heart of nested dissection is the minimum vertex separator problem, an NP-Hard problem. Recent years have seen rapid development of quantum annealers, a class of quantum computers designed to solve optimization problems. This thesis investigates the possible role of quantum annealers as a method to improve elimination orderings produced by nested dissection.

This report is part of the WiECG project. The goal of the WiECG project is to create a prototype device that makes it possible to perform a 12-lead ECG on patients without wires from a patient to the monitor. The solution consists of a transmitter and receiver of which one is close or on the patients body and the other is connected to a monitor.

This thesis describes the design and implementation process for the communication protocols. This concerns mainly the WiFi communication from transmitter to receiver and the I2C pairing protocol. The WiFi communication protocol was extended with retransmission and encryption to ensure the reliability and discreteness of the data, which was indicated to be of high priority by ambulance personnel. The channel needs to minimally support 9 samples of 16 bits with a frequency of 500 samples per second. The pairing protocol needs to enable the transmitter and receiver to pair in mere seconds.

A prototype is made which successfully pairs and transfers data from transmitter to receiver. This prototype still needs to be tested thoroughly.