An Investigation of Binary Coded Excitation Methods Using Golay Code Pairs for High Frequency Ultrasound Imaging

We are investigating the feasibility of binary coded excitation methods using Golay code pairs for high frequency ultrasound imaging as a way to increase the signal to noise ratio. I present some theoretical models used to simulate the coded excitation method and results generated from the models. A new coded excitation high frequency ultrasound prototype system was built to verify the simulation results. Both the simulation and the experimental results show that binary coded excitation can improve the signal to noise ratio in high frequency ultrasound backscatter signals. These results are confirmed in phantoms and excised bovine liver. If just white noise is considered, the encoding gain is 15dB for a Golay pair of length 4. We find the system to be very sensitive to motion (i.e. phase shift) and frequency dependent (FD) attenuation, creating sidelobes and degrading axial resolution and encoding gain. Methods to address these issues are discussed.

An Investigation of Binary Coded Excitation Methods Using Golay Code Pairs for High Frequency Ultrasound Imaging

We are investigating the feasibility of binary coded excitation methods using Golay code pairs for high frequency ultrasound imaging as a way to increase the signal to noise ratio. I present some theoretical models used to simulate the coded excitation method and results generated from the models. A new coded excitation high frequency ultrasound prototype system was built to verify the simulation results. Both the simulation and the experimental results show that binary coded excitation can improve the signal to noise ratio in high frequency ultrasound backscatter signals. These results are confirmed in phantoms and excised bovine liver. If just white noise is considered, the encoding gain is 15dB for a Golay pair of length 4. We find the system to be very sensitive to motion (i.e. phase shift) and frequency dependent (FD) attenuation, creating sidelobes and degrading axial resolution and encoding gain. Methods to address these issues are discussed.

Magic state distillation with the ternary Golay code

The ternary Golay code—one of the first and most beautiful classical error-correcting codes discovered—naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distil the ‘most magic’ qutrit state—an eigenstate of the qutrit Fourier transform known as the strange state —with cubic error suppression and a remarkably high threshold. It also distils the ‘second-most magic’ qutrit state, the Norell state, with quadratic error suppression and an equally high threshold to depolarizing noise.

On the 486-Vertex Distance-Regular Graphs of Koolen-Riebeek and Soicher

This paper considers three imprimitive distance-regular graphs with $486$ vertices and diameter $4$: the Koolen--Riebeek graph (which is bipartite), the Soicher graph (which is antipodal), and the incidence graph of a symmetric transversal design obtained from the affine geometry $\mathrm{AG}(5,3)$ (which is both). It is shown that each of these is preserved by the same rank-$9$ action of the group $3^5:(2\times M_{10})$, and the connection is explained using the ternary Golay code.

Convolution of Barker and Golay Codes for Low Voltage Ultrasonic Testing

Ultrasonic Testing (UT) is one of the most important technologies in Non-Detective Testing (NDT) methods. Recently, Barker code and Golay code pairs as coded excitation signals have been applied in ultrasound imaging system with improved quality. However, the signal-to-noise ratio (SNR) of existing UT system based on Barker code or Golay code can be influenced under high high attenuation materials or noisy conditions. In this paper, we apply the convolution of Barker and Golay codes as coded excitation signals for low voltage UT devices that combines the advantages of Barker code and Golay code together. There is no need to change the hardware of UT system in this method. The proposed method has been analyzed theoretically and then in extensive simulations. The experimental results demonstrated that the main lobe level of the code produced by convolution of Barker code and Golay code pairs is much higher than the simple pulse and the main lobe of the combined code is higher than the traditional Barker code, sidelobe is the same as the baker code that constitutes this combined code. So the peak sidelobe level (PSL) of the combined code is lower than the traditional Barker code. Equipped with this, UT devices can be applied in low voltage situations.