Dissertation Defense- Xuebin Wu
Name: Xuebin Wu,
Date: Thursday, June 2nd, 2011
Time: 10:30 AM
Location: Packard, 258
Title: Efficient Signal Processing Algorithms and Their Applications
Efficient signal processing algorithms are essential in various communication systems, such as on-chip interconnect buses, wireless communication systems, magnetic recording channels, cryptosystems, etc. These efficient algorithms either have low computational complexities or have modular structures that are favorable in hardware implementations. In this dissertation, we investigate several efficient signal processing algorithms in different areas. These areas include the crosstalk avoidance codes, multiple-input and multiple-output (MIMO) communication systems, and computational complexity reduction of the discrete Fourier transforms (DFTs) over finite fields.
The defense will focus on the efficient algorithms of DFTs over finite fields. The DFTs over finite fields find wide applications in various communication systems, and cyclotomic fast Fourier transforms can reduce their multiplicative complexities greatly. As the DFTs over non-characteristic-2 fields are taken into consideration in modern communication systems, we generalize the CFFTs to arbitrary finite fields by devising efficient algorithms for cyclic convolutions over arbitrary finite fields. We also analyze the computational complexities of CFFTs in theory, and our results confirm the advantages of CFFTs. To further reduce the computational complexity of the DFTs, we propose composite cyclotomic Fourier transforms, which integrate the CFFTs and the idea of the prime-factor algorithm as well as the Cooley-Turkey algorithm.
Prof. Zhiyuan Yan (advisor and chair)
Prof. Meghanad D. Wagh,
Prof. Shalinee Kishore,
Dr. Ying Wang (Qualcomm)