Dissertation Defense, Peiyu Tan

Dissertation Defense, Peiyu Tan

Title:                     Exploring Error-Correction Technology
in Source Coding and Quantum

Date:                    September 25, 2009

Time:                     1:00PM, Friday
Location:              Packard Lab 508


The explosive demand for capacity in wireless and wire line communication systems has promoted tremendous research in error control technologies. The discovery and re-discovery of capacity-achieving error correction codes (ECC) in the last decade have not only revolutionalized the coding theory, but also opened up a very pervasive scope of well-proven and emerging practical applications, including, for example, wireless communications, multi-user detection, turbo equalization, digital data storage systems, distributed compression, and quantum error correction. This dissertation studies refreshing topics on the theory and practice of error correction coding technologies and explores their capabilities beyond their conventional applications.

The first topic involves the Slepian-Wolf coding problem on binary memory less sources. The Slepian-Wolf coding problem considers multiple physically-separated non-communicating sources sending statistically-correlated data to a common destination. I propose a simple and powerful framework for symmetric and asymmetric Slepian-Wolf coding on binary memory fewer sources, named as symmetric syndrome-former inverse-syndrome-former framework (SSIF). This study covers both theoretical and practical aspects, including the practical implementation of the source encoder and decoder for both approaches, the criterion for designing the base channel codes, and their respective performances and robustness in both the noiseless and the noisy transmission environments. We show that the
syndrome approach is optimal for the noiseless (syndrome) channel case, yet the
parity approach is more robust and less error-sensitive.

The second problem we study is on quantum stabilizer codes. Quantum information technology and computing belong to the class of the most innovative and revolutionary computing, whose development is now a national project that will be vital to our future economy and national defense. The majority of the up-to-date research on quantum ECC codes focuses on one subclass of stabilizer codes, known as CSS codes. We first propose a novel classification from the perspective of constructing stabilizer codes based on classical binary codes. To fill the gap of limited constructions, we develop systematic ways to construct two rich classes of non-CSS stabilizer codes: quantum LDPC codes based on classical quaci-cyclic (QC) LDPC codes, and quantum convolution codes based on classical LDPC-convolution codes. To the best of the authors' knowledge, they are the first non-CSS quantum LDPC codes and non-CSS convolution quantum codes reported to date. Besides constructions, we also investigate decoding strategies, especially for quantum convolution codes, where no performance curves were shown before our work.

Ph.D. Committee:

Prof. Tiffany Jing Li (Chair), ECE, Lehigh University
Prof. Meghanad Wagh, ECE, Lehigh University
Prof. Zhiyuan Yan, ECE, Lehigh University
Prof. Garth Isaak, Mathematics, Lehigh University