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Title: Polar codes and polar lattices for efficient communication and source quantization
Author: Liu, Ling
ISNI:       0000 0004 6347 0229
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2016
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In the past several decays, lattice codes played an important role in coding theory and information theory. Lattice codes with good performance in communication and source compression have attracted considerable interest. A typical method of constructing good lattice codes is to use existing linear codes. For instance, the famous Barnes-Wall lattices are generated by Reed-Muller (RM) codes, and more recently, the emerging low density Construction-A (LDA) lattices are resulted from low density parity check (LDPC) codes. In this thesis, we develop a new class of lattices, called polar lattices, based on polar codes. The invention of polar codes is considered to be one of the major breakthroughs in coding theory for the past ten years. We show that polar lattices provide explicit solutions for many interesting problems in information theory. For channel coding, we prove that polar lattices are capable of achieving the capacity of the additive white Gaussian noise (AWGN) channel. For the dual side, i.e., source compression, polar lattices can also achieve the rate-distortion bound for the independent and identically distributed (i.i.d.) Gaussian source. Moreover, a combining design of polar lattices for both channel coding and source coding gives us explicit solutions to the Gaussian version of the Wyner-Ziv and Gelfand-Pinsker problems. For physical layer security, we prove that polar lattices are able to approach the secrecy capacity of the Gaussian wiretap channel under the strong secrecy criterion. Two more applications of polar lattices are achieving the capacity of the i.i.d. fading channel and extracting the common information of two joint Gaussian sources. The explicit construction of polar lattices provides us better insights on the study of lattice coding. Many interesting problems of lattice coding, such as AWGN goodness, secrecy-goodness, lattice shaping, and lattice Gaussian distribution will be addressed from the perspective of polar lattices.
Supervisor: Ling, Cong Sponsor: China Scholarship Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral