Polar codes and polar lattices for efficient communication and source quantization
File(s)
Author(s)
Liu, Ling
Type
Thesis
Abstract
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.
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.
Version
Open Access
Date Issued
2016-09
Date Awarded
2017-06
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Ling, Cong
Sponsor
China Scholarship Council
Publisher Department
Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)