Design of Network Coding Schemes and RF Energy Transfer in Wireless Communication Networks

This thesis focuses on the design of network coding schemes and radio frequency (RF) energy transfer in wireless communication networks. During the past few years, network coding has attracted significant attention because of its capability to transmit maximum possible information in a network from multiple sources to multiple destinations via a relay. Normally, the destinations are only able to decode the information with sufficient prior knowledge. To enable the destinations to decode the information in the cases with less/no prior knowledge, a pattern of nested codes with multiple interpretations using binary convolutional codes is constructed in a multi-source multi-destination wireless relay network. Then, I reconstruct nested codes with convolutional codes and lattice codes in multi-way relay channels to improve the spectrum efficiency. Moreover, to reduce the high decoding complexity caused by the adopted convolutional codes, a network coded non-binary low-density generator matrix (LDGM) code structure is proposed for a multi-access relay system. Another focus of this thesis is on the design of RF-enabled wireless energy transfer (WET) schemes. Much attention has been attracted by RF-enabled WET technology because of its capability enabling wireless devices to harvest energy from wireless signals for their intended applications. I first configure a power beacon (PB)-assisted wireless-powered communication network (PB-WPCN), which consists of a set of hybrid access point (AP)-source pairs and a PB. Both cooperative and non-cooperative scenarios are considered, based on whether the PB is cooperative with the APs or not. Besides, I develop a new distributed power control scheme for a power splitting-based interference channel (IFC) with simultaneous wireless information and power transfer (SWIPT), where the considered IFC consists of multiple source-destination pairs

The satisfiability threshold for random linear equations

Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entries per row and let $y\in F_q^m$ be a random vector chosen independently of $A$. We identify the threshold $m/n$ up to which the linear system $A x=y$ has a solution with high probability and analyse the geometry of the set of solutions. In the special case $q=2$, known as the random $k$-XORSAT problem, the threshold was determined by [Dubois and Mandler 2002, Dietzfelbinger et al. 2010, Pittel and Sorkin 2016], and the proof technique was subsequently extended to the cases $q=3,4$ [Falke and Goerdt 2012]. But the argument depends on technically demanding second moment calculations that do not generalise to $q>3$. Here we approach the problem from the viewpoint of a decoding task, which leads to a transparent combinatorial proof