Dissertation Defence: Design and Analysis of Lattice-Based Communication Schemes: A Study of Constructions A and D
August 19 at 9:00 am - 1:00 pm
Maryam Sadeghi, supervised by Dr. Chen Feng, will defend their dissertation titled “Design and Analysis of Lattice-Based Communication Schemes: A Study of Constructions A and D” in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering.
An abstract for Maryam Sadeghi’s dissertation is included below.
Examinations are open to all members of the campus community as well as the general public. Please email chen.feng@ubc.ca to receive the Zoom link for this exam.
Abstract
Lattice codes play a central role in modern communication theory, providing a unifying framework for error correction, efficient data transmission, and secure encoding. Among the many lattice constructions, Construction A and Construction D have emerged as particularly effective for achieving both coding and quantization gains, especially in challenging environments such as additive white Gaussian noise (AWGN) and block fading (BF) channels. This thesis investigates the design, analysis, and application of algebraic lattice constructions, with an emphasis on enhancing reliability and performance in such channels.
The first part of the work focuses on Construction A lattices built over the ring of imaginary quadratic integers, tailored for AWGN channels. A simplified and rigorous proof is presented for the existence of lattices that are simultaneously good for both coding and mean squared error (MSE) quantization. This construction exploits the arithmetic of imaginary quadratic fields and leverages discrete dithering to streamline the proof technique. The analysis provides foundational insights into the structure and behaviour of algebraic lattices, demonstrating their potential for high-performance communication.
The second part introduces a novel framework for Construction D lattices suited for block fading channels, where signal quality varies across transmission blocks. For the first time, these lattices are defined using a combination of nested linear codes and prime ideals in number fields. A semi-systematic generator matrix is derived to enable structured encoding, and a decoding algorithm is proposed that integrates maximum-likelihood decoding in early layers with successive cancellation for deeper layers. This hybrid strategy ensures full diversity and maintains linear complexity with respect to the lattice dimension.
Extensive simulations confirm the superior frame error rate (FER) performance of these lattices over their Construction A counterparts, particularly in high-diversity scenarios. The results also reveal that while multilayer designs offer flexibility, increasing the number of layers may introduce error propagation challenges, highlighting the importance of tuning depth and code rates for practical performance.
Altogether, this thesis presents a unified treatment of algebraic lattice constructions for both AWGN and block fading channels. By combining rigorous theory with practical design and evaluation, the work contributes to the advancement of lattice-based techniques for reliable and efficient communication, with potential applications in coding, modulation, and physical-layer security.
