Bent Vectorial Functions, Codes and Designs

Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group (\gf(2^{2m}), +), have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective of this paper is to use bent vectorial functions for a construction of a two-parameter family of binary linear codes that do not satisfy the conditions of the Assmus-Mattson theorem, but nevertheless hold $2$-designs. A new coding-theoretic characterization of bent vectorial functions is presented

On some codes from rank 3 primitive actions of the simple Chevalley group G2(q)

Please read abstract in the article.The National Research Foundation of South Africahttp://aimsciences.org/journals/amc/index.htmhj2022Mathematics and Applied Mathematic

Switching codes and designs

AbstractVarious local transformations of combinatorial structures (codes, designs, and related structures) that leave the basic parameters unaltered are here unified under the principle of switching. The purpose of the study is threefold: presentation of the switching principle, unification of earlier results (including a new result for covering codes), and applying switching exhaustively to some common structures with small parameters

Sequence Design via Semidefinite Programming Relaxation and Randomized Projection

Wideband is a booming technology in the field of wireless communications. The receivers in wideband communication systems are expected to cover a very wide spectrum and adaptively extract the parts of interest. The literature has focused on mixing the input spectrum to baseband using a pseudorandom sequence modulation and recovering the received signals from linearly independent measurements by parallel branches to mitigate the pressures from required extreme high sampling frequency. However, a pseudorandom sequence provides no rejection for the strong interferers received together with weak signals from distant sources. The interferers cause significant distortion due to the nonlinearity of the subsequent amplifier and mask the weak signals. In this dissertation, we optimize the modulation sequences with a specific spectrum shape to mitigate interferers while preserving messages; the sequences have binary entries to simplify hardware implementation. Though the resulting sequence design problems are NP-hard, we solve them approximately by semidefinite relaxation and randomized projection. First, we formulate the design algorithm for a single spectrally shaped binary sequence base on a randomized convex optimization method. We analyze the performance of the algorithm in obtaining binary sequences and show its advantages compared with method available in the literature. And, we show a comparison between the proposed sequence design method with the exhaustive approaches when feasible. Additionally, we propose several custom sequence scoring functions that allow for an improved selection of binary sequences for message preservation and interference rejection. Second, we propose an algorithm to design a multi-branch set of binary sequences one by one by introducing the constrains on the orthogonality between pairs of sequences. Numerical results show the proposed algorithm obtains sequences with a small search size compared with the exhaustive search. Finally, we extend the randomized method to multi-branch sequence design. In order to avoid the unstable performance and high complexity of designing multi-branch sequence iteratively, the whole branch sequences will be obtained directly via matrix randomized projection from the relaxed problems

Optimization in multi-relay wireless networks

The concept of cooperation in communications has drawn a lot of research attention in recent years due to its potential to improve the efficiency of wireless networks. This new form of communications allows some users to act as relays and assist the transmission of other users' information signals. The aim of this thesis is to apply optimization techniques in the design of multi-relay wireless networks employing cooperative communications. In general, the thesis is organized into two parts: ``Distributed space-time coding' (DSTC) and ``Distributed beamforming', which cover two main approaches in cooperative communications over multi-relay networks. In Part I of the thesis, various aspects of distributed implementation of space-time coding in a wireless relay network are treated. First, the thesis proposes a new fully-diverse distributed code which allows noncoherent reception at the destination. Second, the problem of coordinating the power allocation (PA) between source and relays to achieve the optimal performance of DSTC is studied and a novel PA scheme is developed. It is shown that the proposed PA scheme can obtain the maximum diversity order of DSTC and significantly outperform other suboptimal PA schemes. Third, the thesis presents the optimal PA scheme to minimize the mean-square error (MSE) in channel estimation during training phase of DSTC. The effect of imperfect channel estimation to the performance of DSTC is also thoroughly studied. In Part II of the thesis, optimal distributed beamforming designs are developed for a wireless multiuser multi-relay network. Two design criteria for the optimal distributed beamforming at the relays are considered: (i) minimizing the total relay power subject to a guaranteed Quality of Service (QoS) measured in terms of signal-to-noise-ratio (SNR) at the destinations, and (ii) jointly maximizing the SNR margin at the destinations subject to power constraints at the relays. Based on convex optimization techniques, it is shown that these problems can be formulated and solved via second-order conic programming (SOCP). In addition, this part also proposes simple and fast iterative algorithms to directly solve these optimization problems

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more