arXiv subjects
Publications and source records attributed to Mathew Goonewardena.
We investigate finite right-distributive binary algebraic structures called shelves. We first use symbolic computations with Python to classify (up to isomorphism) all connected shelves with order less than six. We explore the group structure generated by the rows of \textit{latin} shelves. We also define two-variable shelf polynomial by analogy with the quandle polynomial and then state a conjecture about connected idempotent shelves.
This paper analyzes the communication between two energy harvesting wireless sensor nodes. The nodes use automatic repeat request and forward error correction mechanism for the error control. The random nature of available energy and arrivals of harvested energy may induce interruption to the signal sampling and decoding operations. We propose a selective sampling scheme where the length of the transmitted packet to be sampled depends on the available energy at the receiver. The receiver performs the decoding when complete samples of the packet are available. The selective sampling information bits are piggybacked on the automatic repeat request messages for the transmitter use. This way, the receiver node manages more efficiently its energy use. Besides, we present the partially observable Markov decision process formulation, which minimizes the long-term average pairwise error probability and optimizes the transmit power. Optimal and suboptimal power assignment strategies are introduced for retransmissions, which are adapted to the selective sampling and channel state information. With finite battery size and fixed power assignment policy, an analytical expression for the average packet drop probability is derived. Numerical simulations show the performance gain of the proposed scheme with power assignment strategy over the conventional scheme.
This work considers the problem of user association to small-cell base stations (SBSs) in a heterogeneous and small-cell network (HetSNet). Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under signal-to-interference-plus-noise ratio (SINR) constraints. Both problems are formulated as linear integer programs. The weighted problem is known to be NP-hard and, in this paper, the unweighted problem is proved to be NP-hard as well. Therefore, this paper develops two heuristic polynomial-time algorithms to solve both problems. The computational complexity of the proposed algorithms is evaluated and is shown to be far more efficient than the complexity of the optimal brute-force (BF) algorithm. Moreover, the paper benchmarks the performance of the proposed algorithms against the BF algorithm, the branch-and-bound (B\&B) algorithm and standard algorithms, through numerical simulations. The results demonstrate the close-to-optimal performance of the proposed algorithms. They also show that the weighted problem can be solved to provide solutions that are fair between users or to balance the load among SBSs.
This paper addresses the problem of competition vs. cooperation in the downlink, between base stations (BSs), of a multiple input multiple output (MIMO) interference, heterogeneous wireless network (HetNet). This research presents a scenario where a macrocell base station (MBS) and a cochannel femtocell base station (FBS) each simultaneously serving their own user equipment (UE), has to choose to act as individual systems or to cooperate in coordinated multipoint transmission (CoMP). The paper employes both the theories of non-cooperative and cooperative games in a unified procedure to analyze the decision making process. The BSs of the competing system are assumed to operate at the\emph{}maximum expected sum rate\emph{}(MESR)\emph{}correlated equilibrium\emph{}(CE), which is compared against the value of CoMP to establish the stability of the coalition. It is proven that there exists a threshold geographical separation, $d_{\text{th}}$, between the macrocell user equipment (MUE) and FBS, under which the region of coordination is non-empty. Theoretical results are verified through simulations.