Computing the channel capacity of a communication system affected by uncertain transition probabilities

We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been formulated in the literature as a max-min problem. We use the robust optimization methodology to convert the max-min problem to a standard convex optimization problem. For small-sized problems, and for many types of uncertainty, such a problem can be solved in principle using interior point methods (IPM). However, for large-scale problems, IPM are not practical. Here, we suggest an $\mathcal{O}(1/T)$ first-order algorithm based on Nemirovski (2004) which is applied directly to the max-min problem.Comment: 22 pages, 2 figure

Large-System Analysis of Multiuser Detection with an Unknown Number of Users: A High-SNR Approach

We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. In this environment, users' activity must be estimated along with any other parameters such as data, power, and location. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency. Special attention is paid to the fixed-point equation whose solution yields the multiuser efficiency of the optimal (maximum a posteriori) detector in the large signal-to-noise ratio regime. Our analysis yields closed-form approximate bounds to the minimum mean-squared error in this regime. These illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. Next, we study the maximum load that the detector can support for a given quality of service (specified by error probability).Comment: to appear in IEEE Transactions on Information Theor

Computing with Coloured Tangles

We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of computation is Turing complete, and that with bounded resources it can moreover decide any language in complexity class IP, sometimes with better performance parameters than corresponding classical protocols.Comment: 36 pages,; Introduction entirely rewritten, Section 4.3 adde

Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey

Wireless sensor networks (WSNs) consist of autonomous and resource-limited devices. The devices cooperate to monitor one or more physical phenomena within an area of interest. WSNs operate as stochastic systems because of randomness in the monitored environments. For long service time and low maintenance cost, WSNs require adaptive and robust methods to address data exchange, topology formulation, resource and power optimization, sensing coverage and object detection, and security challenges. In these problems, sensor nodes are to make optimized decisions from a set of accessible strategies to achieve design goals. This survey reviews numerous applications of the Markov decision process (MDP) framework, a powerful decision-making tool to develop adaptive algorithms and protocols for WSNs. Furthermore, various solution methods are discussed and compared to serve as a guide for using MDPs in WSNs

Spatial Throughput Maximization of Wireless Powered Communication Networks

Wireless charging is a promising way to power wireless nodes' transmissions. This paper considers new dual-function access points (APs) which are able to support the energy/information transmission to/from wireless nodes. We focus on a large-scale wireless powered communication network (WPCN), and use stochastic geometry to analyze the wireless nodes' performance tradeoff between energy harvesting and information transmission. We study two cases with battery-free and battery-deployed wireless nodes. For both cases, we consider a harvest-then-transmit protocol by partitioning each time frame into a downlink (DL) phase for energy transfer, and an uplink (UL) phase for information transfer. By jointly optimizing frame partition between the two phases and the wireless nodes' transmit power, we maximize the wireless nodes' spatial throughput subject to a successful information transmission probability constraint. For the battery-free case, we show that the wireless nodes prefer to choose small transmit power to obtain large transmission opportunity. For the battery-deployed case, we first study an ideal infinite-capacity battery scenario for wireless nodes, and show that the optimal charging design is not unique, due to the sufficient energy stored in the battery. We then extend to the practical finite-capacity battery scenario. Although the exact performance is difficult to be obtained analytically, it is shown to be upper and lower bounded by those in the infinite-capacity battery scenario and the battery-free case, respectively. Finally, we provide numerical results to corroborate our study.Comment: 15 double-column pages, 8 figures, to appear in IEEE JSAC in February 2015, special issue on wireless communications powered by energy harvesting and wireless energy transfe