The upper layer can be exploited in Device-To-Device (D2D) coded caching storage systems to decode encoded data. In this study, we propose a decoding algorithm for Luby Transform (LT) codes called GiAnds to be used in D2D coded caching storage systems where the communication cost of the upper layer is higher than the communication cost between local nodes. In this context, we define an optimization problem to explore check-node distributions that can decode LT codes at a lower cost. This optimization problem is solved by using the interior point algorithm to obtain check node distributions satisfying low decoding costs. In order to analyze the communication cost of the LT codes obtained from the optimization problem solution, simulations are carried out in addition to the theoretical results, and these results are compared with the decoding communication cost of Maximum Distance Separable (MDS) codes in the same system. Moreover, the decoding complexity of newly designed LT codes is also analyzed. According to the results, it is proven that the obtained LT codes can be used as a practical alternative to the MDS codes in D2D coded caching systems, especially for specific scales between the upper layer communication cost and the local layer communication cost.

The guesswork refers to the distribution of the minimum number of trials needed to guess a realization of a random variable accurately. In this study, a non-trivial generalization of the guesswork called guessing cost (also referred to as cost of guessing) is introduced, and an optimal strategy for finding the$\rho $-th moment of guessing cost is provided for a random variable defined on a finite set whereby each choice is associated with a positive finite cost value (unit cost corresponds to the original guesswork). Moreover, we drive asymptotically tight upper and lower bounds on the logarithm of guessing cost moments. Similar to previous studies on the guesswork, established bounds on the moments of guessing cost quantify the accumulated cost of guesses required for correctly identifying the unknown choice and are expressed in terms of Rényi’s entropy. Moreover, new random variables are introduced to establish connections between the guessing cost and the guesswork, leading to induced strategies. Establishing this implicit connection helped us obtain improved bounds for the non-asymptotic region. As a consequence, we establish the guessing cost exponent in terms of Rényi entropy rate on the moments of the guessing cost using the optimal strategy by considering a sequence of independent random variables with different cost distributions. Finally, with slight modifications to the original problem, these results are shown to be applicable for bounding the overall repair bandwidth for distributed data storage systems backed up by base stations and protected by bipartite graph codes.

Maintenance of connectivity in mobile ad hoc networks (MANETs) and especially in flying ad hoc networks, consisting of unmanned aerial vehicles (UAV), has crucial importance. Missions planned within these types of networks can be interrupted due to node failures, link errors, etc. This case becomes more critical when the application is heavily communication-dependent. To alleviate such problems, in this article, we propose a distributed proactive$k$-connectivity recovery algorithm (DP$k$CR) for UAV-based MANETs. To this end, the algorithm has been developed and tested by providing realistic scenarios. The time and message complexity analysis of the algorithm is presented. Moreover, to analyze the performance of the proposed algorithm, we compared it with other$k$-connectivity restoration algorithms in the literature. Simulation results revealed that DP$k$CR outperforms the alternatives in terms of convergence time for the recovery phase and, subsequently, in terms of energy consumption. Furthermore, DP$k$CR provides improvements to the bandwidth requirements for the restoration.

Random geometric graphs can be used in constructing topology formations for wireless ad-hoc networks (WANETs), including wireless sensor networks, flying ad-hoc networks, and others. They are useful for energy-saving schemes where a randomly alternating subset of deployed nodes is turned off temporarily (without compromising the network connectivity). This also improves network security by periodically rerouting the data flow, which makes it harder for third parties to run a traffic analysis. In the area and target coverage scenarios, a WANET deployment is desired to have maximal area coverage efficiency, which implies covering the largest possible area using the fewest number of nodes by maintaining the connectivity as well. Although deterministic topology formations offering optimal area coverage are known, a random node deployment method that grants connectivity and area coverage maximality has not been presented, to the best of our knowledge. This study introduces a novel topology formation method, called CoRMAC, that consistently yields tree-formed random geometric graphs that are guaranteed to be connected and offer maximal area coverage for any given area size and node cardinality. The area coverage maximality of CoRMAC is formally proven. Extensive theoretical and computational analyses have been provided to demonstrate its graph-theoretic, Euclidean, and networking features. Moreover, comparisons were made with other approaches to show the effectiveness of the proposed method.

Guessing a random variable with finite or countably infinite support in which each selection leads to a positive cost value has recently been studied within the context of "guessing cost". In those studies, similar to standard guesswork, upper and lower bounds for the ρ-th moment of guessing cost are described in terms of the known measure Rényi’s entropy. In this study, we non-trivially improve the known bounds using previous techniques along with new notions such as balancing cost. We have demonstrated that the novel lower bound proposed in this work, achieves 5.84%, 18.47% higher values than that of the known lower bound for ρ = 1 and ρ = 5, respectively. As for the upper bound, the novel expression provides 10.93%, 5.54% lower values than that of the previously presented bounds for ρ = 1 and ρ = 5, respectively.

We consider a novel distributed data storage/caching scenario in a cellular network, where multiple nodes may fail/depart simultaneously To meet reliability, we allow cooperative regeneration of lost nodes with the help of base stations allocated in a set of hierarchical layers1. Due to this layered structure, a symbol download from each base station has a different cost, while the link capacities between the nodes of the cellular system and the base stations are also constrained. Under such a setting, we formulate the fundamental trade-off with closed form expressions between repair bandwidth cost and the storage space per node. Particularly, the minimum storage as well as bandwidth cost points are formulated. Finally, we provide an explicit optimal code construction for the minimum storage regeneration point for a special set of system parameters.

The base station-mobile device communication traffic has dramatically increased recently due to mobile data, which in turn heavily overloaded the underlying infrastructure. To decrease Base Station (BS) interaction, intra-cell communication between local devices, known as Device-to-Device, is utilized for distributed data caching. Nevertheless, due to the continuous departure of existing nodes and the arrival of newcomers, the missing cached data may lead to permanent data loss. In this study, we propose and analyze a class of Low-Density Parity Check (LDPC) codes for distributed data caching in cellular networks. Contrary to traditional distributed storage, a novel repair algorithm for LDPC codes is proposed which is designed to exploit the minimal direct BS communication. To assess the versatility of LDPC codes and establish performance comparisons to classic coding techniques, novel theoretical and experimental evaluations are derived. Essentially, the theoretical/numerical results for repair bandwidth cost in presence of BS are presented in a distributed caching setting. Accordingly, when the gap between the cost of downloading a symbol from BS and from other local network nodes is not dramatically high, we demonstrate that LDPC codes can be considered as a viable fault-tolerance alternative in cellular systems with caching capabilities for both low and high code rates.

In this paper, we introduce the notion of cost of guessing and provide an optimal strategy for guessing a random variable taking values on a finite set whereby each choice may be associated with a positive finite cost value. Moreover, we drive asymptotically tight upper and lower bounds on the moments of cost of guessing problem. Similar to previous studies on the standard guesswork, established bounds on moments quantify the accumulated cost of guesses required for correctly identifying the unknown choice and are expressed in terms of the Rényi's entropy. A new random variable is introduced to bridge between cost of guessing and the standard guesswork and establish the guessing cost exponent on the moments of the optimal guessing. Furthermore, these bounds are shown to serve quite useful for finding repair latency cost for distributed data storage in which sparse graph codes may be utilized.