Wireless Caching Research Articles

On Numerical Characteristics of а Simplex and their Estimates

Let \(n\in {\mathbb N}\), and let \(Q_n=[0,1]^n\) be the \(n\)-dimensional unit cube. For a nondegenerate simplex \(S\subset {\mathbb R}^n\), by \(\sigma S\) we denote the homothetic image of \(S\) with the center of homothety in the center of gravity of S and the ratio of homothety \(\sigma\). We apply the following numerical characteristics of the simplex. Denote by \(\xi(S)\) the minimal \(\sigma>0\) with the property \(Q_n\subset \sigma S\). By \(\alpha(S)\) we denote the minimal \(\sigma>0\) such that \(Q_n\) is contained in a translate of a simplex \(\sigma S\). By \(d_i(S)\) we mean the \(i\)th axial diameter of \(S\), i.\,e. the maximum length of a segment contained in \(S\) and parallel to the \(i\)th coordinate axis. We apply the computational formulae for \(\xi(S)\), \(\alpha(S)\), \(d_i(S)\) which have been proved by the first author. In the paper we discuss the case \(S\subset Q_n\). Let \(\xi_n=\min\{ \xi(S): S\subset Q_n\}. \) Earlier the first author formulated the conjecture: {\it if \(\xi(S)=\xi_n\), then \(\alpha(S)=\xi(S)\).} He proved this statement for \(n=2\) and the case when \(n+1\) is an Hadamard number, i.\,e. there exists an Hadamard matrix of order \(n+1\). The following conjecture is a stronger proposition: {\it for each \(n\), there exist \(\gamma\geq 1\), not depending on \(S\subset Q_n\), such that \(\xi(S)-\alpha(S)\leq \gamma (\xi(S)-\xi_n).\)} By \(\varkappa_n\) we denote the minimal \(\gamma\) with such a property. If \(n+1\) is an Hadamard number, then the precise value of \(\varkappa_n\) is 1. The existence of \(\varkappa_n\) for other \(n\) was unclear. In this paper with the use of computer methods we obtain an equality $$\varkappa_2 = \frac{5+2\sqrt{5}}{3}=3.1573\ldots $$ Also we prove a new estimate $$\xi_4\leq \frac{19+5\sqrt{13}}{9}=4.1141\ldots,$$ which improves the earlier result \(\xi_4\leq \frac{13}{3}=4.33\ldots\) Our conjecture is that \(\xi_4\) is precisely \(\frac{19+5\sqrt{13}}{9}\). Applying this value in numerical computations we achive the value $$\varkappa_4 = \frac{4+\sqrt{13}}{5}=1.5211\ldots$$ Denote by \(\theta_n\) the minimal norm of interpolation projection on the space of linear functions of \(n\) variables as an operator from \(C(Q_n)\) in \(C(Q_n)\). It is known that, for each \(n\), $$\xi_n\leq \frac{n+1}{2}\left(\theta_n-1\right)+1,$$ and for \(n=1,2,3,7\) here we have an equality. Using computer methods we obtain the result \(\theta_4=\frac{7}{3}\). Hence, the minimal \(n\) such that the above inequality has a strong form is equal to 4. %, a principal architecture of common purpose CPU and its main components are discussed, CPUs evolution is considered and drawbacks that prevent future CPU development are mentioned. Further, solutions proposed so far are addressed and new CPU architecture is introduced. The proposed architecture is based on wireless cache access that enables reliable interaction between cores in multicore CPUs using terahertz band, 0.1-10THz. The presented architecture addresses the scalability problem of existing processors and may potentially allow to scale them to tens of cores. As in-depth analysis of the applicability of suggested architecture requires accurate prediction of traffic in current and next generations of processors we then consider a set of approaches for traffic estimation in modern CPUs discussing their benefits and drawbacks. The authors identify traffic measurements using existing software tools as the most promising approach for traffic estimation, and use Intel Performance Counter Monitor for this purpose. Three types of CPU loads are considered including two artificial tests and background system load. For each load type the amount of data transmitted through the L2-L3 interface is reported for various input parameters including the number of active cores and their dependences on number of cores and operational frequency.

Efficient Scheduling and Power Allocation for D2D-Assisted Wireless Caching Networks

We study a one-hop device-to-device (D2D)-assisted wireless caching network, where popular files are randomly and independently cached in the memory of end users. Each user may obtain the requested files from its own memory without any transmission, or from a helper through a one-hop D2D transmission, or from the base station. We formulate a joint D2D link scheduling and power allocation problem to maximize the system throughput. However, the problem is non-convex, and obtaining an optimal solution is computationally hard. Alternatively, we decompose the problem into a D2D link-scheduling problem and an optimal power allocation problem. To solve the two subproblems, we first develop a D2D link-scheduling algorithm to select the largest number of D2D links satisfying both the signal to interference plus noise ratio and the transmit power constraints. Then, we develop an optimal power allocation algorithm to maximize the minimum transmission rate of the scheduled D2D links. Numerical results indicate that both the number of the scheduled D2D links and the system throughput can be improved simultaneously with the Zipf-distribution caching scheme, the proposed D2D link-scheduling algorithm, and the proposed optimal power allocation algorithm compared with the state of the arts.

Data Rate Estimation for Wireless Core-to-Cache Communication in Multicore CPUs

In this paper, a principal architecture of common purpose CPU and its main components are discussed, CPUs evolution is considered and drawbacks that prevent future CPU development are mentioned. Further, solutions proposed so far are addressed and a new CPU architecture is introduced. The proposed architecture is based on wireless cache access that enables a reliable interaction between cores in multicore CPUs using terahertz band, 0.1-10THz. The presented architecture addresses the scalability problem of existing processors and may potentially allow to scale them to tens of cores. As in-depth analysis of the applicability of the suggested architecture requires accurate prediction of traffic in current and next generations of processors, we consider a set of approaches for traffic estimation in modern CPUs discussing their benefits and drawbacks. The authors identify traffic measurements by using existing software tools as the most promising approach for traffic estimation, and they use Intel Performance Counter Monitor for this purpose. Three types of CPU loads are considered including two artificial tests and background system load. For each load type the amount of data transmitted through the L2-L3 interface is reported for various input parameters including the number of active cores and their dependences on the number of cores and operational frequency.

Partial Repair for Wireless Caching Networks With Broadcast Channels

We investigate the repair problem for wireless caching networks when parts of stored packets in cashing nodes are lost. We first develop theoretical lower bounds on the number of necessary transmission packets over error-free broadcast channels for repair. Then we discuss the impact of the distribution of the lost packets among caching nodes. Finally, we study the construction of repair codes and propose the optimal exact repair for some special scenarios.

Deployment Versus Data Retrieval Costs for Caches in the Plane

We consider the problem of finding the Pareto front of the expected deployment cost of wireless caches in the plane and the expected retrieval cost of a client requesting data from the caches. The data is stored at the caches according to partitioning and coding strategies. We show that under coding, it is optimal to deploy many caches with low storage capacity. For partitioning, we derive a simple relation between the cost of the cache deployment and the cost of retrieving the data from the caches. We quantify the improvements offered by optimal coding in comparison to partitioning, i.e., we derive a relation for the difference in deployment cost required to achieve a given retrieval cost. Finally, we show that even non-optimal coding is better than partitioning in the sense that no coded deployment can be dominated by a partitioning strategy.

A Cooperative Hybrid Caching Strategy for P2P Mobile Network

Recently mobile network technologies develop quickly. To meet the increasing demand of wireless users, many multimedia proxies have been deployed over wireless networks. The caching nodes constitute a wireless caching system with an architecture of P2P and provide better service to mobile users. In this paper, we formulate the caching system to optimize the consumption of network bandwidth and guarantee the response time of mobile users. Two strategies: single greedy caching strategy and cooperative hybrid caching strategy are proposed to achieve this goal. Single greedy caching aims to reduce bandwidth consumption from the standpoint of each caching node, while cooperative hybrid caching allows sharing and coordination of multiple nodes, taking both bandwidth consumption and popularity into account. Simulation results show that cooperative hybrid caching outperforms single greedy caching in both bandwidth consumption and delay time.

Wireless cache invalidation schemes with link adaptation and downlink traffic

Providing on-demand data access in client-server wireless networks is an important support to many interesting mobile computing applications. Caching frequently accessed data by mobile clients can conserve wireless bandwidth and battery power, at the expense of some system resources to maintain cache consistency. The basic cache consistency strategy is the use of periodic invalidation reports (IRS) broadcast by the server. Recently, IR-based approaches have been further improved by using additional updated invalidation reports (UIRs) (i.e., the IR+UIR algorithm) to reduce the long query latency. However, the performance of the IR+UIR approach in a practical system is still largely unknown. Specifically, previous results are based on two impractical simplifying assumptions: 1) broadcast traffic is error-free and 2) no other downlink traffic (e.g., voice) exists in the system. The first assumption is clearly unrealistic as signal propagation impairments (e.g., multipath fading) and, hence, packet reception failures are inevitable in a practical situation. The second assumption is also inapplicable in real life because mobile devices are usually multipurposed (e.g., a mobile phone equipped with a browser may be used for Web surfing while having a phone conversation). In this paper, we first study the performance of the IR+UIR approach under a realistic system model: The quality of the wireless channel is time-varying, and there are other downlink traffics in the system. Our simulation results show that query delay significantly increases as a result of broadcast error and the additional downlink traffics experience longer delay due to extended broadcast period. Exploiting link adaptation (i.e., transmission rate is adjusted dynamically according to channel quality), we then propose three schemes to tackle these two problems. Our results indicate that the proposed schemes outperform IR+UIR under a wide range of system parameters.