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In wireless distributed computing systems, mobile devices that are connected wirelessly to the Fog (e.g., small base stations) collaboratively solve a given computational task. Unfortunately, wireless distributed computing systems suffer from packet losses due to severe channel fading. Moreover, a wireless device can drop out of the system when leaving the coverage of a master node in the Fog layer. We model this unreliability between a device and a master node as a packet erasure channel. When a packet fails to be detected at the receiver, the corresponding packet is retransmitted, which would significantly increase the overall run-time to finish the task. We take a coding-theoretic approach to tackle this straggler-like problem in wireless distributed computing. We first investigate the expected latency using an $(n, k)$ maximum-distance separable (MDS) code. We obtain the lower and upper bounds on the latency in closed forms and provide guidelines to design MDS codes depending on the channel condition characterized by packet erasure probability. Then, we introduce another important performance metric called minimum latency, and also provide guidelines on designing optimal codes. Based on optimal codes, we obtain the performance curves of achievable minimum latency and achievable workload as functions of packet erasure probability. [ABSTRACT FROM AUTHOR]

Distributed learning plays a key role in reducing the training time of modern deep neural networks with massive datasets. In this article, we consider a distributed learning problem where gradient computation is carried out over a number of computing devices at the wireless edge. We propose hierarchical broadcast coding, a provable coding-theoretic framework to speed up distributed learning at the wireless edge. Our contributions are threefold. First, motivated by the hierarchical nature of real-world edge computing systems, we propose a layered code which mitigates the effects of not only packet losses at the wireless computing nodes but also straggling access points (APs) or small base stations. Second, by strategically allocating data partitions to nodes in the overlapping areas between cells, our technique achieves the fundamental lower bound on computational load to combat stragglers. Finally, we take advantage of the broadcast nature of wireless networks by which wireless devices in the overlapping cell coverage broadcast to more than one AP. This further reduces the overall training time in the presence of straggling APs. Experimental results on Amazon EC2 confirm the advantage of the proposed methods in speeding up learning. Our design targets any gradient descent based learning algorithms, including linear/logistic regressions and deep learning. [ABSTRACT FROM AUTHOR]

This paper investigates interplay among storage overhead, bandwidth requirement, and security constraint in distributed storage. In the model used in our analysis, storage nodes are dispersed in multiple clusters. When a node fails, necessary content gets restored by downloading data from different nodes that may possibly be in other clusters. The bandwidth required for transferring data for node repair is assumed more scarce for cluster-to-cluster links than the links connecting intra-cluster nodes. Eavesdropping takes place on links across clusters only, and a fraction of the total number of clusters is assumed compromised. When a cluster is compromised, any repair traffic going in and out of it is eavesdropped. For this clustered model with eavesdroppers, we analyze the security of distributed storage systems (DSSs) and provide guidelines on designing system solutions for securing the data. First, under the setting of functional repair, we derive a general upper bound on the secrecy capacity, the maximum data size that can be stored in DSSs with perfect secrecy. In the practically important bandwidth-limited regime where the node storage size is equal to the repair bandwidth, the upper bound is shown to be achievable through proposed code constructions. Moreover, we obtain a closed-form expression for the required system resources-node storage size and repair bandwidth-to store a given amount of data with perfect secrecy. Second, we investigate the behavior of secrecy capacity as the number of compromised clusters increases. According to our mathematical analysis, the secrecy capacity decreases as a quadratic function until the number of compromised clusters reaches a certain threshold. Finally, based on the fundamental relationship between the system resources and the secrecy capacity, we provide a guideline on balancing intra- and cross-cluster repair bandwidths depending on the given system security level. [ABSTRACT FROM AUTHOR]

A new system model reflecting the clustered structure of distributed storage is suggested to investigate interplay between storage overhead and repair bandwidth as storage node failures occur. Large data centers with multiple racks/disks or local networks of storage devices (e.g., sensor network) are good applications of the suggested clustered model. In realistic scenarios involving clustered storage structures, repairing storage nodes using intact nodes residing in other clusters are more bandwidth consuming than restoring nodes based on information from intra-cluster nodes. Therefore, it is important to differentiate between intra-cluster repair bandwidth and cross-cluster repair bandwidth in modeling distributed storage. Capacity of the suggested model is obtained as a function of fundamental resources of distributed storage systems, namely, node storage capacity, intra-cluster repair bandwidth, and cross-cluster repair bandwidth. The capacity is shown to be asymptotically equivalent to a monotonic decreasing function of number of clusters, as the number of storage nodes increases without bound. Based on the capacity expression, feasible sets of required resources which enable reliable storage are obtained in a closed-form solution. Specifically, it is shown that the cross-cluster traffic can be minimized to zero (i.e., intra-cluster local repair becomes possible) by allowing extra resources on storage capacity and intra-cluster repair bandwidth, according to the law specified in the closed form. The network coding schemes with zero cross-cluster traffic are defined as intra-cluster repairable codes, which are shown to be a class of the previously developed locally repairable codes. [ABSTRACT FROM AUTHOR]

In low-latency applications for 5G and beyond, precise synchronization becomes more challenging. In this correspondence, we generalized the analytical tool to design combined window-filter waveform, which can tolerate imperfect synchronization scenarios. Compared to the previous work focusing on an ideal channel, the generalized tool considers the effect of multipath fading with instantaneous or statistical channel state information at the transmitter (CSIT). The waveform designed by the proposed tool yields lower bit error rates compared to the design with no CSIT and other waveform candidates. [ABSTRACT FROM AUTHOR]

Pilot contamination, caused by the reuse of pilots among interfering cells, remains a significant obstacle that limits the performance of massive multi-input multi-output antenna systems. To handle this problem, less aggressive reuse of pilots involving allocation of additional pilots for interfering users is closely examined in this paper. Hierarchical pilot reuse methods are proposed, which effectively mitigate pilot contamination and increase the net throughput of the system. Among the suggested hierarchical pilot reuse schemes, the optimal way of assigning pilots to different users is obtained in a closed-form solution, which maximizes the net sum-rate in a given coherence time. Simulation results confirm that when the ratio of the channel coherence time to the number of users in each cell is sufficiently large, less aggressive reuse of pilots yields significant performance advantage relative to the case, where all cells reuse the same pilot set. [ABSTRACT FROM PUBLISHER]

Pilot reuse in the multi-cell massive multi-input multi-output system is investigated where user groups with different priorities exist. Recent investigation on pilot reuse has revealed that when the ratio of the coherent time interval to the number of users is reasonably high, it is beneficial not to fully reuse pilots from interfering cells. This paper finds the optimum pilot assignment strategy that would maximize the weighted sum rate (WSR) given the user groups with different priorities. A closed-form solution for the optimal pilot assignment is derived and is shown to make intuitive sense. Performance comparison shows that under wide range of channel conditions, the optimal pilot assignment that uses extra set of pilots achieves better WSR performance than conventional full pilot reuse. [ABSTRACT FROM AUTHOR]