Having timely and fresh knowledge about the current state of information sources is critical in a variety of applications. In particular, a status update may arrive at the destination much later than its generation time due to processing and communication delays. The freshness of the status update at the destination is captured by the notion of age of information. In this study, we first analyze a network with a single source, n servers, and the monitor (destination). The servers independently sense the source of information and send the status update to the monitor. We then extend our result to multiple independent sources of information in the presence of n servers. We assume that updates arrive at the servers according to Poisson random processes. Each server sends its update to the monitor through a direct link, which is modeled as a queue. The service time to transmit an update is considered to be an exponential random variable. We examine both homogeneous and heterogeneous service and arrival rates for the single-source case, and only homogeneous arrival and service rates for the multiple sources case. We derive a closed-form expression for the average age of information under a last-come-first-serve (LCFS) queue for a single source and arbitrary n homogeneous servers. For n = 2, 3, we derive the explicit average age of information for arbitrary sources and homogeneous servers, and for a single source and heterogeneous servers. For n = 2 we find the optimal arrival rates given fixed sum arrival rate and service rates.

In a distributed storage system, recovering from multiple failures is a critical and frequent task that is crucial for maintaining the system's reliability and fault-tolerance. In this work, we focus on the problem of repairing multiple failures in a centralized way, which can be desirable in many data storage configurations, and we show that a significant repair traffic reduction is possible. First, the fundamental tradeoff between the repair bandwidth and the storage size for functional repair is established. Using a graph-theoretic formulation, the optimal tradeoff is identified as the solution to an integer optimization problem, for which a closed-form expression is derived. Expressions of the extreme points, namely the minimum storage multi-node repair (MSMR) and minimum bandwidth multi-node repair (MBMR) points, are obtained. Second, we describe a general framework for converting single erasure minimum storage regenerating codes to MSMR codes. The repair strategy for e failures is similar to that for single failure, however certain extra requirements need to be satisfied by the repairing functions for single failure. For illustration, the framework is applied to product-matrix codes and interference alignment codes. Furthermore, we prove that the functional MBMR point is not achievable for linear exact repair codes. We also show that exact-repair minimum bandwidth cooperative repair (MBCR) codes achieve an interior point, that lies near the MBMR point, when k ≡ 1 mod e, k being the minimum number of nodes needed to reconstruct the entire data. Finally, for k > 2e, e | k and e | d, where d is the number of helper nodes during repair, we show that the functional repair tradeoff is not achievable under exact repair, except for maybe a small portion near the MSMR point, which parallels the results for single erasure repair by Shah et al.

No abstract

No abstract

No abstract

We study the problem of centralized exact repair of multiple failures in distributed storage. We describe constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction by Tian et al in [1], designed for exact repair of single failure. We firstly improve upon the layered construction for general system parameters. Then, we extend the improved construction to support the repair of multiple failures, with varying number of helpers. In particular, we prove the optimality of one point on the functional repair tradeoff of multiple failures for some parameters. Finally, considering minimum bandwidth cooperative repair (MBCR) codes as centralized repair codes, we determine explicitly the best achievable region obtained by space-sharing among all known points, including the MBCR point.

No abstract

Resistive memories are considered a promising memory technology enabling high storage densities with inmemory computing capabilities. However, the readout reliability of resistive memories is impaired due to the inevitable existence of wire resistance, resulting in the sneak path problem. Motivated by this problem, we study polar coding over channels with different reliability levels, termed non-stationary polar codes, and we propose a technique improving its bit error rate (BER) performance. We then apply the framework of non-stationary polar codes to the crossbar array and evaluate its BER performance under two modeling approaches, namely binary symmetric channels (BSCs) and binary asymmetric channels (BSCs). Finally, we propose a technique for biasing the proportion of high-resistance states in the crossbar array and show its advantage in reducing further the BER. Several simulations are carried out using a SPICE-like simulator, exhibiting significant reduction in BER.