Coded Slotted ALOHA with Varying Packet Loss Rate across Users

The recent research has established an analogy between successive interference cancellation in slotted ALOHA framework and iterative belief-propagation erasure-decoding, which has opened the possibility to enhance random access protocols by utilizing theory and tools of erasure-correcting codes. In this paper we present a generalization of the and-or tree evaluation, adapted for the asymptotic analysis of the slotted ALOHA-based random-access protocols, for the case when the contending users experience different channel conditions, resulting in packet loss probability that varies across users. We apply the analysis to the example of frameless ALOHA, where users contend on a slot basis. We present results regarding the optimal access probabilities and contention period lengths, such that the throughput and probability of user resolution are maximized.Comment: 4 pages, submitted to GlobalSIP 201

Fast Data Retrieval and Enhanced Data Security of Cloud Storage in Luby Transform

AbstractCloud computing is a set of IT services that are provided to a customer over a network on a leased basis and with the ability to scale up or down their service requirements. It advantages to mention but a few include scalability, resilience, flexibility, efficiency and outsourcing non-core activities.Despite the potential gains achieved from the cloud computing, the organizations are slow in accepting it due to security issues and challenges associated with it. The idea of handing over important data to another company is worrisome; such that the consumers need to be vigilant in understanding the risks of data breaches in this new environment. This paper introduces analysis of the cloud computing security issues and challenges focusing on providing data confidentiality along with high requirement of data availability in cloud technology

Low-Sensitivity Functions from Unambiguous Certificates

We provide new query complexity separations against sensitivity for total Boolean functions: a power $3$ separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power $2.22$ separation between certificate complexity and sensitivity. We get these separations by using a new connection between sensitivity and a seemingly unrelated measure called one-sided unambiguous certificate complexity ($UC_{min}$). We also show that $UC_{min}$ is lower-bounded by fractional block sensitivity, which means we cannot use these techniques to get a super-quadratic separation between $bs(f)$ and $s(f)$. We also provide a quadratic separation between the tree-sensitivity and decision tree complexity of Boolean functions, disproving a conjecture of Gopalan, Servedio, Tal, and Wigderson (CCC 2016). Along the way, we give a power $1.22$ separation between certificate complexity and one-sided unambiguous certificate complexity, improving the power $1.128$ separation due to G\"o\"os (FOCS 2015). As a consequence, we obtain an improved $\Omega(\log^{1.22} n)$ lower-bound on the co-nondeterministic communication complexity of the Clique vs. Independent Set problem.Comment: 25 pages. This version expands the results and adds Pooya Hatami and Avishay Tal as author