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Register a new userAn asymptotically optimal push-pull method for multicasting over a random network
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Added by
Rajesh Sundaresan
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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We consider allcast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session. Traffic from each node in the session has to be sent to every other node in the session. If the session does not consist of all the nodes, the remaining nodes act as relays. The nodes are connected by undirected links whose capacities are independent and identically distributed random variables. We study the asymptotics of the capacity region (with network coding) in the limit of a large number of nodes, and show that the normalized sum rate converges to a constant almost surely. We then provide a decentralized push-pull algorithm that asymptotically achieves this normalized sum rate without network coding.
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The problem of constructing effective statistical tests for random number generators (RNG) is considered. Currently, statistical tests for RNGs are a mandatory part of cryptographic information protection systems, but their effectiveness is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p-value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p-value for any (unknown) stationary ergodic source.
In a heterogeneous unreliable multiaccess network, wherein terminals share a common wireless channel with distinctive error probabilities, existing works have showed that a persistent round-robin (RR-P) scheduling policy (i.e., greedy policy) can be arbitrarily worse than the optimum in terms of Age of Information (AoI) under standard Automatic Repeat reQuest (ARQ), and one must resort to Whittles index approach for optimal AoI. In this paper, practical Hybrid ARQ (HARQ) schemes which are widely-used in todays wireless networks are considered. We show that RR-P is very close to optimum with asymptotically many terminals in this case, by explicitly deriving tight, closed-form AoI gaps between optimum and achievable AoI by RR-P. In particular, it is rigorously proved that for RR-P, under HARQ models concerning fading channels (resp. finite-blocklength regime), the relative AoI gap compared with the optimum is within a constant of $(sqrt{e}-1)^2/4sqrt{e} cong 6.4%$ (resp. $6.2%$ with error exponential decay rate of $0.5$). In addition, RR-P enjoys the distinct advantage of implementation simplicity with channel-unaware and easy-to-decentralize operations, making it favorable in practice.
Batched network coding is a variation of random linear network coding which has low computational and storage costs. In order to adapt to random fluctuations in the number of erasures in individual batches, it is not optimal to recode and transmit the same number of packets for all batches. Different distributed optimization models, which are called adaptive recoding schemes, were formulated for this purpose. The key component of these optimization problems is the expected value of the rank distribution of a batch at the next network node, which is also known as the expected rank. In this paper, we put forth a unified adaptive recoding framework with an arbitrary recoding field size. We show that the expected rank functions are concave when the packet loss pattern is a stationary stochastic process, which covers but not limited to independent packet loss and Gilbert-Elliott packet loss model. Under this concavity assumption, we show that there always exists a solution which not only can minimize the randomness on the number of recoded packets but also can tolerate rank distribution errors due to inaccurate measurements or limited precision of the machine. We provide an algorithm to obtain such an optimal optimal solution, and propose tuning schemes that can turn any feasible solution into a desired optimal solution.
We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work of Koetter and Kschischang, we introduce a probabilistic model for errors. We compute the capacity of this channel and we define an error-correction scheme based on random sparse graphs and a low-complexity decoding algorithm. By optimizing over the code degree profile, we show that this construction achieves the channel capacity in complexity which is jointly quadratic in the number of coded information bits and sublogarithmic in the error probability.
A large body of applications that involve monitoring, decision making, and forecasting require timely status updates for their efficient operation. Age of Information (AoI) is a newly proposed metric that effectively captures this requirement. Recent research on the subject has derived AoI optimal policies for the generation of status updates and AoI optimal packet queueing disciplines. Unlike previous research we focus on low-end devices that typically support monitoring applications in the context of the Internet of Things. We acknowledge that these devices host a diverse set of applications some of which are AoI sensitive while others are not. Furthermore, due to their limited computational resources they typically utilize a simple First-In First-Out (FIFO) queueing discipline. We consider the problem of optimally controlling the status update generation process for a system with a source-destination pair that communicates via a wireless link, whereby the source node is comprised of a FIFO queue and two applications, one that is AoI sensitive and one that is not. We formulate this problem as a dynamic programming problem and utilize the framework of Markov Decision Processes to derive optimal policies for the generation of status update packets. Due to the lack of comparable methods in the literature, we compare the derived optimal policies against baseline policies, such as the zero-wait policy, and investigate the performance of all policies for a variety of network configurations. Results indicate that existing status update policies fail to capture the trade-off between frequent generation of status updates and queueing delay and thus perform poorly.
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