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    Sample path large deviations of Poisson shot noise with heavy tail semi-exponential distributions


    Cui, Ying and Medard, Muriel and Yeh, Edmund and Leith, Douglas J. and Duffy, Ken R. (2011) Sample path large deviations of Poisson shot noise with heavy tail semi-exponential distributions. Journal of Applied Probability, 48 (3). pp. 688-698. ISSN 0021-9002

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    Official URL: http://projecteuclid.org/euclid.jap/1316796907


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    Abstract

    The problem of finding network codes for general connections is inherently difficult. Resource minimization for general connections with network coding is further complicated. The existing solutions mainly rely on very restricted classes of network codes, and are almost all centralized. In this paper, we introduce linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections. For such code constructions, we pose the problem of cost minimization for the subgraph involved in the coding solution and relate this minimization to a Constraint Satisfaction Problem (CSP) which we show can be simplified to have a moderate number of constraints. While CSPs are NP-complete in general, we present a probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Our approach allows fairly general coding across flows, guarantees no greater cost than routing, and shows a possible distributed implementation.

    Item Type: Article
    Additional Information: This is the preprint version of the published article, which is available at doi:10.1239/jap/1316796907
    Keywords: Heavy-tailed distribution; sample path large deviation; Poisson shot noise;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 6217
    Identification Number: https://doi.org/10.1239/jap/1316796907
    Depositing User: Dr Ken Duffy
    Date Deposited: 29 Jun 2015 14:40
    Journal or Publication Title: Journal of Applied Probability
    Publisher: Applied Probability Trust
    Refereed: Yes
    URI:

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