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The one-out-of-k retrieval problem and linear network coding

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  • In this paper we show how linear network coding can reduce the number of queries needed to retrieve one specific message among $k$ distinct ones replicated across a large number of randomly accessed nodes storing one message each. Without network coding, this would require $k$ queries on average. After proving that no scheme can perform better than a straightforward lower bound of $0.5k$ average queries, we propose and asymptotically evaluate, using mean field arguments, a few example practical schemes, the best of which attains $0.794k$ queries on average. The paper opens two complementary challenges: a systematic analysis of practical schemes so as to identify the best performing ones and design guideline strategies, as well as the need to identify tighter, nontrivial, lower bounds.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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