Exact repair problems with multiple sources

Abstract

We consider a new variant of the exact repair distributed storage problem, the multi-source exact repair problem, wherein the reconstruction decoders are each only required to provide a subset of the source variables. To best illustrate the idea, we generalize the (n, k, d) = (3, 2, 2) exact repair distributed storage problem to the multisource case. When every decoder demands all source variables, the rate region of the (3, 2, 2) exact repair problem is known to be same as that of the (3, 2, 2) functional repair problem, while the rate region for (3, 2, 2) case with multiple sources is unknown. We find achievable rate regions for vector binary and scalar binary codes via an automated approach.

Explicit Polyhedral Bounds on Network Coding Rate Regions via Entropy Function Region: Algorithms, Symmetry, and Computation

“…Nevertheless, utilizing the constraints L A described in the previous section with the adaptation of reproduction of edges, and a common rate limitation for edges of the same type (storage or repair), one can obtain the storage repair tradeoff as an instance of a polyhedral projection problem [7]. While must of the research on these problems is typically focussed on a single source representing all of the information to be stored and an associated two dimensional tradeoff between storage and repair, multisource formulations [33], for instance reflecting data with different latency requirements, or heterogenous storage sizes and repair bandwidths, are possible and can be derived as polyhedral projections of largely the same form as (2).…”