50,418 research outputs found

    Cumulative-Separable Codes

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    q-ary cumulative-separable Γ(L,G(j))\Gamma(L,G^{(j)})-codes L={αGF(qm):G(α)0}L=\{ \alpha \in GF(q^{m}):G(\alpha )\neq 0 \} and G(j)(x)=G(x)j,1iqG^{(j)}(x)=G(x)^{j}, 1 \leq i\leq q are considered. The relation between different codes from this class is demonstrated. Improved boundaries of the minimum distance and dimension are obtained.Comment: 14 pages, 1 figur

    Systematic MDS erasure codes based on vandermonde matrices

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    An increasing number of applications in computer communications uses erasure codes to cope with packet losses. Systematic maximum-distance separable (MDS) codes are often the best adapted codes. This letter introduces new systematic MDS erasure codes constructed from two Vandermonde matrices. These codes have lower coding and decoding complexities than the others systematic MDS erasure codes

    Ideal codes over separable ring extensions

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    This paper investigates the application of the theoretical algebraic notion of a separable ring extension, in the realm of cyclic convolutional codes or, more generally, ideal codes. We work under very mild conditions, that cover all previously known as well as new non trivial examples. It is proved that ideal codes are direct summands as left ideals of the underlying non-commutative algebra, in analogy with cyclic block codes. This implies, in particular, that they are generated by an idempotent element. Hence, by using a suitable separability element, we design an efficient algorithm for computing one of such idempotents

    Caching at the Edge with Fountain Codes

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    We address the use of linear randon fountain codes caching schemes in a heterogeneous satellite network. We consider a system composed of multiple hubs and a geostationary Earth orbit satellite. Coded content is memorized in hubs' caches in order to serve immediately the user requests and reduce the usage of the satellite backhaul link. We derive the analytical expression of the average backhaul rate, as well as a tight upper bound to it with a simple expression. Furthermore, we derive the optimal caching strategy which minimizes the average backhaul rate and compare the performance of the linear random fountain code scheme to that of a scheme using maximum distance separable codes. Our simulation results indicate that the performance obtained using fountain codes is similar to that of maximum distance separable codes
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