50,418 research outputs found
Cumulative-Separable Codes
q-ary cumulative-separable -codes and 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
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
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
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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