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A particular instance of the shortest vector problem (SVP) appears in the context of compute-and-forward. Despite the NP-hardness of the SVP, we will show that this certain instance can be solved in complexity order $O(n\psi \log (n\psi ))$ , where $\psi = \sqrt {P\|{\text{h}}\|^{2}+1}$ depends on the transmission power and the norm of the channel vector. We will then extend our results to integer-forcing...
The classical distributed storage problem can be modeled by a k-uniform complete hyper-graph where vertices represent servers and hyper-edges represent users. Hence each hyper-edge should be able to recover the full file using only the memories of the vertices associated with it. This paper considers the generalization of this problem to arbitrary hyper-graphs and to the case of multiple files, where...
We study the problem of coded caching when the server has access to several libraries and each user makes independent requests from every library. The single-library scenario has been well studied and it has been proved that coded caching can significantly improve the delivery rate compared to uncoded caching. In this work we show that when all the libraries have the same number of files, memory-sharing...
Caching is an approach to smoothen the variability of traffic over time. Recently it has been proved that the local memories at the users can be exploited for reducing the peak traffic in a much more efficient way than previously believed. In this work we improve upon the existing results and introduce a novel caching strategy that takes advantage of simultaneous coded placement and coded delivery...
Compute-and-Forward is an emerging technique to deal with interference. It allows the receiver to decode a suitably chosen integer linear combination of the transmitted messages. The integer coefficients should be adapted to the channel fading state. Optimizing these coefficients is a Shortest Lattice Vector (SLV) problem. In general, the SLV problem is known to be prohibitively complex. In this paper,...
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