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For an $m\times n$ binary matrix with $d$ nonzero elements per column, it is interesting to identify the minimal column degree $d$ that corresponds to the best recovery performance. Consider this problem is hard to be addressed with currently known performance parameters, we propose a new performance parameter, the average of nonzero correlations between normalized columns. The parameter is proved...
With the advent of "big-data" processing and analytics, organizations and enterprises have increased the collection of data from individuals, and are increasingly developing business models involving analytics to gain deep insights into the collected data. Often, it becomes essential to release and merge said data to third-parties for more extensive analytics for which an organization may...
In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with (r, δ)-localitty are further proposed. Since hot data is not uncommon in a distributed storage system, both Zeh et al. and Kadhe et al. focus on the LRCs with multiple localities or unequal localities (ML-LRCs) recently,...
This paper studies a class of binary matrices with correlations between distinct columnsequal to zero or one, which has reported comparable performance with random matrices inrecent studies of compressed sensing. For such matrix, we analyze its structure propertyand provide an improved performance estimation.
Recently, constant dimension codes were introduced to correct errors and/or erasures over the operator channel in random network coding. In this paper, we study the problem of maximum number of codewords for constant dimension codes by linear programming (LP)approach. We give LP bounds and then show that the compact Johnson bound is a special case of the proposed LP bounds.
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