MathDB5 problems
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Capacity-region equality for erasure-prone quantum and classical storage
Capacity-region equality conjecture. The capacity regions are identical in all cases, including the remaining open regime:
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The triangle-free storage-code rate conjecture
Triangle-free storage-code rate conjecture. For triangle-free graphs, is the largest attainable rate value.
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Inner-bound optimality conjecture for Case 3 storage capacity
Inner-bound optimality conjecture. In the remaining open regime, the inner bound is tight, so that
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The logarithmic systematic-node conjecture for optimal-bandwidth MDS codes
Logarithmic systematic-node conjecture. The lower bound is more accurate; in fact,
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Trade-offs between recovery I/O and storage efficiency
In a storage code, recovery I/O measures the amount of data read during node repair, while storage efficiency measures how efficiently the stored data represents the file. Trade-of…