On the Non-Existence of Minimum Storage Regenerating Codes With Repair-by-Transfer Property

Regenerating codes are the family of distributed storage codes that achieve the optimal trade-off between storage overhead and the bandwidth consumption for the repair of a single node failure. Recent research reveals that, with certain regenerating codes, the amount of disk read for the repair can be reduced to as much as the repair bandwidth (i.e., the amount of data to be transferred), which makes encoding at the helper nodes unnecessary. In literature, such a property is often referred to as the repair-by-transfer property. Searching for regenerating codes with the repair-by-transfer property has been of great interest. In this manuscript, we prove that there does not exist a minimum storage regenerating (MSR) code with the repair-by-transfer property for the case of k ≥ 3, β <; d - k + 1, where k is the number of storage nodes required to reconstruct the original file, d is the number of helper nodes, and β is the number of symbols transmitted from each helper node.