High-Rate MSR Code With Polynomial Sub-Packetization Level

We present a high-rate (n, k, d = n - 1)-MSR code with a sub-packetization level that is polynomial in the dimension k of the code. While polynomial sub-packetization level was achieved earlier for vector MDS codes that repair systematic nodes optimally, no such MSR code construction is known. In the low-rate regime (i. e., rates less than one-half), MSR code constructions with a linear sub-packetization level are available. But in the high-rate regime (i. e., rates greater than one-half), the known MSR code constructions required a sub-packetization level that is exponential in k. In the present paper, we construct an MSR code for d = n - 1 with a fixed rate R = t-1/t, t >= 2, achieveing a sub-packetization level alpha = O(k(t)). The code allows help-by-transfer repair, i. e., no computations are needed at the helper nodes during repair of a failed node.