An Explicit, Coupled-Layer Construction of a High-Rate MSR Code with Low Sub-Packetization Level, Small Field Size and d < (n-1)

This paper presents an explicit construction for an ((n = 2qt, k = 2q(t-1), d = n - (q + 1)), (alpha = q(2q)(t-1), beta = alpha/q)) regenerating code over a field F-Q operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate k/n as close to 1 as desired, sub-packetization level alpha <= r(n/r) for r = (n - k), field size Q no larger than n and where all code symbols can be repaired with the same minimum data download. This is the first-known construction of such an MSR code for d < (n - 1).