Shortened regenerating codes

Abstract

For general exact repair regenerating codes, the optimal trade-offs between storage size and repair bandwith remain undetermined. Various outer bounds and partial results have been proposed. Using a simple chain rule argument we identify nonnegative differences between the functional repair and the exact repair outer bounds. One of the differences is then bounded from below by the repair data of a shortened subcode. Our main result is a new outer bound for an exact repair regenerating code in terms of its shortened subcodes. In general the new outer bound is implicit and depends on the choice of shortened subcodes. For the linear case we obtain explicit bounds.