Improved layered regenerating codes characterizing the exact-repair storage-repair bandwidth tradeoff for certain parameter sets

The characterization of the storage-repair bandwidth tradeoff of (n, k, d)-regenerating codes under the exact-repair setting remains an open problem. The problem has been solved only for the special case of (n, k, d) = (4, 3, 3). In the present paper, we characterize the tradeoff for the larger family of parameters (n, k = 3, d = n - 1). This is accomplished by constructing an (n, k <; d, d)-regenerating code, referred to as the improved layered code. In the case when (n, k = 3, d = n - 1), the code operates on a point that coincides with an interior point of a recently derived outer bound on the tradeoff. The code also achieves an interior point on the outer bound for the parameter set (n, k = 4, d = n - 1).