An outer bound on the storage-bandwidth tradeoff of exact-repair regenerating codes and its asymptotic optimality in high rates

The storage-bandwidth tradeoff of linear and exact-repair regenerating codes is considered. An outer bound on the storage-bandwidth tradeoff is proposed for arbitrary (n, k, d) case. n, k, and d denote typical code parameters of regenerating codes. The proposed outer bound becomes tighter than other existing outer bounds as k gets closer to n. In addition, for the case of d = n − 1, it is shown that the proposed outer bound asymptotically meets the inner bound proposed by Tian et al., which implies the proposed bound converges to the optimal storage-bandwidth tradeoff of exact-repair linear regenerating codes in high rates (k/n ≅ 1).