are almost always considered under the exact-repair scenario. However, in this work, for RCs with DHS, we consider functional-repair as the mode of repair as we aim at understanding the absolute benefits/limits of helper selection in RCs. Albeit our setting is under functional-repair, in Part II, we are able to present an explicit construction of exact-repair codes that achieve the optimal or weakly optimal MBR point of the functional-repair.

Table \[tab:comparison\] also compares the three scenarios in terms of the helper selection mechanisms. The original RCs are codes that do not perform helper selection at all, i.e., BHS, while LRCs are codes that can perform SHS only. In this work, we consider the most general setting in which codes are allowed to have DHS.

Moreover, as shown in Table \[tab:comparison\], the $(n,k,d)$ range of operation of each of the three code settings is different. The original RCs were designed for storage networks with large $d$ values, whereas LRCs are designed for small $d$ values. In contrast, this work allows for arbitrary $(n,k,d)$ values and studies the benefits of helper selection under different $(n,k,d)$ values.

The comparison above illustrates the main differences in the setup and contributions between the three scenarios. 