corresponding index codes and vice versa. However, the equivalence between two problems for a given index coding instance was not presented in [@EQU]. In [@FEQU], they showed an equivalence between network computation and functional index coding for a given network coding instance and also suggested their relation for a given index coding instance with the corresponding models for both a network coding instance and an index coding instance, called the equivalent index coding instance and network coding instance, respectively. However, their models of the corresponding instances are defined in a different manner, that is, if a given network coding instance is converted to the corresponding index coding instance and converted back to the network coding instance again, the re-converted network coding instance differs from the originally given network coding instance. Similarly, the same problem occurs to a given index coding instance. Thus, we propose a method to solve these problems in this paper.

In this paper, we show new equivalences between an NCLE and an ICSIE for both a given network coding instance and a given index coding instance. For a given network coding instance, the corresponding index coding instance is derived in a manner similar to that in an 