Wiretap networks II with partial information leakage

We investigate wiretap networks II with Ozarow-Wyner's coset coding scheme and consider a more powerful wiretapper who can tap some of the channels, and know part of the source messages in advance. A full characterization of the security performance of the linear network code for the network is given. With respect to a set of full-rank linear network code, the relative network generalized Hamming weight (RNGHW) for a nested code, which is a code pair of a linear code and one of its subcodes, is defined. It is proved that the RNGHW of a nested code can completely characterize the security performance of the linear network code for the network. An upper bound on RNGHW is given and the tightness of the upper bound is proved as well.