On Separation Vectors of Static Linear Network Codes with UEP Capability

Separation vectors have long been used to specify unequal error/erasure capability (UEP) of channel codes. In this paper, we tried to extend its definition to cover linear network codes and study its relations with the UEP capability of static linear network codes. Our approach begins with a division of the network coding process into two distinct steps: a codeword dispatch at the source and a message transfer through the network. We can then demonstrate the truthfulness of following two assertions: (1) an optimal UEP dispatch matrix can be found to disseminate the message symbols properly in a multicasting session, and (2) given a sufficiently large base field, the UEP transfer capability of a static linear network code can be determined by nullifying specific local encoding coefficients at selected network nodes. The finding of a UEP static network code can thus be reduced to a graph problem. As the first attempt, we used our technique to induce UEP capability among randomized static broadcasting network codes.