Scalable Network Coding over Embedded Fields

In complex network environments, there always exist heterogeneous devices with different computational powers. In this work, we propose a novel scalable random linear network coding (RLNC) framework based on a chain of embedded fields, so as to endow heterogeneous receivers with different decoding capabilities. In this framework, the source linearly combines the original packets over embedded fields in an encoding matrix and then combines the coded packets over GF(2) before transmission to the network. Based on the arithmetic compatibility over embedded fields in the encoding process, we derive a sufficient and necessary condition for decodability over these fields of different sizes. Moreover, we theoretically study the construction of an optimal encoding matrix in terms of decodability. The numerical analysis in classical wireless broadcast networks illustrates that the proposed scalable RLNC not only provides a nice decoding compatibility over different fields, but also performs better than classical RLNC in terms of decoding complexity.