Scalable Network Coding for Heterogeneous Devices 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 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 based on a precoding matrix and then encodes the precoded packets over GF(2) before transmission to the network. After justifying the arithmetic compatibility over different finite fields in the encoding process, we derive a sufficient and necessary condition for decodability over different fields. Moreover, we theoretically study the construction of an optimal precoding matrix in terms of decodability. The numerical analysis in classical wireless broadcast networks illustrates that the proposed scalable RLNC not only guarantees a better decoding compatibility over different fields compared with classical RLNC over a single field, but also outperforms Fulcrum RLNC in terms of a better decoding performance over GF(2). Moreover, we take the sparsity of the received binary coding vector into consideration, and demonstrate that for a large enough batch size, this sparsity does not affect the completion delay performance much in a wireless broadcast network.