On the Optimality of Superposition Coding for Symmetric MDCS with Linear Computations

The rise of artificial intelligence and the increasing computational requirements tend to facilitate the integration of computations and communication networks. Multilevel diversity coding systems (MDCS) are universal models abstracted from the scenarios of diversity coding with higher-priority sources decoded before lower ones. In this paper, the optimality of superposition coding in L-level symmetric MDCS with linear computations (SMDCS-LC) is investigated with linearly independent and dependent coefficient matrices, respectively. In such a system, decoders are only differentiated by the cardinality of the encoders, say α, they are connected to and can decode the linear combinations of the first α level sources. We prove that the superposition coding achieves the entire coding rate region of SMDCS-LC with linearly independent coefficient matrices, indicating optimality and no savings in transmission. However, this optimality does not hold for the linearly dependent cases, indicating that integrating computations in communication networks such as SMDCS indeed reduces the amount of information transmitted. Future work will focus on characterizing the explicit coding rate region of general SMDCS-LC.