Linear Network Coding for Erasure Broadcast Channel With Feedback: Complexity and Algorithms.

This paper investigates the linear network coding problem for erasure broadcast channel with user feedback. An innovative linear network code is shown to be uniformly optimal for the system. In general, determining the existence of innovative packets is proved to be NP-complete. When the finite field size is larger than the number of users, innovative packets always exist and the problem of finding an innovative encoding vector with smallest Hamming weight is considered. The corresponding decision problem is shown to be NP-complete. Optimal and approximate network coding algorithms for maximizing the sparsity of encoding vectors are designed. [ABSTRACT FROM AUTHOR]