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Multirate multicasting is a generalization of single-rate multicasting to prevent destinations with good connections from being limited by the capacity of bottleneck connections. While multirate multicasting has been traditionally performed over fixed trees, advances in network coding theory have enabled higher throughput and have helped us move beyond the restriction of tree structures for routing the multicast data. In this paper, we address the questions of optimal rate allocation and low-complexity network coding solutions to the problem of multirate multicasting in general multihop networks. Our work considers intralayer network coding capabilities, where the session is conceptually divided into layers optimally and coding is performed across packets belonging to the same layer. Our approach differs from earlier works in this domain in its separation of the problem into rate allocation and content distribution items, which allows a number of optimization and graphical techniques in their solution. Noting the complexities involved in the optimal rate allocation and content distribution solutions, we then propose and investigate two novel approaches for reducing the complexity of the original scheme for more practical implementation based on a layered multicasting mechanism and nested optimization approach. We demonstrate the implementation advantages of these low-complexity schemes via extensive numerical studies.