There are two common network models for network coded traffic: one is the fractional rate model (the primary model for non-coded communication) and the other is the integer rate model used for detailed coding analysis on packet-by-packet behaviors. The existing approach of finding minimum-cost multicast network codes is based on the fractional rate model and solves the corresponding linear-programming (LP) problem. The LP-based network optimization generally converges slowly due to the small step size and does not take care of the packet-by-packet coding behavior of network coding. This paper develops a minimum-cost multicast scheme based on the integer rate model. The new scheme exploits a new concept of coded feedback, takes full advantages of the forward network-coded traffic, and possesses many practical advantages for efficient implementation. The complexity and performance of the coded-feedback scheme are studied both analytically and through simulations.
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