Compute-and-Forward in Large Relaying Systems: Limitations and Asymptotically Optimal Scheduling

Compute and Forward (CF) is a coding scheme which enables receivers to decode linear combinations of simultaneously transmitted messages while exploiting the properties lattice codes additive nature shared medium. The was originally designed for relay networks, yet, it found useful in other communication problems, such as MIMO communication. Works current literature assume fixed number transmitters system. However, following increase networks density, interesting investigate performance CF when large. In this work, we show that transmitters, L, grows, becomes degenerated, sense prefers only one (strongest) user instead any combination codewords, treating users noise. Moreover, system's sum-rate tends zero well. This makes scheduling necessary order maintain superior abilities provides. We thus examine problem CF. start with insights on why good opportunities can be found. Then, provide an asymptotically optimal, polynomial-time algorithm analyze its performance. conclude proper scheduling, not merely non-degenerated, but, fact, provides gain system sum-rate, up optimal scaling law O(loglogL).