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

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    9 Scopus citations

    Abstract

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

    Original languageEnglish
    Article number9467308
    Pages (from-to)6243-6265
    Number of pages23
    JournalIEEE Transactions on Information Theory
    Volume67
    Issue number9
    DOIs
    StatePublished - 1 Sep 2021

    Keywords

    • Relay networks
    • compute and forward
    • lattice codes
    • user-scheduling

    ASJC Scopus subject areas

    • Information Systems
    • Computer Science Applications
    • Library and Information Sciences

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