TY - JOUR
T1 - Compute-and-Forward in Large Relaying Systems
T2 - Limitations and Asymptotically Optimal Scheduling
AU - Shmuel, Ori
AU - Cohen, Asaf
AU - Gurewitz, Omer
N1 - Funding Information:
Manuscript received May 10, 2020; revised March 5, 2021; accepted June 15, 2021. Date of publication June 29, 2021; date of current version August 25, 2021. This work was supported in part by the European Union’s Horizon 2020 Research and Innovation Program through Superfluidity Project under Agreement 671566 and in part by MAFAT. This article was presented in part at the 2017 IEEE Information Theory Workshop (ITW) and in part at the 2018 IEEE Information Theory Workshop (ITW).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/9/1
Y1 - 2021/9/1
N2 - 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}}).
AB - 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}}).
KW - Relay networks
KW - compute and forward
KW - lattice codes
KW - user-scheduling
UR - http://www.scopus.com/inward/record.url?scp=85112208075&partnerID=8YFLogxK
U2 - 10.1109/TIT.2021.3093454
DO - 10.1109/TIT.2021.3093454
M3 - Article
SN - 0018-9448
VL - 67
SP - 6243
EP - 6265
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 9
M1 - 9467308
ER -