Abstract

The generalized degrees of freedom (GDoF) characterization of the symmetric K-user interference channel is obtained under finite precision channel state information at the transmitters (CSIT). The symmetric setting is where each cross channel is capable of carrying α degrees of freedom (DoF) while each direct channel is capable of carrying 1 DoF. Remarkably, under finite precision CSIT the symmetric K-user interference channel loses all the GDoF benefits of interference alignment. The GDoF per user diminish with the number of users everywhere except in the very strong (optimal for every receiver to decode all messages) and very weak (optimal to treat all interference as noise) interference regimes. The result stands in sharp contrast to prior work on the symmetric setting under perfect CSIT, where the GDoF per user remain undiminished due to interference alignment. The result also stands in contrast to prior work on a subclass of asymmetric settings under finite precision CSIT, i.e., the topological interference management problem, where interference alignment plays a crucial role and provides substantial GDoF benefits.

Highlights

  • The capacity of the K user wireless interference channel is one of the holy grails of network information theory

  • For the K user interference channel, the generalized degrees of freedom (GDoF) under finite precision channel state information at the transmitters (CSIT) are available implicitly for two regimes of interest, based on separate works focusing on interference that is weak enough to be optimally treated as white noise [28] and on interference that is strong enough to be comparable to the desired signal [29, 30]

  • We characterized the GDoF of the K-user symmetric interference channel under finite precision CSIT

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Summary

Introduction

The capacity of the K user wireless interference channel is one of the holy grails of network information theory. For the K user interference channel, the GDoF under finite precision CSIT are available implicitly for two regimes of interest, based on separate works focusing on interference that is weak enough to be optimally treated as white noise [28] and on interference that is strong enough to be comparable to the desired signal [29, 30]. Standing in contrast with the 2 user X channel setting where all GDoF benefits of interference alignment are lost under finite precision CSIT [22], the re-emergence of interference alignment as a critical ingredient for TIM with K users [29] underscores how new aspects of the problem are revealed only as the number of users increases In particular it motivates further study of the K user setting. For sets A, B, the notation A/B refers to the set of elements that are in A but not in B

GDoF of Symmetric K User Interference Channel
Finite Precision CSIT
Outer Bound
Key Lemmas
Proof of each of the 5 cases of Theorem 1
Achievability
Conclusion
Real Setting
Complex Setting
Findings
Real and Complex Setting
Full Text
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