Research

Research Summary

My research interests fall into the broad area of network information theory, machine learning, statistical signal processing and their applications. My previous research topics include the following:

Treating Interference as Noise and Power Control

Treating interference as noise (TIN) is the simplest interference management scheme for wireless networks. It is attractive and widely adopted in practice (accompanied with other more sophisticated interference management schemes, e.g., frequency reuse, scheduling, zero-forcing, interference alignment, multihop relaying, etc.) due to its simplicity and robustness to channel uncertainty. We identify a broad TIN-optimal regime from the generalized degrees-of-freedom (GDoF) perspective [J1.1]. In the same regime, TIN is also optimal for the entire channel capacity region up to a constant gap, which is independent of SNR and channel realizations and only relates to the number of users in the network. In words, the TIN-optimality condition can be stated as

“for each user the desired signal strength is no less than the sum of the strengths of the strongest interference caused by this user and the strongest interference suffered by this user (all values in dB scale)”.

The optimality of TIN is also extended to X networks [J1.2], compound networks (i.e., multiple-groupcast networks) [J1.3], and MIMO networks [C1.1]. The GDoF-based power control problem is studied in [J1.3] and [J1.4].

• [J1.1] C. Geng, N. Naderializadeh, S. Avestimehr, and S. Jafar, "On the optimality of treating interference as noise," IEEE Transactions on Information Theory, vol. 61, no.4, pp. 1753-1767, Apr. 2015.

• [J1.2] C. Geng, H. Sun, and S. Jafar, "On the optimality of treating interference as noise: General message sets," IEEE Transactions on Information Theory, vol. 61, no. 7, pp. 3722-3736, Jul. 2015.

• [J1.3] C. Geng and S. Jafar, "On the optimality of treating interference as noise: Compound interference networks," IEEE Transactions on Information Theory, vol. 62, no. 8, pp. 4630-4653, Aug. 2016.

• [J1.4] C. Geng and S. Jafar, "Power control by GDoF duality of treating interference as noise," IEEE Communications Letters, vol. 22, no. 2, pp. 244-247, Feb. 2018.

• [C1.1] C. Geng and S. Jafar, "On the optimality of zero-forcing and treating interference as noise for K-user MIMO interference channels," IEEE ISIT, Barcelona, Spain, Jul. 2016.

Generalized Degrees-of-freedom (GDoF) of Arbitrary Wireless Networks

Understanding the capacity of wireless networks is the holy grail of network information theory. Recent research mainly focuses on the DoF characterization and attains remarkable progress. However, the coarse DoF metric has its Achilles’ heel: it essentially treats all non-zero channels as equally strong in the high SNR limit and ignores the distinction between strong and weak channels in practice. The GDoF perspective is precisely the generalization of DoF, which allows to study the settings with disparate signal strengths, and usually leads to constant gap results at finite SNRs.

Characterizing GDoF for general wireless networks is challenging. To address this problem, based on the recent progress in Topological Interference Management (TIM) and Treating Interference as Noise (TIN), in [R2.1] we formulate a TIM-TIN framework and propose two baseline approaches (i.e., an analytical decomposition approach and a distributed numerical approach) to jointly optimize signal vector space and signal power level allocations. The information-theoretic optimality of these approaches in some non-trivial settings is also investigated.

• [R2.1] C. Geng, H. Sun, and S. Jafar, "Multilevel topological interference management: A TIM-TIN perspective," e-print Arxiv:2102.04355 (a short version was presented in IEEE ITW 2013).

Wireless Information Theoretic Security

The security issue in wireless networks becomes increasingly important. Different from traditional cryptographic encryption, the basic idea of information theoretic security is to exploit the randomness in physical layer for security purpose. Some canonical networks are investigated [C3.1][J3.1]. One example is the two user symmetric deterministic interference channels [C3.1]. The derived inner and outer bounds are shown in the following.

We also consider the secure capacity of TIN-optimal networks identified in [J1.1]. Surprisingly, under the TIN-optimality condition, the secrecy constraints do not incur any penalty from the GDoF perspective, and a simple scheme based on Gaussian signaling, cooperative jamming and smart power splitting is shown to achieve the entire secure capacity region within a constant gap [J3.1]. This scheme is further proved to be optimal in a wide class of network settings under finite-precision CSIT [R3.1].

• [C3.1] C. Geng, R. Tandon, and S. Jafar, "On the symmetric 2-user deterministic interference channel with confidential messages," IEEE Globecom 2015, San Diego, CA, Dec. 2015.

• [J3.1] J. Chen and C. Geng, "Optimal secure GDoF of symmetric Gaussian wiretap channel with a helper," IEEE Transactions on Information Theory, vol. 67, no.4, pp. 2334-2352, Arp. 2021.

• [J3.2] C. Geng and S. Jafar, "Secure GDoF of K-user Gaussian interference channels: When secrecy incurs no penalty," IEEE Communications Letters, vol. 19, no. 8, pp. 1287-1290, Aug. 2015.

• [R3.1] Y. Chan, C. Geng, and S. Jafar "Robust optimality of TIN under secrecy constraints", e-print UC-escholarship.