Significant progress has been made recently in Generalized Degrees of Freedom (GDoF) characterizations of wireless interference channels (IC) and broadcast channels (BC) under the assumption of finite precision channel state information at the transmitters (CSIT), especially for smaller or highly symmetric network settings. A critical barrier in extending these results to larger and asymmetric networks is the inherent combinatorial complexity of such networks. Motivated by other fields such as extremal combinatorics and extremal graph theory, we explore the possibility of an extremal network theory, i.e., a study of extremal networks within particular regimes of interest. As our test application, we study the GDoF benefits of transmitter cooperation in a K user IC over the simple scheme of power control and treating interference as Gaussian noise (TIN) for three regimes of interest -a TIN regime identified by Geng et al. where TIN was shown to be GDoF optimal for the K user interference channel, a CTIN regime identified by Yi and Caire where the GDoF region achievable by TIN is convex without time-sharing, and an SLS regime identified by Davoodi and Jafar where a simple layered superposition (SLS) scheme is shown to be optimal in the K user MISO BC, albeit only for K ≤ 3. The SLS regime includes the CTIN regime, and the CTIN regime includes the TIN regime. As our first result, we show that under finite precision CSIT, TIN is GDoF optimal for the K user IC throughout the CTIN regime. Furthermore, under finite precision CSIT, appealing to extremal network theory we obtain the following results. In the TIN regime as well as the CTIN regime, we show that the extremal GDoF gain from transmitter cooperation over TIN is bounded regardless of the number of users. In fact, the gain is exactly a factor of 3/2 in the TIN regime, and 2 − 1/K in the CTIN regime, for arbitrary number of users K > 1. However, in the SLS regime, the gain is Θ(log 2 (K)), i.e., it scales logarithmically with the number of users.Finding the capacity limits of wireless networks is one of the grand challenges of network information theory. While exact capacity characterizations remain elusive, much progress has been made on this problem within the past decade through Degrees of Freedom (DoF) [1] and Generalized Degrees of Freedom (GDoF) [2] studies. This includes both new achievable schemes, including those inspired by the idea of interference alignment (IA) [3][4][5][6], and new outer bounds, such as those based on the aligned images (AI) approach [7]. With these advances as stepping stones, a worthy goal at this stage is to bring the theory closer to practice by adapting the models and metrics to increasingly incorporate practical concerns. As a step in this direction, this work is motivated by three practical concerns -robustness, simplicity, and scalability.By robustness we refer specifically to the channel state information at the transmitters (CSIT). GDoF characterizations under perfect CSIT provide important theoretical benchmarks, but often ...

BackgroundAllergic rhinitis (AR) is a common allergic disease. It affects people worldwide and traditional Chinese medicine is becoming popular among AR patients because it has a definite clinical effect and there are few adverse reactions. Lung qi deficiency and cold syndrome (LQDCS) is a frequent type of AR, and the Chinese herbal medicine bimin decoction (BMD) is prescribed for it. This study compared the clinical efficacy of BMD for AR patients with LQDCS to the conventional medicine loratadine and fluticasone nasal spray.MethodsThe study was an open-label non-inferiority randomized controlled trial. A total of 108 AR patients with LQDCS aged 19 to 60 were randomly allocated in a 1:1 ratio to the BMD group or the control group by the central computer system in Beijing Hospital of Traditional Chinese Medicine from January 2017 to April 2018. In total, 98 participants completed the study (BMD group n = 51 and control group n = 47). Patients in the BMD group received BMD while those in the control group received fluticasone nasal spray and loratadine tablets for 4 weeks. The primary outcome was the change in the Total Nasal Symptom Score (TNSS) between the baseline and the end of treatment. Changes in the Rhinoconjunctivitis Quality of Life Questionnaire (RQLQ), nasal resistance, and acoustic rhinometry parameters were secondary outcomes. All side effects due to the treatments were recorded.ResultsAfter the 4-week treatment, the total TNSS was significantly reduced in both groups compared to the baseline (P <  0.05). No significant between-groups differences were observed for changes in TNSS scores [− 0.298 (95% confidence interval −0.640 to 0.140)], which was within the defined non-inferiority margin. RQLQ in both groups decreased significantly (P <  0.001) from baseline, though a more obvious reduction was observed for the BMD group (P <  0.001). There were no significant differences in nasal resistance, nasal volume, or nasal minimum cross-sectional area between groups after treatment (P > 0.05).ConclusionsThese findings indicate that BMD helps relieve the symptoms of perennial AR and improves rhinitis-related quality of life. Our study indicates that BMD is non-inferior to loratadine tablets and fluticasone nasal spray for AR patients with LQDCS.Trial registrationChinese Clinical Trial Registry, ChiCTR-INR-16010063. Registered on 2 December 2016.

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