Capacity Region of the Symmetric Injective K-User Deterministic Interference Channel

We characterize the capacity region of the symmetric injective K-user Deterministic Interference Channel (DIC) for all channel parameters. The achievable rate region is derived by first projecting the achievable rate region of Han-Kobayashi (HK) scheme, which is in terms of common and private rates for each user, along the direction of aggregate rates for each user (i.e., the sum of common and private rates). We then show that the projected region is characterized by only the projection of those facets in the HK region for which the coefficient of common rate and private rate are the same for all users, hence simplifying the region. Furthermore, we derive a tight converse for each facet of the simplified achievable rate region.Comment: A shorter version of this paper to appear in International Symposium on Information Theory (ISIT) 201

COVID-19 Risk Estimation using a Time-varying SIR-model

Policy-makers require data-driven tools to assess the spread of COVID-19 and inform the public of their risk of infection on an ongoing basis. We propose a rigorous hybrid model-and-data-driven approach to risk scoring based on a time-varying SIR epidemic model that ultimately yields a simplified color-coded risk level for each community. The risk score $\Gamma_t$ that we propose is proportional to the probability of someone currently healthy getting infected in the next 24 hours. We show how this risk score can be estimated using another useful metric of infection spread, $R_t$, the time-varying average reproduction number which indicates the average number of individuals an infected person would infect in turn. The proposed approach also allows for quantification of uncertainty in the estimates of $R_t$ and $\Gamma_t$ in the form of confidence intervals. Code and data from our effort have been open-sourced and are being applied to assess and communicate the risk of infection in the City and County of Los Angeles