Diversity-Multiplexing Tradeoffs in MIMO Relay Channels

A multi-hop relay channel with multiple antenna terminals in a quasi-static slow fading environment is considered. For both full-duplex and half-duplex relays the fundamental diversity-multiplexing tradeoff (DMT) is analyzed. It is shown that, while decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, the dynamic decode-and-forward (DDF) protocol is needed to achieve the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static protocols are considered as well, and the corresponding achievable DMT performance is characterized.Comment: To appear at IEEE Global Communications Conf. (Globecom), New Orleans, LA, Nov. 200

Minimum Sparsity of Unobservable Power Network Attacks

Physical security of power networks under power injection attacks that alter generation and loads is studied. The system operator employs Phasor Measurement Units (PMUs) for detecting such attacks, while attackers devise attacks that are unobservable by such PMU networks. It is shown that, given the PMU locations, the solution to finding the sparsest unobservable attacks has a simple form with probability one, namely, $\kappa(G^M) + 1$, where $\kappa(G^M)$ is defined as the vulnerable vertex connectivity of an augmented graph. The constructive proof allows one to find the entire set of the sparsest unobservable attacks in polynomial time. Furthermore, a notion of the potential impact of unobservable attacks is introduced. With optimized PMU deployment, the sparsest unobservable attacks and their potential impact as functions of the number of PMUs are evaluated numerically for the IEEE 30, 57, 118 and 300-bus systems and the Polish 2383, 2737 and 3012-bus systems. It is observed that, as more PMUs are added, the maximum potential impact among all the sparsest unobservable attacks drops quickly until it reaches the minimum sparsity.Comment: submitted to IEEE Transactions on Automatic Contro

Distortion Exponent in MIMO Channels with Feedback

The transmission of a Gaussian source over a block-fading multiple antenna channel in the presence of a feedback link is considered. The feedback link is assumed to be an error and delay free link of capacity 1 bit per channel use. Under the short-term power constraint, the optimal exponential behavior of the end-to-end average distortion is characterized for all source-channel bandwidth ratios. It is shown that the optimal transmission strategy is successive refinement source coding followed by progressive transmission over the channel, in which the channel block is allocated dynamically among the layers based on the channel state using the feedback link as an instantaneous automatic repeat request (ARQ) signal.Comment: Presented at the IEEE Information Theory Workshop (ITW), Taormina, Italy, Oct. 200

English Language Learners’ Perceptions Regarding Media as Learning Technology

With the education field of English language teaching constantly evolving and the COVID-19 pandemic temporarily leading to more classes becoming on an online format, I wanted to see what English Language Learners (ELL) preferred when it came to learning English as an additional language in today’s day and age. The Research Questions in this study consist of: 1. Do students prefer textbooks and hands-on activities over assignments done online? 2. Do students have a preference for particular forms of instructional media? This paper analyzes the media preferences of English Language Learners. Using a Likert Scale, participants select from four answers, Strongly Disagree, Disagree, Agree and Strongly Agree. The statements cover a variety of instructional media styles, from low-tech media of handwriting all the way to social media. The research conducted in this study found that tactile learning and social media was the most preferred type of instructional media for learning English. With these results, I hope that teachers can incorporate more tactile learning strategies, activities, and tools that students use every day in their daily life. Lastly, it is important that teachers see what their students prefer and try to make changes to support their English language learning journey

The red-yolked egg of the touraco, Tauraco corythaix

The touracos are of biochemical interest because of the striking red and green colors imparted to their plumage by the copper porphyrins turacin and turacoverdin…

Sosa, Customary International Law, and the Continuing Relevance of Erie

Ten years ago, the conventional wisdom among international law academics was that customary international law (CIL) had the status of self-executing federal common law to be applied by courts without any need for political branch authorization. This modern position came under attack by so-called revisionist critics who argued that CIL had the status of federal common law only in the relatively rare situations in which the Constitution or political branches authorized courts to treat it as such. Modern position proponents are now claiming that the Supreme Court\u27s 2004 decision in Sosa v. Alvarez-Machain confirms that CIL has the status of self-executing federal common law. As this Article explains, the decision in Sosa did not in fact embrace the modern position, and, indeed, is best read as rejecting it. Commentators who construe Sosa as embracing the modern position have confounded the automatic incorporation of CIL as domestic federal law in the absence of political branch authorization (i.e., the modern position) with the entirely different issue of whether and to what extent a particular statute, the Alien Tort Statute ( ATS ), authorizes courts to apply CIL as domestic federal law. The Article also explains how CIL continues to be relevant to domestic federal common law despite Sosa\u27s rejection of the modern position. The fundamental flaw of the modern position is that it ignores the justifications for, and limitations on, post-Erie federal common law. As the Article shows, however, there are a number of contexts in addition to the ATS in which it is appropriate for courts to develop federal common law by reference to CIL, including certain jurisdictional contexts not amenable to state regulation (namely admiralty and interstate disputes), and gap-filling and interpretation of foreign affairs statutes and treaties. The Article concludes by considering several areas of likely debate during the next decade concerning the domestic status of CIL: corporate aiding and abetting liability under the ATS; application of CIL to the war on terrorism; and the use of foreign and international materials in constitutional interpretation

Joint Source-Channel Cooperative Transmission over Relay-Broadcast Networks

Reliable transmission of a discrete memoryless source over a multiple-relay relay-broadcast network is considered. Motivated by sensor network applications, it is assumed that the relays and the destinations all have access to side information correlated with the underlying source signal. Joint source-channel cooperative transmission is studied in which the relays help the transmission of the source signal to the destinations by using both their overheard signals, as in the classical channel cooperation scenario, as well as the available correlated side information. Decode-and-forward (DF) based cooperative transmission is considered in a network of multiple relay terminals and two different achievability schemes are proposed: i) a regular encoding and sliding-window decoding scheme without explicit source binning at the encoder, and ii) a semi-regular encoding and backward decoding scheme with binning based on the side information statistics. It is shown that both of these schemes lead to the same source-channel code rate, which is shown to be the "source-channel capacity" in the case of i) a physically degraded relay network in which the side information signals are also degraded in the same order as the channel; and ii) a relay-broadcast network in which all the terminals want to reconstruct the source reliably, while at most one of them can act as a relay.Comment: Submitted to IEEE Transactions on Information Theory, 201