On Linear Operator Channels over Finite Fields

Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size. Specifically, the optimality of subspace coding over LOCs is investigated. A lower bound on the maximum achievable rate of subspace coding is obtained and it is shown to be tight for some cases. The maximum achievable rate of constant-dimensional subspace coding is characterized and the loss of rate incurred by using constant-dimensional subspace coding is insignificant. The maximum achievable rate of channel training is close to the lower bound on the maximum achievable rate of subspace coding. Two coding approaches based on channel training are proposed and their performances are evaluated. Our first approach makes use of rank-metric codes and its optimality depends on the existence of maximum rank distance codes. Our second approach applies linear coding and it can achieve the maximum achievable rate of channel training. Our code designs require only the knowledge of the expectation of the rank of the transformation matrix. The second scheme can also be realized ratelessly without a priori knowledge of the channel statistics.Comment: 53 pages, 3 figures, submitted to IEEE Transaction on Information Theor

Chinaman and the Constitution: The Development of Federal Power over Immigration in 19th- Century United States

About the author: Raymond Yang is currently a fourth-year political science and economics student at University of California, Merced. His research interest focuses on 19th century American and East Asian legal history. He plans to attend law school after graduation

e-EVN detection of AGN activity in NGC 2617

NGC 2617 is a Seyfert 1.8 spiral galaxy at z=0.0142 (~60 Mpc, 1 mas = 0.3 pc) that is currently in outburst. We carried out European VLBI Network real-time e-VLBI observations at 1.6 GHz on 2013 June 7

Bridging Separate Worlds— Application of Human Rights Law in Investment Treaty Arbitration

With the proliferation of investor-state treaty arbitration, international investment law has been increasingly caught in a “legitimacy” crisis, with concerns looming large over resultant disruptive effects on human rights. Amid existing scholarship seeking to recalibrate the balance between investment protection and public interests, what is relatively undertheorized is a public international law dimension. In this regard, this Article explores the role of human rights law in integrating human rights considerations into investment tribunals’ decision-making, bridging the normative divide between international investment law and human rights. It makes three contributions. First, it systemizes the normative tensions and potential conflicts between international investment law and human rights, analyzing the primary manifestations and root causes thereof. Second, from the position of a respondent state, this Article typologizes the application of human rights law to investor-state treaty disputes, providing legal grounds to alleviate the potential conflicts between investment protection and human rights. In so doing, it also provides a clearer clarification of the relationship between international investment law and human rights law. Third, this Article evaluates the relative strengths and weaknesses of these human rights arguments, shedding light on how international investment agreements could be reformed to better balance investment protection with noneconomic issues

Analysis and Design of Multiple-Antenna Cognitive Radios with Multiple Primary User Signals

We consider multiple-antenna signal detection of primary user transmission signals by a secondary user receiver in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary user. We first derive exact expressions for the moments of the generalized likelihood ratio test (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate. Further, using results from large random matrix theory, we derive expressions to compute the detection probability without explicit knowledge of the channel, and then particularize these expressions for two scenarios of practical interest: 1) a single primary user sending spatially multiplexed signals, and 2) multiple spatially distributed primary users. Our analytical results are finally used to obtain simple design rules for the signal detection threshold.Comment: Revised version (14 pages). Change in titl

Batched Sparse Codes

Network coding can significantly improve the transmission rate of communication networks with packet loss compared with routing. However, using network coding usually incurs high computational and storage costs in the network devices and terminals. For example, some network coding schemes require the computational and/or storage capacities of an intermediate network node to increase linearly with the number of packets for transmission, making such schemes difficult to be implemented in a router-like device that has only constant computational and storage capacities. In this paper, we introduce BATched Sparse code (BATS code), which enables a digital fountain approach to resolve the above issue. BATS code is a coding scheme that consists of an outer code and an inner code. The outer code is a matrix generation of a fountain code. It works with the inner code that comprises random linear coding at the intermediate network nodes. BATS codes preserve such desirable properties of fountain codes as ratelessness and low encoding/decoding complexity. The computational and storage capacities of the intermediate network nodes required for applying BATS codes are independent of the number of packets for transmission. Almost capacity-achieving BATS code schemes are devised for unicast networks, two-way relay networks, tree networks, a class of three-layer networks, and the butterfly network. For general networks, under different optimization criteria, guaranteed decoding rates for the receiving nodes can be obtained.Comment: 51 pages, 12 figures, submitted to IEEE Transactions on Information Theor