688 research outputs found

    An ALMA Spectroscopic Survey of the Brightest Submillimeter Galaxies in the SCUBA-2-COSMOS Field (AS2COSPEC): Physical Properties of z = 2–5 Ultra- and Hyperluminous Infrared Galaxies

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    We report the physical properties of the 18 brightest (S 870 μm = 12.4–19.2 mJy) and not strongly lensed 870 μm–selected dusty star-forming galaxies (DSFGs), also known as submillimeter galaxies (SMGs), in the COSMOS field. This sample is part of an ALMA band 3 spectroscopic survey (AS2COSPEC), and spectroscopic redshifts are measured in 17 of them at z = 2–5. We perform spectral energy distribution analyses and deduce a median total infrared luminosity of L IR = (1.3 ± 0.1) × 1013 L ⊙, infrared-based star formation rate (SFR) of SFRIR = 1390 ± 150 M ⊙ yr−1, stellar mass of M * = (1.4 ± 0.6) × 1011 M ⊙, dust mass of M dust = (3.7 ± 0.5) × 109 M ⊙, and molecular gas mass of M gas = (α CO/0.8)(1.2 ± 0.1) × 1011 M ⊙, suggesting that they are one of the most massive, ISM-enriched, and actively star-forming systems at z = 2–5. In addition, compared to less massive and less active galaxies at similar epochs, SMGs have comparable gas fractions; however, they have a much shorter depletion time, possibly caused by more active dynamical interactions. We determine a median dust emissivity index of β = 2.1 ± 0.1 for our sample, and by combining our results with those from other DSFG samples, we find no correlation of β with redshift or infrared luminosity, indicating similar dust grain compositions across cosmic time for infrared luminous galaxies. We also find that AS2COSPEC SMGs have one of the highest dust-to-stellar mass ratios, with a median of 0.02 ± 0.01, significantly higher than model predictions, possibly due to too-strong active galactic nucleus feedback implemented in the model. Finally, our complete and uniform survey enables us to put constraints on the most massive end of the dust and molecular gas mass functions

    Summary Statistic Privacy in Data Sharing

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    We study a setting where a data holder wishes to share data with a receiver, without revealing certain summary statistics of the data distribution (e.g., mean, standard deviation). It achieves this by passing the data through a randomization mechanism. We propose summary statistic privacy, a metric for quantifying the privacy risk of such a mechanism based on the worst-case probability of an adversary guessing the distributional secret within some threshold. Defining distortion as a worst-case Wasserstein-1 distance between the real and released data, we prove lower bounds on the tradeoff between privacy and distortion. We then propose a class of quantization mechanisms that can be adapted to different data distributions. We show that the quantization mechanism's privacy-distortion tradeoff matches our lower bounds under certain regimes, up to small constant factors. Finally, we demonstrate on real-world datasets that the proposed quantization mechanisms achieve better privacy-distortion tradeoffs than alternative privacy mechanisms

    Complementary Graph Entropy, AND Product, and Disjoint Union of Graphs

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    In the zero-error Slepian-Wolf source coding problem, the optimal rate is given by the complementary graph entropy H\overline{H} of the characteristic graph. It has no single-letter formula, except for perfect graphs, for the pentagon graph with uniform distribution G5G_5, and for their disjoint union. We consider two particular instances, where the characteristic graphs respectively write as an AND product \wedge, and as a disjoint union \sqcup. We derive a structural result that equates H()\overline{H}(\wedge \: \cdot) and H()\overline{H}(\sqcup \: \cdot) up to a multiplicative constant, which has two consequences. First, we prove that the cases where H()\overline{H}(\wedge \:\cdot) and H()\overline{H}(\sqcup \: \cdot) can be linearized coincide. Second, we determine H\overline{H} in cases where it was unknown: products of perfect graphs; and G5GG_5 \wedge G when GG is a perfect graph, using Tuncel et al.'s result for H(G5G)\overline{H}(G_5 \sqcup G). The graphs in these cases are not perfect in general

    Algorithmic and Coding-theoretic Methods for Group Testing and Private Information Retrieval

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    In the first part of this dissertation, we consider the Group Testing (GT) problem and its two variants, the Quantitative GT (QGT) problem and the Coin Weighing (CW) problem. An instance of the GT problem includes a ground set of items that includes a small subset of defective items. The GT procedure consists of a number of tests, such that each test indicates whether or not a given subset of items includes one or more defective items. The goal of the GT procedure is to identify the subset of defective items with the minimum number of tests. Motivated by practical scenarios where the outcome of the tests can be affected by noise, we focus on the noisy GT setting, in which the outcome of a test can be flipped with some probability. In the noisy GT setting, the goal is to identify the set of defective items with high probability. We investigate the performance of two variants of the Belief Propagation (BP) algorithm for decoding of noisy non-adaptive GT under the combinatorial model for defective items. Through extensive simulations, we show that the proposed algorithms achieve higher success probability and lower false-negative and false-positive rates when compared to the traditional BP algorithm. We also consider a variation of the probabilistic GT model in which the prior probability of each item to be defective is not uniform and in which there is a certain amount of side information on the distribution of the defective items available to the GT algorithm. This dissertation focuses on leveraging the side information for improving the performance of decoding algorithms for noisy GT. First, we propose a probabilistic model, referred to as an interaction model, that captures the side information about the probability distribution of the defective items. Next, we present a decoding scheme, based on BP, that leverages the interaction model to improve the decoding accuracy. Our results indicate that the proposed algorithm achieves higher success probability and lower false-negative and false-positive rates when compared to the traditional BP, especially in the high noise regime. In the QGT problem, the result of a test reveals the number of defective items in the tested group. This is in contrast to the standard GT where the result of each test is either 1 or 0 depending on whether the tested group contains any defective items or not. In this dissertation, we study the QGT problem for the combinatorial and probabilistic models of defective items. We propose non-adaptive QGT algorithms using sparse graph codes over bi-regular and irregular bipartite graphs, and binary t-error-correcting BCH codes. The proposed schemes provide exact recovery with a probabilistic guarantee, i.e. recover all the defective items with high probability. The proposed schemes outperform existing non-adaptive QGT schemes for the sub-linear regime in terms of the number of tests required to identify all defective items with high probability. The CW problem lies at the intersection of GT and compressed sensing problems. Given a collection of coins and the total weight of the coins, where the weight of each coin is an unknown integer, the problem is to determine the weight of each coin by weighing subsets of coins on a spring scale. The goal is to minimize the average number of weighings over all possible weight configurations. Toward this goal, we propose and analyze a simple and effective adaptive weighing strategy. This is the first non-trivial achievable upper bound on the minimum expected required number of weighings. In the second part of this dissertation, we focus on the private information retrieval problem. In many practical settings, the user needs to retrieve information messages from a server in a periodic manner, over multiple rounds of communication. The messages are retrieved one at a time and the identity of future requests is not known to the server. We study the private information retrieval protocols that ensure that the identities of all the messages retrieved from the server are protected. This scenario can occur in practical settings such as periodic content download from text and multimedia repositories. We refer to this problem of minimizing the rate of data download as online private information retrieval problem. Following the previous line of work by Kadhe et al., we assume that the user knows a subset of messages in the database as side information. The identities of these messages are initially unknown to the server. Focusing on scalar-linear settings, we characterize the per-round capacity, i.e., the maximum achievable download rate at each round. The key idea of our achievability scheme is to combine the data downloaded during the current round and the previous rounds with the original side information messages and use the resulting data as side information for the subsequent rounds

    Causal Sampling, Compressing, and Channel Coding of Streaming Data

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    With the emergence of the Internet of Things, communication systems, such as those employed in distributed control and tracking scenarios, are becoming increasingly dynamic, interactive, and delay-sensitive. The data in such real-time systems arrive at the encoder progressively in a streaming fashion. An intriguing question is: what codes can transmit streaming data with both high reliability and low latency? Classical non-causal (block) encoding schemes can transmit data reliably but under the assumption that the encoder knows the entire data block before the transmission. While this is a realistic assumption in delay-tolerant systems, it is ill-suited to real-time systems due to the delay introduced by collecting data into a block. This thesis studies causal encoding: the encoder transmits information based on the causally received data while the data is still streaming in and immediately incorporates the newly received data into a continuing transmission on the fly. This thesis investigates causal encoding of streaming data in three scenarios: causal sampling, causal lossy compressing, and causal joint source-channel coding (JSCC). In the causal sampling scenario, a sampler observes a continuous-time source process and causally decides when to transmit real-valued samples of it under a constraint on the average number of samples per second; an estimator uses the causally received samples to approximate the source process in real time. We propose a causal sampling policy that achieves the best tradeoff between the sampling frequency and the end-to-end real-time estimation distortion for a class of continuous Markov processes. In the causal lossy compressing scenario, the sampling frequency constraint in the causal sampling scenario is replaced by a rate constraint on the average number of bits per second. We propose a causal code that achieves the best causal distortion-rate tradeoff for the same class of processes. In the causal JSCC scenario, the noiseless channel and the continuous-time process in the previous scenarios are replaced by a discrete memoryless channel with feedback and a sequence of streaming symbols, respectively. We propose a causal joint sourcechannel code that achieves the maximum exponentially decaying rate of the error probability compatible with a given rate. Remarkably, the fundamental limits in the causal lossy compressing and the causal JSCC scenarios achieved by our causal codes are no worse than those achieved by the best non-causal codes. In addition to deriving the fundamental limits and presenting the causal codes that achieve the limits, we also show that our codes apply to control systems, are resilient to system deficiencies such as channel delay and noise, and have low complexities.</p

    A New Sieving-Style Information-Set Decoding Algorithm

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    The problem of decoding random codes is a fundamental problem for code-based cryptography, including recent code-based candidates in the NIST post-quantum standardization process. In this paper, we present a novel sieving-style information-set decoding (ISD) algorithm, addressing the task of solving the syndrome decoding problem. Our approach involves maintaining a list of weight-2p2p solution vectors to a partial syndrome decoding problem and then creating new vectors by identifying pairs of vectors that collide in pp positions. By gradually increasing the parity-check condition by one and repeating this process iteratively, we find the final solution(s). We show that our novel algorithm performs better than other ISDs in the memory-restricted scenario when applied to McEliece. Notably, in the case of problems with very low relative weight, it seems to significantly outperform all previous algorithms. In particular, for code-based candidates BIKE and HQC, the algorithm has lower bit complexity than the previous best results

    Estimating the Rate-Distortion Function by Wasserstein Gradient Descent

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    In the theory of lossy compression, the rate-distortion (R-D) function R(D)R(D) describes how much a data source can be compressed (in bit-rate) at any given level of fidelity (distortion). Obtaining R(D)R(D) for a given data source establishes the fundamental performance limit for all compression algorithms. We propose a new method to estimate R(D)R(D) from the perspective of optimal transport. Unlike the classic Blahut--Arimoto algorithm which fixes the support of the reproduction distribution in advance, our Wasserstein gradient descent algorithm learns the support of the optimal reproduction distribution by moving particles. We prove its local convergence and analyze the sample complexity of our R-D estimator based on a connection to entropic optimal transport. Experimentally, we obtain comparable or tighter bounds than state-of-the-art neural network methods on low-rate sources while requiring considerably less tuning and computation effort. We also highlight a connection to maximum-likelihood deconvolution and introduce a new class of sources that can be used as test cases with known solutions to the R-D problem.Comment: Accepted as conference paper at NeurIPS 202

    Transformer-aided Wireless Image Transmission with Channel Feedback

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    This paper presents a novel wireless image transmission paradigm that can exploit feedback from the receiver, called DeepJSCC-ViT-f. We consider a block feedback channel model, where the transmitter receives noiseless/noisy channel output feedback after each block. The proposed scheme employs a single encoder to facilitate transmission over multiple blocks, refining the receiver's estimation at each block. Specifically, the unified encoder of DeepJSCC-ViT-f can leverage the semantic information from the source image, and acquire channel state information and the decoder's current belief about the source image from the feedback signal to generate coded symbols at each block. Numerical experiments show that our DeepJSCC-ViT-f scheme achieves state-of-the-art transmission performance with robustness to noise in the feedback link. Additionally, DeepJSCC-ViT-f can adapt to the channel condition directly through feedback without the need for separate channel estimation. We further extend the scope of the DeepJSCC-ViT-f approach to include the broadcast channel, which enables the transmitter to generate broadcast codes in accordance with signal semantics and channel feedback from individual receivers

    Integrated Communication and Receiver Sensing with Security Constraints on Message and State

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    We study the state-dependent wiretap channel with non-causal channel state informations at the encoder in an integrated sensing and communications (ISAC) scenario. In this scenario, the transmitter communicates a message and a state sequence to a legitimate receiver while keeping the message and state-information secret from an external eavesdropper. This paper presents a new achievability result for this doubly-secret scenario, which recovers as special cases the best-known achievability results for the setups without security constraints or with only a security constraint on the message. The impact of the secrecy constraint (no secrecy-constraint, secrecy constraint only on the message, or on the message and the state) is analyzed at hand of a Gaussian-state and Gaussian-channel example

    Two Phases of Scaling Laws for Nearest Neighbor Classifiers

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    A scaling law refers to the observation that the test performance of a model improves as the number of training data increases. A fast scaling law implies that one can solve machine learning problems by simply boosting the data and the model sizes. Yet, in many cases, the benefit of adding more data can be negligible. In this work, we study the rate of scaling laws of nearest neighbor classifiers. We show that a scaling law can have two phases: in the first phase, the generalization error depends polynomially on the data dimension and decreases fast; whereas in the second phase, the error depends exponentially on the data dimension and decreases slowly. Our analysis highlights the complexity of the data distribution in determining the generalization error. When the data distributes benignly, our result suggests that nearest neighbor classifier can achieve a generalization error that depends polynomially, instead of exponentially, on the data dimension
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