{"title":"Information Capacity of BSC and BEC Permutation Channels","authors":"A. Makur","doi":"10.1109/ALLERTON.2018.8636070","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636070","url":null,"abstract":"In this paper, we describe and study the permutation channel model, which constitutes a discrete memoryless channel (DMC) followed by a random permutation block that reorders the output codeword of the DMC. This model naturally emerges in the context of communication networks, and coding theoretic aspects of such channels have been widely studied. In contrast to the bulk of this literature, we analyze the information theoretic aspects of the model by defining an appropriate notion of permutation channel capacity. We consider two special cases of the permutation channel model: the binary symmetric channel (BSC) and the binary erasure channel (BEC). We establish the permutation channel capacity of the BSC, and prove bounds on the permutation channel capacity of the BEC. Somewhat surprisingly, our results illustrate that permutation channel capacities are generally agnostic to the parameters that define the DMCs. Furthermore, our achievability proof yields a conceptually simple, computationally efficient, and capacity achieving coding scheme for the BSC permutation channel.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129597288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Second-order Guarantees of Gradient Algorithms over Networks","authors":"Amir Daneshmand, G. Scutari, V. Kungurtsev","doi":"10.1109/ALLERTON.2018.8636044","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636044","url":null,"abstract":"We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i) the renowned Distributed Gradient Descent (DGD) algorithm likely converges to a neighborhood of a Second-order Stationary (SoS) solution; and (ii) the more recent class of distributed algorithms, based on gradient tracking (termed SONATA), likely converges to exact SoS solutions, thus avoiding (strict) saddle points.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127279871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computation of Feedback Capacity of Single User Multi-Antenna Stationary Gaussian Channel","authors":"A. Rawat, N. Elia, Chong Li","doi":"10.1109/ALLERTON.2018.8635958","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635958","url":null,"abstract":"In this paper, we consider the single user communications through multiple transmitting and receiving antennas over the additive stationary Gaussian channel under input power constraints. We consider the problem of finding the feedback capacity of the aforementioned channel by utilizing the control theoretic interpretation of feedback communications. We connect the problem of finding the strictly causal filter to achieve the feedback capacity with the problem of finding stabilizing feedback controllers with maximum reliable transmission rate over Youla parameters. We then evaluate the asymptotic capacity achieving upper bounds by solving finite dimensional dual optimization problem. Optimal filter obtained from dual problem is then used to derive the sequence of lower bounds. Numerical example shows that the sequence of lower bounds and upper bounds are capacity achieving.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127780265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yagiz Savas, Melkior Ornik, Murat Cubuktepe, U. Topcu
{"title":"Entropy Maximization for Constrained Markov Decision Processes","authors":"Yagiz Savas, Melkior Ornik, Murat Cubuktepe, U. Topcu","doi":"10.1109/ALLERTON.2018.8636066","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636066","url":null,"abstract":"We study the problem of synthesizing a policy that maximizes the entropy of a Markov decision process (MDP) subject to expected reward constraints. Such a policy minimizes the predictability of the paths it generates in an MDP while attaining certain reward thresholds. We first show that the maximum entropy of an MDP can be finite, infinite or unbounded. We provide necessary and sufficient conditions under which the maximum entropy of an MDP is finite, infinite or unbounded. We then present an algorithm to synthesize a policy that maximizes the entropy of an MDP. The proposed algorithm is based on a convex optimization problem and runs in time polynomial in the size of the MDP. Finally, we extend the algorithm to an MDP subject to expected total reward constraints. In numerical examples, we demonstrate the proposed method on different motion planning scenarios and illustrate the trade-off between the predictability of paths and the level of the collected reward.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134401049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ian T. Cummings, T. Schulz, J. Doane, S. Zekavat, T. Havens
{"title":"Information-Theoretic Optimization of Full-Duplex Communication between Digital Phased Arrays","authors":"Ian T. Cummings, T. Schulz, J. Doane, S. Zekavat, T. Havens","doi":"10.1109/ALLERTON.2018.8635860","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635860","url":null,"abstract":"This paper poses full-duplex phase shift keyed communication between two digital phased arrays as an estimation problem and outlines an approach to minimizing the symbol phase estimation error. We develop an information-theoretic bound on the estimation error and a related feasible optimization objective function for the communications link in terms of the transmit and receive beamformers. We also apply a genetic algorithm to search for a transmit/receive aperture partitioning that minimizes the estimation error bound.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129006181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Game theoretic modeling of cyber deception in the Internet of Battlefield Things","authors":"C. Kamhoua","doi":"10.1109/ALLERTON.2018.8636060","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636060","url":null,"abstract":"Internet of Battlefield Things (IoBT) devices such as actuators, sensors, wearable devises, robots, drones, and autonomous vehicles, facilitate the Intelligence, Surveillance and Reconnaissance (ISR) to Command and Control and battlefield services. IoBT devices have the ability to collect operational field data, to compute on the data, and to upload its information to the network. Securing the IoBT presents additional challenges compared with traditional information technology (IT) systems. First, IoBT devices are mass produced rapidly to be low-cost commodity items without security protection in their original design. Second, IoBT devices are highly dynamic, mobile, and heterogeneous without common standards. Third, it is imperative to understand the natural world, the physical process(es) under IoBT control, and how these real-world processes can be compromised before recommending any relevant security counter measure. Moreover, unprotected IoBT devices can be used as “stepping stones” by attackers to launch more sophisticated attacks such as advanced persistent threats (APTs). As a result of these challenges, IoBT systems are the frequent targets of sophisticated cyber attack that aim to disrupt mission effectiveness.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":" 23","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113953391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the zero-error capacity of channels with rate limited noiseless feedback","authors":"Meysam Asadi, N. Devroye","doi":"10.1109/ALLERTON.2018.8636006","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636006","url":null,"abstract":"While it is known that feedback does not increase the small-error capacity of a discrete memoryless channel, noiseless feedback can increase the zero-error capacity from zero (without feedback) all the way to the small-error capacity. This result depends on the availability of noiseless output feedback, which gives the transmitter access to the exact output seen at the destination, as well as the use of variable-length codes. In this work, we consider two more realistic setups: 1) a noiseless feedback link of finite rate (which may not permit transmission of the outputs in their entirety), and 2) a noisy feedback link. We derive rates which may be achieved with zero error. Our results show that the achievable zero-error rate can vary between the zero-undetected-error capacity and the small-error capacity depending on the available feedback link rate and quality.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122960304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Learning Proximal Operators with Gaussian Processes","authors":"Truong X. Nghiem, Giorgos Stathopoulos, C. Jones","doi":"10.1109/ALLERTON.2018.8635898","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635898","url":null,"abstract":"Several distributed-optimization setups involve a group of agents coordinated by a central entity (coordinator), altogether operating in a collaborative framework. In such environments, it is often common that the agents solve proximal minimization problems that are hidden from the central coordinator. We develop a scheme for reducing communication between the agents and the coordinator based on learning the agents’ proximal operators with Gaussian Processes. The scheme learns a Gaussian Process model of the proximal operator associated with each agent from historical data collected at past query points. These models enable probabilistic predictions of the solutions to the local proximal minimization problems. Based on the predictive variance returned by a model, representative of its prediction confidence, an adaptive mechanism allows the coordinator to decide whether to communicate with the associated agent. The accuracy of the Gaussian Process models results in significant communication reduction, as demonstrated in simulations of a distributed optimal power dispatch application.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124570412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rearrangements and information theoretic inequalities","authors":"J. Melbourne","doi":"10.1109/ALLERTON.2018.8636000","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636000","url":null,"abstract":"We investigate the interaction of functional rearrangements with information theoretic inequalities. In particular we will prove the Relative Fisher information from Gaussianity decreases on half-space rearrangement, as a consequence we get a qualitative sharpening of the usual Gaussian log-Sobolev inequality. Additionally, we compare this half space rearrangement’s interaction with distance from Gaussianity, with the spherical rearrangement’s role in entropy power inequalities.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127971983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}