{"title":"On Dual Relationships of Secrecy Codes","authors":"Willie K. Harrison, M. Bloch","doi":"10.1109/ALLERTON.2018.8635841","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635841","url":null,"abstract":"We investigate properties of finite blocklength codes and their duals when used for coset coding over the binary erasure wiretap channel (BEWC). We identify sufficient conditions, related to the ranks of sub-matrices of a generator matrix that codes may satisfy to achieve the maximum equivocation among all codes with given blocklength and dimension, irrespective of the eavesdropper's channel erasure probability. We point out that binary maximum distance separable (MDS) codes are optimal for secrecy and we also show that simplex codes (and Hamming codes) have higher equivocation than families of codes with a single repeated column in the generator matrix (parity-check matrix). We conjecture that simplex and Hamming codes are optimal when used as the base linear code in a coset coding scheme for secrecy over the BEWC.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"50 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":"116569613","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":"Resource Allocation under Sequential Resource Access: Theory and Application","authors":"A. Tajer, Maha Zohdy","doi":"10.1109/ALLERTON.2018.8636038","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636038","url":null,"abstract":"This paper treats the problem of optimal resource allocation over time in a finite-horizon setting, in which the resource become available only sequentially and in incremental values and the utility function is concave and can freely vary over time. Such resource allocation problems have direct applications in data communication networks (e.g., energy harvesting systems). This problem is studied extensively for special choices of the concave utility function (time-invariant and logarithmic) in which case the optimal resource allocation policies are well-understood. This paper treats this problem in its general form and analytically characterizes the structure of the optimal resource allocation policy, and devises an algorithm for computing the exact solutions analytically. An observation instrumental to devising the provided algorithm is that there exist time instances at which the available resources are exhausted, with no carry-over to future. This algorithm identifies all such instances, which in turn facilitates breaking the original problem into multiple problems with significantly reduced dimensions. Furthermore, some widely-used special cases in which the algorithm takes simpler structures are characterized, and the application to the energy harvesting systems is discussed. Numerical evaluations are provided to assess the key properties of the optimal resource allocation structure and to compare the performance with the generic convex optimization algorithms.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"94 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":"116601020","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":"Feedback control of server instances for right sizing in the cloud","authors":"Diego Goldsztajn, Andrés Ferragut, F. Paganini","doi":"10.1109/ALLERTON.2018.8635636","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635636","url":null,"abstract":"We consider a computing system based on sum-moning server instances on the fly, possibly from a remote cloud service. A feedback rule must be designed to track the exogenous load with the right service capacity, taking into account the inherent lags in server creation and deletion. We use fluid and diffusion approximations of queueing models to analyze control schemes that manage the tradeoff between job queueing and idle capacity, in the large scale limit. In particular we propose a method in which the system can achieve negligible queueing while minimizing idle capacity. Theoretical results are supported by simulations.","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":"123713865","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":"Stability of Non-Linear Filters, Observability and Relative Entropy","authors":"Curtis McDonald, S. Yüksel","doi":"10.1109/ALLERTON.2018.8635865","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635865","url":null,"abstract":"For a partially observed Markov chain, an incorrectly initialized non-linear filter is said to be stable if the filter eventually corrects itself with the arrival of new measurement information. In the literature, studies on the stability of non-linear filters have either assumed strong stationary conditions on the hidden Markov process, or have assumed restrictive assumptions on the observation channel structure. In this paper, compared to existing results in the literature, on the one hand we relax the assumptions on the observation channel and on the other hand, by using relative entropy as a versatile tool for proving convergence and stability, we are able to obtain complementary convergence results under observability conditions.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"6 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":"124915021","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 Model-free Reinforcement Learning for Switched Linear Systems: A Subspace Clustering Approach","authors":"Hao Li, Hua Chen, Wei Zhang","doi":"10.1109/ALLERTON.2018.8635985","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635985","url":null,"abstract":"In this paper, we study optimal control of switched linear systems using reinforcement learning. Instead of directly applying existing model-free reinforcement learning algorithms, we propose a Q-learning-based algorithm designed specifically for discrete time switched linear systems. Inspired by the analytical results from optimal control literature, the Q function in our algorithm is approximated by a point-wise minimum form of a finite number of quadratic functions. An associated update scheme based on subspace clustering for such an approximation is also developed which preserves the desired structure during the training process. Numerical examples for both low-dimensional and high-dimensional switched linear systems are provided to demonstrate the performance of our algorithm.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"9 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":"128408523","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 topological entropy of switched linear systems with pairwise commuting matrices","authors":"Guosong Yang, J. Hespanha","doi":"10.1109/ALLERTON.2018.8635894","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635894","url":null,"abstract":"We study a notion of topological entropy for switched systems, formulated in terms of the minimal number of initial states needed to approximate all initial states within a finite precision. This paper focuses on the topological entropy of switched linear systems with pairwise commuting matrices. First, we prove there exists a simultaneous change of basis under which each of the matrices can be decomposed into a diagonal part and a nilpotent part, and all the diagonal and nilpotent parts are pairwise commuting. Then a formula for the topological entropy is established in terms of the component- wise averages of the eigenvalues, weighted by the active time of each mode, which indicates that the topological entropy is independent of the nilpotent parts above. We also present how the formula generalizes known results for the non-switched case and the case with simultaneously diagonalizable matrices, and construct more general but more conservative upper bounds for the entropy. A numerical example is provided to demonstrate properties of the formula and the upper and lower bounds for the topological entropy.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"29 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":"121614753","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 Joint Recovery of Community Structure and Community Features","authors":"Jisang Yoon, Kangwook Lee, Changho Suh","doi":"10.1109/ALLERTON.2018.8636058","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636058","url":null,"abstract":"We study the problem of recovering both K communities and their features from a labeled graph observation. We assume that the edges of an observed graph are generated as per the symmetric Stochastic Block Model (SBM), and that the label of each node is a noisy and partially-observed version of the corresponding community feature. We characterize the information-theoretic limit of this problem, and then propose a computationally efficient algorithm that achieves the information-theoretic limit.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"27 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":"116765366","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":"A Geometric Characterization of Fisher Information from Quantized Samples with Applications to Distributed Statistical Estimation","authors":"L. P. Barnes, Yanjun Han, Ayfer Özgür","doi":"10.1109/ALLERTON.2018.8635899","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8635899","url":null,"abstract":"Consider the Fisher information for estimating a vector $theta in mathbb {R}^{d}$ from the quantized version of a statistical sample $X sim f(x|theta)$. Let M be a k-bit quantization of $X.$ We provide a geometric characterization of the trace of the Fisher information matrix $I_{M}(theta)$ in terms of the score function $S_{theta }(X)$. When $k=1$, we exactly solve the extremal problem of maximizing this geometric quantity for the Gaussian location model, which allows us to conclude that in this model, a half-space quantization is the one-bit quantization that maximizes $Tr(I_{M}(theta))$. Under assumptions on the tail of the distribution of $S_{theta }(X)$ projected onto any unit vector in $mathbb {R}^{d}$, we give upper bounds demonstrating how $Tr(I_{M}(theta))$ can scale with k. We apply these results to find lower bounds on the minimax risk of estimating $theta $ from multiple quantized samples of X, for example in a distributed setting where the samples are distributed across multiple nodes and each node has a total budget of k-bits to communicate its sample to a centralized estimator. Our bounds apply in a unified way to many common statistical models including the Gaussian location model and discrete distribution estimation, and they recover and generalize existing results in the literature with simpler and more transparent proofs.","PeriodicalId":299280,"journal":{"name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"21 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":"122131890","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":"The repair problem under connectivity constraints: Explicit MSR codes for the rack-aware model of distributed storage","authors":"Zitan Chen, A. Barg","doi":"10.1109/ALLERTON.2018.8636062","DOIUrl":"https://doi.org/10.1109/ALLERTON.2018.8636062","url":null,"abstract":"Recent papers of Min Ye and the second-named author introduced constructions of MSR codes based on parity-check equations. In this note we modify the approach of these works to construct explicit MSR codes for the rack-based model of distributed storage. The codes that we construct can recover any single failed node by downloading information from a subset of the surviving nodes relying on the rack structure of the system. The underlying finite field is of size at most $n^{2}/u$, where n is the block length of the code and u is the size of the rack.","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":"129574639","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}