Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541575
Serkan Sarıtaş, S. Yüksel, S. Gezici
In this study, dynamic and repeated quadratic cheap talk and signaling game problems are investigated. These involve encoder and decoders with mismatched performance objectives, where the encoder has a bias term in the quadratic cost functional. We consider both Nash equilibria and Stackelberg equilibria as our solution concepts, under a perfect Bayesian formulation. These two lead to drastically different characteristics for the equilibria. For the cheap talk problem under Nash equilibria, we show that fully revealing equilibria cannot exist and the final state equilibria have to be quantized for a large class of source models; whereas, for the Stackelberg case, the equilibria must be fully revealing regardless of the source model. In the dynamic signaling game where the transmission of a Gaussian source over a Gaussian channel is considered, the equilibrium policies are always linear for scalar sources under Stackelberg equilibria, and affine policies constitute an invariant subspace under best response maps for Nash equilibria.
{"title":"Dynamic signaling games under Nash and Stackelberg equilibria","authors":"Serkan Sarıtaş, S. Yüksel, S. Gezici","doi":"10.1109/ISIT.2016.7541575","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541575","url":null,"abstract":"In this study, dynamic and repeated quadratic cheap talk and signaling game problems are investigated. These involve encoder and decoders with mismatched performance objectives, where the encoder has a bias term in the quadratic cost functional. We consider both Nash equilibria and Stackelberg equilibria as our solution concepts, under a perfect Bayesian formulation. These two lead to drastically different characteristics for the equilibria. For the cheap talk problem under Nash equilibria, we show that fully revealing equilibria cannot exist and the final state equilibria have to be quantized for a large class of source models; whereas, for the Stackelberg case, the equilibria must be fully revealing regardless of the source model. In the dynamic signaling game where the transmission of a Gaussian source over a Gaussian channel is considered, the equilibrium policies are always linear for scalar sources under Stackelberg equilibria, and affine policies constitute an invariant subspace under best response maps for Nash equilibria.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123120410","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541776
S. Haddad, O. Lévêque
We characterize the maximum achievable broadcast rate in a wireless network at low SNR and under line-of-sight fading assumption. Our result shows that this rate depends negatively on the sparsity of the network. This is to be put in contrast with the number of degrees of freedom available in the network, which have been shown previously to increase with the sparsity of the network.
{"title":"On the impact of sparsity on the broadcast capacity of wireless networks","authors":"S. Haddad, O. Lévêque","doi":"10.1109/ISIT.2016.7541776","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541776","url":null,"abstract":"We characterize the maximum achievable broadcast rate in a wireless network at low SNR and under line-of-sight fading assumption. Our result shows that this rate depends negatively on the sparsity of the network. This is to be put in contrast with the number of degrees of freedom available in the network, which have been shown previously to increase with the sparsity of the network.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123660006","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541683
Toshiyuki TANAKA
We study limiting eigenvalue distributions of block random matrix ensembles with one-dimensional coupling structure under the limit where the matrix size tends to infinity. Matrices in the ensembles have independent real symmetric random matrices of Wigner type on the diagonal blocks and a scalar multiple of the identity matrix on the blocks adjacent to the diagonal blocks. Explicit analytical formulas for the limiting eigenvalue distributions are derived for the 2 × 2-block ensemble as well as the 3 × 3-block circular ensemble. Further numerical results for B × B-block ensembles with B ≥ 3 are also shown.
{"title":"Limiting eigenvalue distributions of block random matrices with one-dimensional coupling structure","authors":"Toshiyuki TANAKA","doi":"10.1109/ISIT.2016.7541683","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541683","url":null,"abstract":"We study limiting eigenvalue distributions of block random matrix ensembles with one-dimensional coupling structure under the limit where the matrix size tends to infinity. Matrices in the ensembles have independent real symmetric random matrices of Wigner type on the diagonal blocks and a scalar multiple of the identity matrix on the blocks adjacent to the diagonal blocks. Explicit analytical formulas for the limiting eigenvalue distributions are derived for the 2 × 2-block ensemble as well as the 3 × 3-block circular ensemble. Further numerical results for B × B-block ensembles with B ≥ 3 are also shown.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128873682","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541733
Lan V. Truong, S. Fong, V. Tan
In this paper, we analyze the asymptotic expansion for additive white Gaussian noise (AWGN) channels with feedback under an expected power constraint and the average error probability formalism. We show that the ε-capacity depends on ε in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that the second-order term is bounded between -ln ln n and a term that is proportional to +√(n ln n). The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available.
{"title":"On second-order asymptotics of AWGN channels with feedback under the expected power constraint","authors":"Lan V. Truong, S. Fong, V. Tan","doi":"10.1109/ISIT.2016.7541733","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541733","url":null,"abstract":"In this paper, we analyze the asymptotic expansion for additive white Gaussian noise (AWGN) channels with feedback under an expected power constraint and the average error probability formalism. We show that the ε-capacity depends on ε in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that the second-order term is bounded between -ln ln n and a term that is proportional to +√(n ln n). The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125730275","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541580
H. Nagaoka
It is well known that the relative entropy (Kullback-Leibler divergence) is represented in the form of Bregman divergence on exponential families and mixture families for some coordinate systems. We give a characterization of the class of statistical manifolds (smooth manifolds of probability mass functions on finite sample spaces) having coordinate systems for which the relative entropy is a Bregman divergence.
{"title":"A characterization of statistical manifolds on which the relative entropy is a Bregman divergence","authors":"H. Nagaoka","doi":"10.1109/ISIT.2016.7541580","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541580","url":null,"abstract":"It is well known that the relative entropy (Kullback-Leibler divergence) is represented in the form of Bregman divergence on exponential families and mixture families for some coordinate systems. We give a characterization of the class of statistical manifolds (smooth manifolds of probability mass functions on finite sample spaces) having coordinate systems for which the relative entropy is a Bregman divergence.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122283361","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541452
Siddhartha Brahma, H. Mercier
We consider the allocation of coded data over nodes in a distributed storage system under a budget constraint. A system with failed nodes can recover the original data of unit size if the amount of data in the active nodes is at least a unit. Building on the work of Leong et al. [1], we introduce the concepts of tight allocations and repair bandwidth in this distributed setting. For tight allocations, the amount of data in the failed nodes gives a lower bound to the repair bandwidth required to put the system back to its original state. Using this bound, we define the Minimum Expected Repair Bandwidth (MERB) to study the tradeoffs between reliability and repair bandwidth, both empirically and by proving bounds on MERB in terms of the reliability. We show that even computing MERB for a general allocation is #P-Hard and suggest a simpler objective function to optimize it approximately. Finally, we study the asymptotic behavior of MERB for large systems and show two distinct optimal allocation regimes depending on the failure probability of the storage nodes.
{"title":"Reliability-bandwidth tradeoffs for distributed storage allocations","authors":"Siddhartha Brahma, H. Mercier","doi":"10.1109/ISIT.2016.7541452","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541452","url":null,"abstract":"We consider the allocation of coded data over nodes in a distributed storage system under a budget constraint. A system with failed nodes can recover the original data of unit size if the amount of data in the active nodes is at least a unit. Building on the work of Leong et al. [1], we introduce the concepts of tight allocations and repair bandwidth in this distributed setting. For tight allocations, the amount of data in the failed nodes gives a lower bound to the repair bandwidth required to put the system back to its original state. Using this bound, we define the Minimum Expected Repair Bandwidth (MERB) to study the tradeoffs between reliability and repair bandwidth, both empirically and by proving bounds on MERB in terms of the reliability. We show that even computing MERB for a general allocation is #P-Hard and suggest a simpler objective function to optimize it approximately. Finally, we study the asymptotic behavior of MERB for large systems and show two distinct optimal allocation regimes depending on the failure probability of the storage nodes.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"138 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128468843","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541418
K. Srinath, R. Venkataramanan
This paper considers the problem of estimating a high-dimensional vector θ ∈ ℝn from a noisy one-time observation. The noise vector is assumed to be i.i.d. Gaussian with known variance. For the squared-error loss function, the James-Stein (JS) estimator is known to dominate the simple maximum-likelihood (ML) estimator when the dimension n exceeds two. The JS-estimator shrinks the observed vector towards the origin, and the risk reduction over the ML-estimator is greatest for θ that lie close to the origin. JS-estimators can be generalized to shrink the data towards any target subspace. Such estimators also dominate the ML-estimator, but the risk reduction is significant only when θ lies close to the subspace. This leads to the question: in the absence of prior information about θ, how do we design estimators that give significant risk reduction over the ML-estimator for a wide range of θ? In this paper, we attempt to infer the structure of θ from the observed data in order to construct a good attracting subspace for the shrinkage estimator. We provide concentration results for the squared-error loss and convergence results for the risk of the proposed estimators, as well as simulation results to support the claims. The estimators give significant risk reduction over the ML-estimator for a wide range of θ, particularly for large n.
{"title":"Cluster-seeking shrinkage estimators","authors":"K. Srinath, R. Venkataramanan","doi":"10.1109/ISIT.2016.7541418","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541418","url":null,"abstract":"This paper considers the problem of estimating a high-dimensional vector θ ∈ ℝn from a noisy one-time observation. The noise vector is assumed to be i.i.d. Gaussian with known variance. For the squared-error loss function, the James-Stein (JS) estimator is known to dominate the simple maximum-likelihood (ML) estimator when the dimension n exceeds two. The JS-estimator shrinks the observed vector towards the origin, and the risk reduction over the ML-estimator is greatest for θ that lie close to the origin. JS-estimators can be generalized to shrink the data towards any target subspace. Such estimators also dominate the ML-estimator, but the risk reduction is significant only when θ lies close to the subspace. This leads to the question: in the absence of prior information about θ, how do we design estimators that give significant risk reduction over the ML-estimator for a wide range of θ? In this paper, we attempt to infer the structure of θ from the observed data in order to construct a good attracting subspace for the shrinkage estimator. We provide concentration results for the squared-error loss and convergence results for the risk of the proposed estimators, as well as simulation results to support the claims. The estimators give significant risk reduction over the ML-estimator for a wide range of θ, particularly for large n.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122639680","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541772
Jun Chen, Amir Salimi, Tie Liu, C. Tian
The notion of orbit-entropy cone is introduced. Specifically, orbit-entropy cone equation is the projection of equation induced by G, where equation is the closure of entropy region for n random variables and G is a permutation group over {0; 1;...; n-1}. For symmetric group Sn (with arbitrary n) and cyclic group Cn (with n ≤ 5), the associated orbit-entropy cones are shown to be characterized by the Shannon type inequalities. Moreover, the extremal pairwise relationship between orbit-entropies is determined completely for partitioned symmetric groups and partially for cyclic groups.
{"title":"Orbit-entropy cones and extremal pairwise orbit-entropy inequalities","authors":"Jun Chen, Amir Salimi, Tie Liu, C. Tian","doi":"10.1109/ISIT.2016.7541772","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541772","url":null,"abstract":"The notion of orbit-entropy cone is introduced. Specifically, orbit-entropy cone equation is the projection of equation induced by G, where equation is the closure of entropy region for n random variables and G is a permutation group over {0; 1;...; n-1}. For symmetric group Sn (with arbitrary n) and cyclic group Cn (with n ≤ 5), the associated orbit-entropy cones are shown to be characterized by the Shannon type inequalities. Moreover, the extremal pairwise relationship between orbit-entropies is determined completely for partitioned symmetric groups and partially for cyclic groups.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125594692","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541548
Yunhao Sun, Ruchen Duan, Yingbin Liang, A. Khisti, S. Shamai
This paper investigates the two-user state-dependent Gaussian multiple access channel (MAC) with a helper. The channel is corrupted by an additive Gaussian state sequence known to neither the transmitters nor the receiver, but to a helper noncausally, which assists state cancellation at the receiver. Inner and outer bounds on the capacity region are first derived, which improve the previous bounds given by Duan et al. Further comparison of these bounds yields either segments on the capacity region boundary or the full capacity region by considering various cases of channel parameters.
{"title":"Helper-assisted state cancelation for multiple access channels","authors":"Yunhao Sun, Ruchen Duan, Yingbin Liang, A. Khisti, S. Shamai","doi":"10.1109/ISIT.2016.7541548","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541548","url":null,"abstract":"This paper investigates the two-user state-dependent Gaussian multiple access channel (MAC) with a helper. The channel is corrupted by an additive Gaussian state sequence known to neither the transmitters nor the receiver, but to a helper noncausally, which assists state cancellation at the receiver. Inner and outer bounds on the capacity region are first derived, which improve the previous bounds given by Duan et al. Further comparison of these bounds yields either segments on the capacity region boundary or the full capacity region by considering various cases of channel parameters.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134017972","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}
Pub Date : 2016-08-11DOI: 10.1109/ISIT.2016.7541646
Abdulrahman Baknina, S. Ulukus
We consider online transmission scheduling for an energy harvesting broadcast channel with a finite-sized battery. The energy harvests are independent and identically distributed (i.i.d.) in time, and the transmitter gets to know them only causally as they happen. We first consider the case of Bernoulli energy arrivals, and determine the optimum online strategy that allocates power over time and between users optimally. We then consider the case of general i.i.d. energy arrivals, and propose a sub-optimum strategy coined fractional power constant cut-off (FPCC) policy. We develop a lower bound for the performance of the proposed FPCC policy, and a universal upper bound for the capacity region of the energy harvesting broadcast channel. We show that the proposed FPCC policy is near-optimal in that it yields rates that are within a constant gap from the optimum online policy, for all system parameters.
{"title":"Online scheduling for energy harvesting broadcast channels with finite battery","authors":"Abdulrahman Baknina, S. Ulukus","doi":"10.1109/ISIT.2016.7541646","DOIUrl":"https://doi.org/10.1109/ISIT.2016.7541646","url":null,"abstract":"We consider online transmission scheduling for an energy harvesting broadcast channel with a finite-sized battery. The energy harvests are independent and identically distributed (i.i.d.) in time, and the transmitter gets to know them only causally as they happen. We first consider the case of Bernoulli energy arrivals, and determine the optimum online strategy that allocates power over time and between users optimally. We then consider the case of general i.i.d. energy arrivals, and propose a sub-optimum strategy coined fractional power constant cut-off (FPCC) policy. We develop a lower bound for the performance of the proposed FPCC policy, and a universal upper bound for the capacity region of the energy harvesting broadcast channel. We show that the proposed FPCC policy is near-optimal in that it yields rates that are within a constant gap from the optimum online policy, for all system parameters.","PeriodicalId":198767,"journal":{"name":"2016 IEEE International Symposium on Information Theory (ISIT)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121375168","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}
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