Pub Date : 2008-12-01DOI: 10.1109/ALLERTON.2008.4797610
Waheed U. Bajwa, A. Sayeed, Robert Nowak
Coherent data communication over doubly-selective channels requires that the channel response be known at the receiver. Training-based schemes, which involve probing of the channel with known signaling waveforms and processing of the corresponding channel output to estimate the channel parameters, are commonly employed to learn the channel response in practice. Conventional training-based methods, often comprising of linear least squares channel estimators, are known to be optimal under the assumption of rich multipath channels. Numerous measurement campaigns have shown, however, that physical multipath channels tend to exhibit a sparse structure at high signal space dimension (time-bandwidth product), and can be characterized with significantly fewer parameters compared to the maximum number dictated by the delay-Doppler spread of the channel. In this paper, it is established that traditional training-based channel learning techniques are ill-suited to fully exploiting the inherent low-dimensionality of sparse channels. In contrast, key ideas from the emerging theory of compressed sensing are leveraged to propose sparse channel learning methods for both single-carrier and multicarrier probing waveforms that employ reconstruction algorithms based on convex/linear programming. In particular, it is shown that the performance of the proposed schemes come within a logarithmic factor of that of an ideal channel estimator, leading to significant reductions in the training energy and the loss in spectral efficiency associated with conventional training-based methods.
{"title":"Learning sparse doubly-selective channels","authors":"Waheed U. Bajwa, A. Sayeed, Robert Nowak","doi":"10.1109/ALLERTON.2008.4797610","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797610","url":null,"abstract":"Coherent data communication over doubly-selective channels requires that the channel response be known at the receiver. Training-based schemes, which involve probing of the channel with known signaling waveforms and processing of the corresponding channel output to estimate the channel parameters, are commonly employed to learn the channel response in practice. Conventional training-based methods, often comprising of linear least squares channel estimators, are known to be optimal under the assumption of rich multipath channels. Numerous measurement campaigns have shown, however, that physical multipath channels tend to exhibit a sparse structure at high signal space dimension (time-bandwidth product), and can be characterized with significantly fewer parameters compared to the maximum number dictated by the delay-Doppler spread of the channel. In this paper, it is established that traditional training-based channel learning techniques are ill-suited to fully exploiting the inherent low-dimensionality of sparse channels. In contrast, key ideas from the emerging theory of compressed sensing are leveraged to propose sparse channel learning methods for both single-carrier and multicarrier probing waveforms that employ reconstruction algorithms based on convex/linear programming. In particular, it is shown that the performance of the proposed schemes come within a logarithmic factor of that of an ideal channel estimator, leading to significant reductions in the training energy and the loss in spectral efficiency associated with conventional training-based methods.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116689783","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 : 2008-12-01DOI: 10.1109/ALLERTON.2008.4797629
L. Sankar, Xiaohu Shang, E. Erkip, H. Poor
The optimality of separable encoding and decoding over parallel channels (fading states) for ergodic fading two-user interference channels (IFCs) is studied using a one-sided IFC as a model. For an ergodic fading one-sided IFC with non-fading direct links and a fading cross-channel link, it is shown that separability can be strictly suboptimal except for the cases where all the parallel channels are of the same type, i.e., all of them are either strong but not very strong or very strong channels. A recent result on the sum-capacities of classes of ergodic strong and very strong IFCs is used to show that encoding and decoding jointly over all parallel channels is optimal when either the strong or very strong interference conditions hold on average over all channels.
{"title":"Ergodic two-user interference channels: Is separability optimal?","authors":"L. Sankar, Xiaohu Shang, E. Erkip, H. Poor","doi":"10.1109/ALLERTON.2008.4797629","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797629","url":null,"abstract":"The optimality of separable encoding and decoding over parallel channels (fading states) for ergodic fading two-user interference channels (IFCs) is studied using a one-sided IFC as a model. For an ergodic fading one-sided IFC with non-fading direct links and a fading cross-channel link, it is shown that separability can be strictly suboptimal except for the cases where all the parallel channels are of the same type, i.e., all of them are either strong but not very strong or very strong channels. A recent result on the sum-capacities of classes of ergodic strong and very strong IFCs is used to show that encoding and decoding jointly over all parallel channels is optimal when either the strong or very strong interference conditions hold on average over all channels.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125890670","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 : 2008-12-01DOI: 10.1109/ALLERTON.2008.4797585
A. Barg, A. Mazumdar, G. Zémor
Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hypergraphs whose minimum distance improves earlier estimates of the distance of bipartite-graph codes. In this talk we compute asymptotic weight distribution of several ensembles of hypergraph codes, establishing conditions under which they attain the Gilbert-Varshamov bound and deriving estimates of their distance. In particular, we show that this bound is attained by codes constructed on a fixed bipartite graph with a large spectral gap.
{"title":"Weight distribution of codes on hypergraphs","authors":"A. Barg, A. Mazumdar, G. Zémor","doi":"10.1109/ALLERTON.2008.4797585","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797585","url":null,"abstract":"Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hypergraphs whose minimum distance improves earlier estimates of the distance of bipartite-graph codes. In this talk we compute asymptotic weight distribution of several ensembles of hypergraph codes, establishing conditions under which they attain the Gilbert-Varshamov bound and deriving estimates of their distance. In particular, we show that this bound is attained by codes constructed on a fixed bipartite graph with a large spectral gap.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126088204","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 : 2008-12-01DOI: 10.1109/ALLERTON.2008.4797648
O. Simeone, D. Gunduz, H. Poor, A. Goldsmith, S. Shamai
A two-user discrete memoryless compound multiple access channel with a common message and conferencing decoders is considered. The capacity region is characterized in the special cases of physically degraded channels and unidirectional cooperation, while achievable rate regions are provided for the general case. The results are then extended to the corresponding Gaussian model. In the Gaussian setup, the provided achievable rates are shown to lie within a fraction of one bit from the boundary of the capacity region in several special cases. Numerical results are also provided to obtain insights about the potential gains of decoder cooperation in the underlying model.
{"title":"Compound multiple access channels with conferencing decoders","authors":"O. Simeone, D. Gunduz, H. Poor, A. Goldsmith, S. Shamai","doi":"10.1109/ALLERTON.2008.4797648","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797648","url":null,"abstract":"A two-user discrete memoryless compound multiple access channel with a common message and conferencing decoders is considered. The capacity region is characterized in the special cases of physically degraded channels and unidirectional cooperation, while achievable rate regions are provided for the general case. The results are then extended to the corresponding Gaussian model. In the Gaussian setup, the provided achievable rates are shown to lie within a fraction of one bit from the boundary of the capacity region in several special cases. Numerical results are also provided to obtain insights about the potential gains of decoder cooperation in the underlying model.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133643951","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 : 2008-12-01DOI: 10.1109/ALLERTON.2008.4797595
S. Mohajer, S. Diggavi, C. Fragouli, David Tse
In this paper we study the relay-interference wireless network, in which relay (helper) nodes are to facilitate competing information flows over a wireless network. We examine this in the context of a deterministic wireless interaction model, which eliminates the channel noise and focuses on the signal interactions. Using this model, we show that almost all the known schemes such as interference suppression, interference alignment and interference separation are necessary for relay-interference networks. In addition, we discover a new interference management technique, which we call interference neutralization, which allows for over-the-air interference removal, without the transmitters having complete access the interfering signals. We show that interference separation, suppression, and neutralization arise in a fundamental manner, since we show complete characterizations for special configurations of the relay-interference network.
{"title":"Transmission techniques for relay-interference networks","authors":"S. Mohajer, S. Diggavi, C. Fragouli, David Tse","doi":"10.1109/ALLERTON.2008.4797595","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797595","url":null,"abstract":"In this paper we study the relay-interference wireless network, in which relay (helper) nodes are to facilitate competing information flows over a wireless network. We examine this in the context of a deterministic wireless interaction model, which eliminates the channel noise and focuses on the signal interactions. Using this model, we show that almost all the known schemes such as interference suppression, interference alignment and interference separation are necessary for relay-interference networks. In addition, we discover a new interference management technique, which we call interference neutralization, which allows for over-the-air interference removal, without the transmitters having complete access the interfering signals. We show that interference separation, suppression, and neutralization arise in a fundamental manner, since we show complete characterizations for special configurations of the relay-interference network.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134363360","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 : 2008-10-09DOI: 10.1109/ALLERTON.2008.4797617
Danny Bickson, O. Shental, D. Dolev
Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm twice on the matching inputs, has several interesting interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight parameter beta = 1. Third, we discuss the relation to the Affine-scaling interior-point method and show it is a special case of Kalman filter. Besides of the theoretical interest of this linking estimation, compression/clustering and optimization, we allow a single distributed implementation of those algorithms, which is a highly practical and important task in sensor and mobile ad-hoc networks. Application to numerous problem domains includes collaborative signal processing and distributed allocation of resources in a communication network.
{"title":"Distributed Kalman filter via Gaussian Belief Propagation","authors":"Danny Bickson, O. Shental, D. Dolev","doi":"10.1109/ALLERTON.2008.4797617","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797617","url":null,"abstract":"Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm twice on the matching inputs, has several interesting interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight parameter beta = 1. Third, we discuss the relation to the Affine-scaling interior-point method and show it is a special case of Kalman filter. Besides of the theoretical interest of this linking estimation, compression/clustering and optimization, we allow a single distributed implementation of those algorithms, which is a highly practical and important task in sensor and mobile ad-hoc networks. Application to numerous problem domains includes collaborative signal processing and distributed allocation of resources in a communication network.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"446 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115611594","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 : 2008-10-09DOI: 10.1109/ALLERTON.2008.4797652
Danny Bickson, Y. Tock, O. Shental, D. Dolev
Interior-point methods are state-of-the-art algorithms for solving linear programming (LP) problems with polynomial complexity. Specifically, the Karmarkar algorithm typically solves LP problems in time O(n3.5), where n is the number of unknown variables. Karmarkar's celebrated algorithm is known to be an instance of the log-barrier method using the Newton iteration. The main computational overhead of this method is in inverting the Hessian matrix of the Newton iteration. In this contribution, we propose the application of the Gaussian belief propagation (GaBP) algorithm as part of an efficient and distributed LP solver that exploits the sparse and symmetric structure of the Hessian matrix and avoids the need for direct matrix inversion. This approach shifts the computation from realm of linear algebra to that of probabilistic inference on graphical models, thus applying GaBP as an efficient inference engine. Our construction is general and can be used for any interior-point algorithm which uses the Newton method, including non-linear program solvers.
{"title":"Polynomial Linear Programming with Gaussian belief propagation","authors":"Danny Bickson, Y. Tock, O. Shental, D. Dolev","doi":"10.1109/ALLERTON.2008.4797652","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797652","url":null,"abstract":"Interior-point methods are state-of-the-art algorithms for solving linear programming (LP) problems with polynomial complexity. Specifically, the Karmarkar algorithm typically solves LP problems in time O(n3.5), where n is the number of unknown variables. Karmarkar's celebrated algorithm is known to be an instance of the log-barrier method using the Newton iteration. The main computational overhead of this method is in inverting the Hessian matrix of the Newton iteration. In this contribution, we propose the application of the Gaussian belief propagation (GaBP) algorithm as part of an efficient and distributed LP solver that exploits the sparse and symmetric structure of the Hessian matrix and avoids the need for direct matrix inversion. This approach shifts the computation from realm of linear algebra to that of probabilistic inference on graphical models, thus applying GaBP as an efficient inference engine. Our construction is general and can be used for any interior-point algorithm which uses the Newton method, including non-linear program solvers.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121306671","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 : 2008-09-24DOI: 10.1109/ALLERTON.2008.4797604
S. Sridharan, A. Jafarian, S. Vishwanath, S. Jafar, S. Shamai
The paper studies a class of three user Gaussian interference channels. A new layered lattice coding scheme is introduced as a transmission strategy. The use of lattice codes allows for an ldquoalignmentrdquo of the interference observed at each receiver. The layered lattice coding is shown to achieve more than one degree of freedom for a class of interference channels and also achieves rates which are better than the rates obtained using the Han-Kobayashi coding scheme.
{"title":"A layered lattice coding scheme for a class of three user Gaussian interference channels","authors":"S. Sridharan, A. Jafarian, S. Vishwanath, S. Jafar, S. Shamai","doi":"10.1109/ALLERTON.2008.4797604","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797604","url":null,"abstract":"The paper studies a class of three user Gaussian interference channels. A new layered lattice coding scheme is introduced as a transmission strategy. The use of lattice codes allows for an ldquoalignmentrdquo of the interference observed at each receiver. The layered lattice coding is shown to achieve more than one degree of freedom for a class of interference channels and also achieves rates which are better than the rates obtained using the Han-Kobayashi coding scheme.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"49 11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121197824","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797553
S. Shadbakht, B. Hassibi
It has recently been shown that there is a connection between Cayley's hypdeterminant and the principal minors of a symmetric matrix. With an eye towards characterizing the entropy region of jointly Gaussian random variables, we obtain three new results on the relationship between Gaussian random variables and the hyperdeterminant. The first is a new (determinant) formula for the 2times2times2 hyperdeterminant. The second is a new (transparent) proof of the fact that the principal minors of an ntimesn symmetric matrix satisfy the 2 times 2 times .... times 2 (n times) hyperdeterminant relations. The third is a minimal set of 5 equations that 15 real numbers must satisfy to be the principal minors of a 4 times 4 symmetric matrix.
{"title":"Cayley's hyperdeterminant, the principal minors of a symmetric matrix and the entropy region of 4 Gaussian random variables","authors":"S. Shadbakht, B. Hassibi","doi":"10.1109/ALLERTON.2008.4797553","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797553","url":null,"abstract":"It has recently been shown that there is a connection between Cayley's hypdeterminant and the principal minors of a symmetric matrix. With an eye towards characterizing the entropy region of jointly Gaussian random variables, we obtain three new results on the relationship between Gaussian random variables and the hyperdeterminant. The first is a new (determinant) formula for the 2times2times2 hyperdeterminant. The second is a new (transparent) proof of the fact that the principal minors of an ntimesn symmetric matrix satisfy the 2 times 2 times .... times 2 (n times) hyperdeterminant relations. The third is a minimal set of 5 equations that 15 real numbers must satisfy to be the principal minors of a 4 times 4 symmetric matrix.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115603251","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797749
S. Vedantam, W. Zhang, U. Mitra
The problem of communicating over a two hop network while estimating the channel states to within a distortion constraint is explored. The end to end capacity of this network is upper and lower bounded. Under certain conditions, it is shown that the upper and lower bounds match and we have the capacity of the network. An example is also presented to apply the results developed.
{"title":"Joint communication and channel estimation: the two hop case","authors":"S. Vedantam, W. Zhang, U. Mitra","doi":"10.1109/ALLERTON.2008.4797749","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797749","url":null,"abstract":"The problem of communicating over a two hop network while estimating the channel states to within a distortion constraint is explored. The end to end capacity of this network is upper and lower bounded. Under certain conditions, it is shown that the upper and lower bounds match and we have the capacity of the network. An example is also presented to apply the results developed.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115339173","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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