Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447072
A. Wachter-Zeh, Eitan Yaakobi
This paper studies defect memory cells and in particular partially stuck-at memory cells, which occur when charge is trapped in multi-level cells of non-volatile memories such as flash memories. If a cell can store the q levels 0, 1, ..., q - 1, we say that it is partially stuck-at level s, where 1 ≤ s ≤ q - 1, if it can only store values which are at least s. We follow the common setup where the encoder knows the positions and levels of the partially stuck-at cells whereas the decoder does not. In this paper, we study codes for masking u partially stuck-at cells. We derive lower and upper bounds on the redundancy of such codes and present code constructions. Furthermore, we analyze the dual defect model in which cells cannot reach higher levels, and show that codes for partially stuck-at cells can be used to mask this type of defects as well. Lastly, we analyze the capacity of the partially stuck-at memory channel and study how far our constructions are from the capacity.
{"title":"Masking trapped charge in flash memories","authors":"A. Wachter-Zeh, Eitan Yaakobi","doi":"10.1109/ALLERTON.2015.7447072","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447072","url":null,"abstract":"This paper studies defect memory cells and in particular partially stuck-at memory cells, which occur when charge is trapped in multi-level cells of non-volatile memories such as flash memories. If a cell can store the q levels 0, 1, ..., q - 1, we say that it is partially stuck-at level s, where 1 ≤ s ≤ q - 1, if it can only store values which are at least s. We follow the common setup where the encoder knows the positions and levels of the partially stuck-at cells whereas the decoder does not. In this paper, we study codes for masking u partially stuck-at cells. We derive lower and upper bounds on the redundancy of such codes and present code constructions. Furthermore, we analyze the dual defect model in which cells cannot reach higher levels, and show that codes for partially stuck-at cells can be used to mask this type of defects as well. Lastly, we analyze the capacity of the partially stuck-at memory channel and study how far our constructions are from the capacity.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126250315","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7557347
M. Rasekh, Dongning Guo, Upamanyu Madhow
The exponential growth in demand for mobile data requires significant increases in spatial reuse, motivating an evolution towards picocellular architectures with densely deployed base stations. Providing backhaul for such a network is a key challenge, because of the high access link rates, and the cost and difficulty of running optical fiber to base stations that might be opportunistically placed on lampposts and rooftops. Wireless backhaul using millimeter (mm) wave spectrum is therefore an attractive and flexible approach, given the plentiful availability of spectrum and the possibility of synthesizing highly directive, steerable links. In this paper, we formulate and investigate the problem of joint resource allocation and routing on such a mm wave backhaul network, providing a linear programming formulation that accounts for mutual interference across simultaneously active links. While the number of variables grows exponentially in network size, it is possible to prune the problem size so that it is manageable for moderately sized networks. Numerical results and design implications are briefly discussed.
{"title":"Interference-aware routing and spectrum allocation for millimeter wave backhaul in urban picocells","authors":"M. Rasekh, Dongning Guo, Upamanyu Madhow","doi":"10.1109/ALLERTON.2015.7557347","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7557347","url":null,"abstract":"The exponential growth in demand for mobile data requires significant increases in spatial reuse, motivating an evolution towards picocellular architectures with densely deployed base stations. Providing backhaul for such a network is a key challenge, because of the high access link rates, and the cost and difficulty of running optical fiber to base stations that might be opportunistically placed on lampposts and rooftops. Wireless backhaul using millimeter (mm) wave spectrum is therefore an attractive and flexible approach, given the plentiful availability of spectrum and the possibility of synthesizing highly directive, steerable links. In this paper, we formulate and investigate the problem of joint resource allocation and routing on such a mm wave backhaul network, providing a linear programming formulation that accounts for mutual interference across simultaneously active links. While the number of variables grows exponentially in network size, it is possible to prune the problem size so that it is manageable for moderately sized networks. Numerical results and design implications are briefly discussed.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127936415","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447020
P. Babaheidarian, Somayeh Salimi, Panos Papadimitratos
In this work, we consider a K-user Gaussian wiretap multiple-access channel (GW-MAC) in which each transmitter has an independent confidential message for the receiver. There is also an external eavesdropper who intercepts the communications. The goal is to transmit the messages reliably while keeping them confidential from the eavesdropper. To accomplish this goal, two different approaches have been proposed in prior works, namely, i.i.d. Gaussian random coding and real alignment. However, the former approach fails at moderate and high SNR regimes as its achievable result does not grow with SNR. On the other hand, while the latter approach gives a promising result at the infinite SNR regime, its extension to the finite-SNR regime is a challenging task. To fill the gap between the performance of the existing approaches, in this work, we establish a new scheme in which, at the receiver's side, it utilizes an extension of the compute-and-forward decoding strategy and at the transmitters' side it exploits lattice alignment, cooperative jamming, and i.i.d. random codes. For the proposed scheme, we derive a new achievable bound on sum secure rate which scales with log(SNR) and hence it outperforms the i.i.d. Gaussian codes in moderate and high SNR regimes. We evaluate the performance of our scheme, both theoretically and numerically. Furthermore, we show that our sum secure rate achieves the optimal sum secure degrees of freedom in the infinite-SNR regime.
{"title":"Finite-SNR regime analysis of the Gaussian wiretap multiple-access channel","authors":"P. Babaheidarian, Somayeh Salimi, Panos Papadimitratos","doi":"10.1109/ALLERTON.2015.7447020","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447020","url":null,"abstract":"In this work, we consider a K-user Gaussian wiretap multiple-access channel (GW-MAC) in which each transmitter has an independent confidential message for the receiver. There is also an external eavesdropper who intercepts the communications. The goal is to transmit the messages reliably while keeping them confidential from the eavesdropper. To accomplish this goal, two different approaches have been proposed in prior works, namely, i.i.d. Gaussian random coding and real alignment. However, the former approach fails at moderate and high SNR regimes as its achievable result does not grow with SNR. On the other hand, while the latter approach gives a promising result at the infinite SNR regime, its extension to the finite-SNR regime is a challenging task. To fill the gap between the performance of the existing approaches, in this work, we establish a new scheme in which, at the receiver's side, it utilizes an extension of the compute-and-forward decoding strategy and at the transmitters' side it exploits lattice alignment, cooperative jamming, and i.i.d. random codes. For the proposed scheme, we derive a new achievable bound on sum secure rate which scales with log(SNR) and hence it outperforms the i.i.d. Gaussian codes in moderate and high SNR regimes. We evaluate the performance of our scheme, both theoretically and numerically. Furthermore, we show that our sum secure rate achieves the optimal sum secure degrees of freedom in the infinite-SNR regime.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127319777","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447131
Jingjing Zhang, Felix Engelmann, P. Elia
The work explores the role of caching content at receiving users for the purpose of reducing the need for feedback in wireless communications. In the K-user broadcast channel (BC), we show how caching, when combined with a rate-splitting broadcast approach, can not only improve performance, but can also reduce the need for channel state information at the transmitter (CSIT), in the sense that the identified cache-aided optimal degrees-of-freedom performance, can in fact be achieved with reduced-quality CSIT. These CSIT savings can be traced back to an inherent relationship between caching, performance, and CSIT; caching improves performance by leveraging multicasting of common information, which automatically reduces the need for CSIT, by virtue of the fact that common information is not a cause of interference. At the same time though, too much multicasting of common information can be detrimental, as it does not utilize existing CSIT. Our caching method builds on the Maddah-Ali and Niesen coded caching scheme, by properly balancing multicast and broadcast opportunities, and by combing caching with rate-splitting communication schemes that are specifically designed to operate under imperfect-quality CSIT. The observed achievable CSIT savings here, are more pronounced for smaller values of K users and N files.
{"title":"Coded caching for reducing CSIT-feedback in wireless communications","authors":"Jingjing Zhang, Felix Engelmann, P. Elia","doi":"10.1109/ALLERTON.2015.7447131","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447131","url":null,"abstract":"The work explores the role of caching content at receiving users for the purpose of reducing the need for feedback in wireless communications. In the K-user broadcast channel (BC), we show how caching, when combined with a rate-splitting broadcast approach, can not only improve performance, but can also reduce the need for channel state information at the transmitter (CSIT), in the sense that the identified cache-aided optimal degrees-of-freedom performance, can in fact be achieved with reduced-quality CSIT. These CSIT savings can be traced back to an inherent relationship between caching, performance, and CSIT; caching improves performance by leveraging multicasting of common information, which automatically reduces the need for CSIT, by virtue of the fact that common information is not a cause of interference. At the same time though, too much multicasting of common information can be detrimental, as it does not utilize existing CSIT. Our caching method builds on the Maddah-Ali and Niesen coded caching scheme, by properly balancing multicast and broadcast opportunities, and by combing caching with rate-splitting communication schemes that are specifically designed to operate under imperfect-quality CSIT. The observed achievable CSIT savings here, are more pronounced for smaller values of K users and N files.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130600626","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447165
Songbai Yan, Kamalika Chaudhuri, T. Javidi
An active learner is given an instance space, a label space and a hypothesis class, where one of the hypotheses in the class assigns ground truth labels to instances. Additionally, the learner has access to a labeling oracle, which it can interactively query for the label of any example in the instance space. The goal of the learner is to find a good estimate of the hypothesis in the hypothesis class that generates the ground truth labels while making as few interactive queries to the oracle as possible. This work considers a more general setting where the labeling oracle can abstain from providing a label in addition to returning noisy labels. We provide a model for this setting where the abstention rate and the noise rate increase as we get closer to the decision boundary of the ground truth hypothesis. We provide an algorithm and an analysis of the number of queries it makes to the labeling oracle; finally we provide matching lower bounds to demonstrate that our algorithm has near-optimal estimation accuracy.
{"title":"Active learning from noisy and abstention feedback","authors":"Songbai Yan, Kamalika Chaudhuri, T. Javidi","doi":"10.1109/ALLERTON.2015.7447165","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447165","url":null,"abstract":"An active learner is given an instance space, a label space and a hypothesis class, where one of the hypotheses in the class assigns ground truth labels to instances. Additionally, the learner has access to a labeling oracle, which it can interactively query for the label of any example in the instance space. The goal of the learner is to find a good estimate of the hypothesis in the hypothesis class that generates the ground truth labels while making as few interactive queries to the oracle as possible. This work considers a more general setting where the labeling oracle can abstain from providing a label in addition to returning noisy labels. We provide a model for this setting where the abstention rate and the noise rate increase as we get closer to the decision boundary of the ground truth hypothesis. We provide an algorithm and an analysis of the number of queries it makes to the labeling oracle; finally we provide matching lower bounds to demonstrate that our algorithm has near-optimal estimation accuracy.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130720708","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447051
G. Kamath, K. Jagannathan, G. Raina
Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles driving on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of two widely-studied car-following models; namely, the classical car-following model and the optimal velocity model. We first conduct a control-theoretic analysis for both models and derive conditions that ensure local stability. We then demonstrate that the transition of traffic flow from the locally stable to the unstable regime occurs via a Hopf bifurcation. Qualitatively, this results in the emergence of limit cycles, which manifest as a back-propagating congestion wave. The analysis is complemented with stability charts and bifurcation diagrams. We also outline some of the implications that our results may have on the design of stable systems in the context of self-driven vehicles.
{"title":"Car-following models with delayed feedback: Local stability and Hopf bifurcation","authors":"G. Kamath, K. Jagannathan, G. Raina","doi":"10.1109/ALLERTON.2015.7447051","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447051","url":null,"abstract":"Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles driving on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of two widely-studied car-following models; namely, the classical car-following model and the optimal velocity model. We first conduct a control-theoretic analysis for both models and derive conditions that ensure local stability. We then demonstrate that the transition of traffic flow from the locally stable to the unstable regime occurs via a Hopf bifurcation. Qualitatively, this results in the emergence of limit cycles, which manifest as a back-propagating congestion wave. The analysis is complemented with stability charts and bifurcation diagrams. We also outline some of the implications that our results may have on the design of stable systems in the context of self-driven vehicles.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128365663","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447126
P. Wang, R. Safavi-Naini, Fuchun Lin
In an erasure adversarial wiretap channel (eAWTP-channel), the adversary can select a fraction ρr of the codeword to read, and a fraction ρe of the codeword to erase. The model can be seen as an extension of the wiretap II model where the adversary not only selects its view of the transmitted word, but also can erase a fraction of the codeword. eAWTP codes provide security and reliability for communication over eAWTP channels. We derive an upper bound on the rate of eAWTP codes, and give an efficient construction of a code family that achieves the bound, hence deriving secrecy capacity of the channel. We then show that the construction can also be used for AWTP channels in which instead of erasing code components, the adversary can add noise to the codeword. The construction is the only AWTP code with constant alphabet size.
{"title":"Erasure adversarial wiretap channels","authors":"P. Wang, R. Safavi-Naini, Fuchun Lin","doi":"10.1109/ALLERTON.2015.7447126","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447126","url":null,"abstract":"In an erasure adversarial wiretap channel (eAWTP-channel), the adversary can select a fraction ρr of the codeword to read, and a fraction ρe of the codeword to erase. The model can be seen as an extension of the wiretap II model where the adversary not only selects its view of the transmitted word, but also can erase a fraction of the codeword. eAWTP codes provide security and reliability for communication over eAWTP channels. We derive an upper bound on the rate of eAWTP codes, and give an efficient construction of a code family that achieves the bound, hence deriving secrecy capacity of the channel. We then show that the construction can also be used for AWTP channels in which instead of erasing code components, the adversary can add noise to the codeword. The construction is the only AWTP code with constant alphabet size.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131964487","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447015
Subrahmanya Swamy Peruru, R. Ganti, K. Jagannathan
In this paper, we consider an adaptive CSMA based scheduling algorithm for a single-hop wireless network under a realistic SINR (signal-to-interference-plus-noise ratio) model for the interference, and propose an efficient local optimization based algorithm to estimate certain parameters of the algorithm called fugacities. It is known that adaptive CSMA based algorithms can achieve throughput optimality, by sampling feasible schedules from a Gibbs distribution with appropriate fugacities. Unfortunately, estimating the optimal fugacities for a desired service rate vector is an NP-hard problem. Further, the existing adaptive CSMA algorithms use a stochastic gradient descent based method, which usually entails an impractically slow (exponential in the size of the network) convergence to the optimal fugacities. In contrast, the convergence rate and the complexity of our algorithm is independent of the network size, and depends only on the neighborhood size of a link. In particular, in spatial networks where the neighborhood size does not scale with the network size, our algorithm is order optimal. We show that the proposed algorithm corresponds exactly to performing the well-known Bethe approximation to the underlying Gibbs distribution. We also consider two special cases of the SINR interference model and obtain the corresponding fugacities in closed form. Numerical results indicate that the proposed method achieves extremely fast convergence to near-optimal fugacities, and often outperforms the convergence rate of the stochastic gradient descent by a few orders of magnitude.
{"title":"Adaptive CSMA under the SINR model: Fast convergence through local gibbs optimization","authors":"Subrahmanya Swamy Peruru, R. Ganti, K. Jagannathan","doi":"10.1109/ALLERTON.2015.7447015","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447015","url":null,"abstract":"In this paper, we consider an adaptive CSMA based scheduling algorithm for a single-hop wireless network under a realistic SINR (signal-to-interference-plus-noise ratio) model for the interference, and propose an efficient local optimization based algorithm to estimate certain parameters of the algorithm called fugacities. It is known that adaptive CSMA based algorithms can achieve throughput optimality, by sampling feasible schedules from a Gibbs distribution with appropriate fugacities. Unfortunately, estimating the optimal fugacities for a desired service rate vector is an NP-hard problem. Further, the existing adaptive CSMA algorithms use a stochastic gradient descent based method, which usually entails an impractically slow (exponential in the size of the network) convergence to the optimal fugacities. In contrast, the convergence rate and the complexity of our algorithm is independent of the network size, and depends only on the neighborhood size of a link. In particular, in spatial networks where the neighborhood size does not scale with the network size, our algorithm is order optimal. We show that the proposed algorithm corresponds exactly to performing the well-known Bethe approximation to the underlying Gibbs distribution. We also consider two special cases of the SINR interference model and obtain the corresponding fugacities in closed form. Numerical results indicate that the proposed method achieves extremely fast convergence to near-optimal fugacities, and often outperforms the convergence rate of the stochastic gradient descent by a few orders of magnitude.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134408900","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447044
F. Rego, Ye Pu, A. Alessandretti, Antonio Pedro Aguiar, C. Jones
In this paper we address the problem of quantized consensus where process noise or external inputs corrupt the state of each agent at each iteration. We propose a quantized consensus algorithm with progressive quantization, where the quantization interval changes in length at each iteration by a pre-specified value. We derive conditions on the design parameters of the algorithm to guarantee ultimate boundedness of the deviation from the average of each agent. Moreover, we determine explicitly the bounds of the consensus error under the assumption that the process disturbances are ultimately bounded within known bounds. A numerical example of cooperative path-following of a network of single integrators illustrates the performance of the proposed algorithm.
{"title":"A consensus algorithm for networks with process noise and quantization error","authors":"F. Rego, Ye Pu, A. Alessandretti, Antonio Pedro Aguiar, C. Jones","doi":"10.1109/ALLERTON.2015.7447044","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447044","url":null,"abstract":"In this paper we address the problem of quantized consensus where process noise or external inputs corrupt the state of each agent at each iteration. We propose a quantized consensus algorithm with progressive quantization, where the quantization interval changes in length at each iteration by a pre-specified value. We derive conditions on the design parameters of the algorithm to guarantee ultimate boundedness of the deviation from the average of each agent. Moreover, we determine explicitly the bounds of the consensus error under the assumption that the process disturbances are ultimately bounded within known bounds. A numerical example of cooperative path-following of a network of single integrators illustrates the performance of the proposed algorithm.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125631918","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 : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447147
Dionysios S. Kalogerias, A. Petropulu
We present a theoretical comparison of the state-of-the-art sufficient conditions required for pathwise (almost sure type of) convergence between grid based and particle approximate filters, as well as discuss the implications of these conditions on the specific mode of convergence achieved. Focusing on general Markov processes observed in conditionally Gaussian noise, we have recently shown that a sufficient condition for pathwise convergence of grid based filters is conditional regularity of stochastic kernels. The respective condition for almost sure convergence of particle filters is the well known Feller property. While our analysis shows that the comparison between the afore-mentioned conditions may be indeed inconclusive, we identify a large class of systems for which conditional regularity may hold true, whereas the Feller property cannot. This is achieved through a structural analysis of both sufficient conditions. This work can be summarized in that there provably exist system classes supported by either grid based or particle filtering approximations, but not necessarily by both; for systems supported by both, grid based filters exhibit a theoretical advantage in terms of convergence robustness.
{"title":"On pathwise convergence of particle & grid based nonlinear filters: Feller vs conditional regularity","authors":"Dionysios S. Kalogerias, A. Petropulu","doi":"10.1109/ALLERTON.2015.7447147","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447147","url":null,"abstract":"We present a theoretical comparison of the state-of-the-art sufficient conditions required for pathwise (almost sure type of) convergence between grid based and particle approximate filters, as well as discuss the implications of these conditions on the specific mode of convergence achieved. Focusing on general Markov processes observed in conditionally Gaussian noise, we have recently shown that a sufficient condition for pathwise convergence of grid based filters is conditional regularity of stochastic kernels. The respective condition for almost sure convergence of particle filters is the well known Feller property. While our analysis shows that the comparison between the afore-mentioned conditions may be indeed inconclusive, we identify a large class of systems for which conditional regularity may hold true, whereas the Feller property cannot. This is achieved through a structural analysis of both sufficient conditions. This work can be summarized in that there provably exist system classes supported by either grid based or particle filtering approximations, but not necessarily by both; for systems supported by both, grid based filters exhibit a theoretical advantage in terms of convergence robustness.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128628738","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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