Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447101
Ron Yadgar, A. Cohen, Omer Gurewitz
The completion time for the dissemination of information to all nodes in a network plays a critical role in the design and analysis of communication systems. In this work, we analyse the completion time of data dissemination in a shared loss (i.e., unreliable links) multicast tree, at the limit of large number of nodes. Specifically, analytic expressions for upper and lower bounds on the expected completion time are provided, and, in particular, it is shown that both these bounds scale as α log n, where n is the number of nodes. Clearly, the completion time is determined by the last end user who receives the message, that is, a maximum over all arrival times. We derive asymptotic bounds on the expectation of this maximum and use them to obtain tight bounds on the completion time. The results are validated by simulations and numerical analysis.
{"title":"Scaling laws for reliable data dissemination in shared loss multicast trees","authors":"Ron Yadgar, A. Cohen, Omer Gurewitz","doi":"10.1109/ALLERTON.2015.7447101","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447101","url":null,"abstract":"The completion time for the dissemination of information to all nodes in a network plays a critical role in the design and analysis of communication systems. In this work, we analyse the completion time of data dissemination in a shared loss (i.e., unreliable links) multicast tree, at the limit of large number of nodes. Specifically, analytic expressions for upper and lower bounds on the expected completion time are provided, and, in particular, it is shown that both these bounds scale as α log n, where n is the number of nodes. Clearly, the completion time is determined by the last end user who receives the message, that is, a maximum over all arrival times. We derive asymptotic bounds on the expectation of this maximum and use them to obtain tight bounds on the completion time. The results are validated by simulations and numerical analysis.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"215 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":"131964762","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.2015.7447014
Kianoush Hosseini, Wei Yu, R. Adve
A base-station (BS) equipped with multiple antennas can use its spatial dimensions in three ways: (1) serve multiple users to achieve a multiplexing gain, (2) provide diversity to its users, and/or (3) null interference at a chosen subset of out-of-cell users. The main contribution of this paper is to answer the following question: what is the optimal balance between the three competing benefits of multiplexing, diversity and interference nulling? We answer this question in the context of the downlink of a cellular network in which each user chooses its best serving BS, and requests nearby interfering BSs for interference nulling. BSs are equipped with a large number of antennas, serve multiple single-antenna users using zero-forcing beamforming and equal power assignment, and null interference at a subset of out-of-cell users. The remaining spatial dimensions provide transmit diversity. We assume perfect channel state information at the BSs and users. Utilizing tools from stochastic geometry, we show that, surprisingly, to maximize the per-BS ergodic sum rate, at the optimal allocation of spatial resources, interference nulling does not bring tangible benefit. A close-to-optimal strategy is to use none of the spatial resources for interference nulling, while reserving 60% of spatial resources for achieving multiplexing and the rest for providing diversity.
{"title":"Optimizing large-scale MIMO cellular downlink: Multiplexing, diversity, or interference nulling?","authors":"Kianoush Hosseini, Wei Yu, R. Adve","doi":"10.1109/ALLERTON.2015.7447014","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447014","url":null,"abstract":"A base-station (BS) equipped with multiple antennas can use its spatial dimensions in three ways: (1) serve multiple users to achieve a multiplexing gain, (2) provide diversity to its users, and/or (3) null interference at a chosen subset of out-of-cell users. The main contribution of this paper is to answer the following question: what is the optimal balance between the three competing benefits of multiplexing, diversity and interference nulling? We answer this question in the context of the downlink of a cellular network in which each user chooses its best serving BS, and requests nearby interfering BSs for interference nulling. BSs are equipped with a large number of antennas, serve multiple single-antenna users using zero-forcing beamforming and equal power assignment, and null interference at a subset of out-of-cell users. The remaining spatial dimensions provide transmit diversity. We assume perfect channel state information at the BSs and users. Utilizing tools from stochastic geometry, we show that, surprisingly, to maximize the per-BS ergodic sum rate, at the optimal allocation of spatial resources, interference nulling does not bring tangible benefit. A close-to-optimal strategy is to use none of the spatial resources for interference nulling, while reserving 60% of spatial resources for achieving multiplexing and the rest for providing diversity.","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":"120997736","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.2015.7447186
A. Makowski, Osman Yağan
We consider the Eschenauer-Gligor key predistribution scheme under the condition of partial visibility with i.i.d. on-off links between pairs of nodes. This situation is modeled as the intersection of two random graphs, namely a random key graph and an Erdös-Rényi (ER) graph. For this class of composite random graphs we give various improvements on a recent result by Yağan [17] concerning zero-one laws for the absence of isolated nodes.
{"title":"On the Eschenauer-Gligor key predistribution scheme under on-off communication channels: The absence of isolated nodes","authors":"A. Makowski, Osman Yağan","doi":"10.1109/ALLERTON.2015.7447186","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447186","url":null,"abstract":"We consider the Eschenauer-Gligor key predistribution scheme under the condition of partial visibility with i.i.d. on-off links between pairs of nodes. This situation is modeled as the intersection of two random graphs, namely a random key graph and an Erdös-Rényi (ER) graph. For this class of composite random graphs we give various improvements on a recent result by Yağan [17] concerning zero-one laws for the absence of isolated nodes.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"7 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":"130916127","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.2015.7447137
Kyu Seob Kim, Chih-Ping Li, I. Kadota, E. Modiano
In this paper we consider a wireless network composed of a base station and a number of clients, with the goal of scheduling real-time traffic. Even though this problem has been extensively studied in the literature, the impact of delayed acknowledgment has not been assessed. Delayed feedback is of increasing importance in systems where the round trip delay is much greater than the packet transmission time, and it has a significant effect on the scheduling decisions and network performance. Previous work considered the problem of scheduling real-time traffic with instantaneous feedback and without feedback. In this work, we address the general case of delayed feedback and use Dynamic Programming to characterize the optimal scheduling policy. An optimal algorithm that fulfills any feasible minimum delivery ratio requirements is proposed. Moreover, we develop a low-complexity suboptimal heuristic algorithm which is suitable for platforms with low computational power. Both algorithms are evaluated through simulations.
{"title":"Optimal scheduling of real-time traffic in wireless networks with delayed feedback","authors":"Kyu Seob Kim, Chih-Ping Li, I. Kadota, E. Modiano","doi":"10.1109/ALLERTON.2015.7447137","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447137","url":null,"abstract":"In this paper we consider a wireless network composed of a base station and a number of clients, with the goal of scheduling real-time traffic. Even though this problem has been extensively studied in the literature, the impact of delayed acknowledgment has not been assessed. Delayed feedback is of increasing importance in systems where the round trip delay is much greater than the packet transmission time, and it has a significant effect on the scheduling decisions and network performance. Previous work considered the problem of scheduling real-time traffic with instantaneous feedback and without feedback. In this work, we address the general case of delayed feedback and use Dynamic Programming to characterize the optimal scheduling policy. An optimal algorithm that fulfills any feasible minimum delivery ratio requirements is proposed. Moreover, we develop a low-complexity suboptimal heuristic algorithm which is suitable for platforms with low computational power. Both algorithms are evaluated through simulations.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"2 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":"134416916","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.2015.7447184
O. Shmuel, A. Cohen, Omer Gurewitz
Consider a multiple access channel with a large number of users. In most practical scenarios, due to decoding complexity, users are not scheduled together, and only one user may transmit at any given time. In this work, we analyze the delay and QoS of such systems under a specific, opportunistic and distributed scheduling algorithm, in which each user, at the beginning of each slot, estimates its channel gain and transmits only if it is greater than a given threshold. Specifically, we analyze the performance while assuming the users are not necessarily fully backlogged, focusing on the queueing problem and, especially, on the strong dependence between the queues. We first adopt the celebrated model of Ephremides and Zhu to give new results on the convergence of the probability of collision to its average value (as the number of users grows), and hence for the ensuing system performance metrics, such as throughput and delay. We then utilize this finding to suggest a much simpler approximate model, which accurately describes the system behaviour when the number of users is large. The system performance as predicted by the approximate models shows excellent agreement with simulation results.
{"title":"Performance analysis for multi-user systems under distributed opportunistic scheduling","authors":"O. Shmuel, A. Cohen, Omer Gurewitz","doi":"10.1109/ALLERTON.2015.7447184","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447184","url":null,"abstract":"Consider a multiple access channel with a large number of users. In most practical scenarios, due to decoding complexity, users are not scheduled together, and only one user may transmit at any given time. In this work, we analyze the delay and QoS of such systems under a specific, opportunistic and distributed scheduling algorithm, in which each user, at the beginning of each slot, estimates its channel gain and transmits only if it is greater than a given threshold. Specifically, we analyze the performance while assuming the users are not necessarily fully backlogged, focusing on the queueing problem and, especially, on the strong dependence between the queues. We first adopt the celebrated model of Ephremides and Zhu to give new results on the convergence of the probability of collision to its average value (as the number of users grows), and hence for the ensuing system performance metrics, such as throughput and delay. We then utilize this finding to suggest a much simpler approximate model, which accurately describes the system behaviour when the number of users is large. The system performance as predicted by the approximate models shows excellent agreement with simulation results.","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":"129813200","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.2015.7447065
Y. Altug, H. Poor, S. Verdú
Variable-length channel codes over discrete memoryless channels subject to probabilistic delay guarantees are examined in the non-vanishing error probability regime. Fundamental limits of these codes in several different settings, which depend on the availability of noiseless feedback and a termination option, are investigated. In stark contrast with average delay guarantees, the first-order terms of the fundamental limits turn out to be the same as those for fixed-length codes in all cases. Further, feedback is shown to improve the second-order term, even in the absence of a termination option.
{"title":"Variable-length channel codes with probabilistic delay guarantees","authors":"Y. Altug, H. Poor, S. Verdú","doi":"10.1109/ALLERTON.2015.7447065","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447065","url":null,"abstract":"Variable-length channel codes over discrete memoryless channels subject to probabilistic delay guarantees are examined in the non-vanishing error probability regime. Fundamental limits of these codes in several different settings, which depend on the availability of noiseless feedback and a termination option, are investigated. In stark contrast with average delay guarantees, the first-order terms of the fundamental limits turn out to be the same as those for fixed-length codes in all cases. Further, feedback is shown to improve the second-order term, even in the absence of a termination option.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"11 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":"114905568","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}
We give a simple information theoretic proof that the public-coin randomized communication complexity of the greater-than function is Ω(logn) for bit-strings of length n.
{"title":"On the communication complexity of greater-than","authors":"Sivaramakrishnan Natarajan Ramamoorthy, Makrand Sinha","doi":"10.1109/ALLERTON.2015.7447037","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447037","url":null,"abstract":"We give a simple information theoretic proof that the public-coin randomized communication complexity of the greater-than function is Ω(logn) for bit-strings of length n.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"221 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":"116339874","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.2015.7447006
S. Dhople, Swaroop S. Guggilam, Y. Chen
This paper explores solutions to linearized power-flow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. We prove that for lossless networks, the voltage profile where the real part of the perturbation is suppressed satisfies active-power balance in the original nonlinear system of equations. This result motivates the development of approximate solutions that improve over conventional DC power-flow approximations, since the model includes ZIP loads. For distribution networks that only contain ZIP loads in addition to a slack bus, we recover a linear relationship between the approximate voltage profile and the constant-current component of the loads and the nodal active-and reactive-power injections.
{"title":"Linear approximations to AC power flow in rectangular coordinates","authors":"S. Dhople, Swaroop S. Guggilam, Y. Chen","doi":"10.1109/ALLERTON.2015.7447006","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447006","url":null,"abstract":"This paper explores solutions to linearized power-flow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. We prove that for lossless networks, the voltage profile where the real part of the perturbation is suppressed satisfies active-power balance in the original nonlinear system of equations. This result motivates the development of approximate solutions that improve over conventional DC power-flow approximations, since the model includes ZIP loads. For distribution networks that only contain ZIP loads in addition to a slack bus, we recover a linear relationship between the approximate voltage profile and the constant-current component of the loads and the nodal active-and reactive-power injections.","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":"114448111","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.2015.7447108
Maryam Hosseini, N. Santhanam
We obtain a condition that is both necessary and sufficient to characterize strong universal compressibility (in the average sense) of sequences generated by iid sampling from a collection cP of distributions over a countably infinite alphabet. Contrary to the worst case regret formulation of universal compression, finite single letter (average case) redundancy of cP does not automatically imply that the expected redundancy of describing length-n strings sampled iid from cP grows sublinearly with n. Instead, we prove that asymptotic per-symbol redundancy of universally compressing length-n iid sequences from cP is characterized by how well the tails of their single letter marginals can be universally described, and we formalize the later as the tail-redundancy of cP.
{"title":"Single letter characterization of average-case strong redundancy of compressing memoryless sequences","authors":"Maryam Hosseini, N. Santhanam","doi":"10.1109/ALLERTON.2015.7447108","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447108","url":null,"abstract":"We obtain a condition that is both necessary and sufficient to characterize strong universal compressibility (in the average sense) of sequences generated by iid sampling from a collection cP of distributions over a countably infinite alphabet. Contrary to the worst case regret formulation of universal compression, finite single letter (average case) redundancy of cP does not automatically imply that the expected redundancy of describing length-n strings sampled iid from cP grows sublinearly with n. Instead, we prove that asymptotic per-symbol redundancy of universally compressing length-n iid sequences from cP is characterized by how well the tails of their single letter marginals can be universally described, and we formalize the later as the tail-redundancy of cP.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"12 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":"114698660","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.2015.7447167
N. Janakiraman, Santosh K. Emmadi, K. Narayanan, K. Ramchandran
We show that the recently proposed Fast Fourier Aliasing-based Sparse Transform (FFAST) algorithm for computing the Discrete Fourier Transform (DFT) [1] of signals with a sparse DFT is equivalent to iterative hard decision decoding of product codes. This connection is used to derive the thresholds for sparse recovery based on a recent analysis by Justensen [2] for computing thresholds for product codes. We first extend Justesen's analysis to d-dimensional product codes and compute thresholds for the FFAST algorithm based on this. Additionally, this connection also allows us to analyze the performance of the FFAST algorithm under a burst sparsity model in addition to the uniformly random sparsity model which was assumed in prior work [1].
{"title":"Exploring connections between Sparse Fourier Transform computation and decoding of product codes","authors":"N. Janakiraman, Santosh K. Emmadi, K. Narayanan, K. Ramchandran","doi":"10.1109/ALLERTON.2015.7447167","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447167","url":null,"abstract":"We show that the recently proposed Fast Fourier Aliasing-based Sparse Transform (FFAST) algorithm for computing the Discrete Fourier Transform (DFT) [1] of signals with a sparse DFT is equivalent to iterative hard decision decoding of product codes. This connection is used to derive the thresholds for sparse recovery based on a recent analysis by Justensen [2] for computing thresholds for product codes. We first extend Justesen's analysis to d-dimensional product codes and compute thresholds for the FFAST algorithm based on this. Additionally, this connection also allows us to analyze the performance of the FFAST algorithm under a burst sparsity model in addition to the uniformly random sparsity model which was assumed in prior work [1].","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"28 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":"114804488","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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