Pub Date : 2009-06-23DOI: 10.1109/WIOPT.2009.5291619
W. Saad, Zhu Han, T. Başar, M. Debbah, A. Hjørungnes
Cooperation between wireless network nodes is a promising technique for improving the physical layer security of wireless transmission, in terms of secrecy capacity, in the presence of multiple eavesdroppers. While existing physical layer security literature answered the question “what are the link-level secrecy capacity gains from cooperation?”, this paper attempts to answer the question of “how to achieve those gains in a practical decentralized wireless network and in the presence of a secrecy capacity cost for information exchange?”. For this purpose, we model the physical layer security cooperation problem as a coalitional game with non-transferable utility and propose a distributed algorithm for coalition formation. Through the proposed algorithm, the wireless users can autonomously cooperate and self-organize into disjoint independent coalitions, while maximizing their secrecy capacity taking into account the security costs during information exchange. We analyze the resulting coalitional structures, discuss their properties, and study how the users can self-adapt the network topology to environmental changes such as mobility. Simulation results show that the proposed algorithm allows the users to cooperate and self-organize while improving the average secrecy capacity per user up to 25.32% relative to the non-cooperative case.
{"title":"Physical layer security: Coalitional games for distributed cooperation","authors":"W. Saad, Zhu Han, T. Başar, M. Debbah, A. Hjørungnes","doi":"10.1109/WIOPT.2009.5291619","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291619","url":null,"abstract":"Cooperation between wireless network nodes is a promising technique for improving the physical layer security of wireless transmission, in terms of secrecy capacity, in the presence of multiple eavesdroppers. While existing physical layer security literature answered the question “what are the link-level secrecy capacity gains from cooperation?”, this paper attempts to answer the question of “how to achieve those gains in a practical decentralized wireless network and in the presence of a secrecy capacity cost for information exchange?”. For this purpose, we model the physical layer security cooperation problem as a coalitional game with non-transferable utility and propose a distributed algorithm for coalition formation. Through the proposed algorithm, the wireless users can autonomously cooperate and self-organize into disjoint independent coalitions, while maximizing their secrecy capacity taking into account the security costs during information exchange. We analyze the resulting coalitional structures, discuss their properties, and study how the users can self-adapt the network topology to environmental changes such as mobility. Simulation results show that the proposed algorithm allows the users to cooperate and self-organize while improving the average secrecy capacity per user up to 25.32% relative to the non-cooperative case.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"61 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120854425","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291567
Kostas Stamatiou, F. Rossetto, M. Haenggi, T. Javidi, J. Zeidler, M. Zorzi
We consider a network where each route comprises a backlogged source, a number of relays and a destination at a finite distance. The locations of the sources and the relays are realizations of independent Poisson point processes. Given that the nodes observe a TDMA/ALOHA MAC protocol, our objective is to determine the number of relays and their placement such that the mean end-to-end delay in a typical route of the network is minimized.We first study an idealistic network model where all routes have the same number of hops, the same distance per hop and their own dedicated relays. Combining tools from queueing theory and stochastic geometry, we provide a precise characterization of the mean end-to-end delay. We find that the delay is minimized if the first hop is much longer than the remaining hops and that the optimal number of hops scales sublinearly with the source-destination distance. Simulating the original network scenario reveals that the analytical results are accurate, provided that the density of the relay process is sufficiently large. We conclude that, given the considered MAC protocol, our analysis provides a delay-minimizing routing strategy for random, multihop networks involving a small number of hops.
{"title":"A delay-minimizing routing strategy for wireless multi-hop networks","authors":"Kostas Stamatiou, F. Rossetto, M. Haenggi, T. Javidi, J. Zeidler, M. Zorzi","doi":"10.1109/WIOPT.2009.5291567","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291567","url":null,"abstract":"We consider a network where each route comprises a backlogged source, a number of relays and a destination at a finite distance. The locations of the sources and the relays are realizations of independent Poisson point processes. Given that the nodes observe a TDMA/ALOHA MAC protocol, our objective is to determine the number of relays and their placement such that the mean end-to-end delay in a typical route of the network is minimized.We first study an idealistic network model where all routes have the same number of hops, the same distance per hop and their own dedicated relays. Combining tools from queueing theory and stochastic geometry, we provide a precise characterization of the mean end-to-end delay. We find that the delay is minimized if the first hop is much longer than the remaining hops and that the optimal number of hops scales sublinearly with the source-destination distance. Simulating the original network scenario reveals that the analytical results are accurate, provided that the density of the relay process is sufficiently large. We conclude that, given the considered MAC protocol, our analysis provides a delay-minimizing routing strategy for random, multihop networks involving a small number of hops.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"48 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120943081","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291634
Neeraj Jaggi, K. Kar
Sensor networks have major applications in environmental monitoring, relief operations, surveillance, health-care and defense. Future sensor networks would comprise of sensing devices with energy harvesting capabilities from renewable energy sources such as solar power. Multiple sensor nodes deployed in the region of interest would collaborate to achieve a global objective, such as detection of application specific events. This paper focuses on the design of efficient algorithms for multi-sensor activation in order to optimize the overall event detection probability. The recharge-discharge dynamics of the individual rechargeable sensor nodes, along with temporally correlated nature of event occurrences makes the optimal multi-sensor event detection question very challenging. We formulate the dynamic multi-sensor event detection question in a stochastic optimization framework, and design efficient sensor activation algorithms. Particularly, we analyze certain classes of threshold activation policies and show that they achieve near-optimal performance when the threshold is chosen carefully. Specifically, we show that a time-invariant threshold policy, which attempts to maintain a fixed number (appropriately chosen) of sensors active at all times, is optimal in absence of temporal correlations. Moreover, the same energy-balancing time-invariant threshold policy approaches optimality in presence of temporal correlations as well, albeit under certain limiting assumptions. Through simulation studies, we compare the performance of this time-invariant policy with energy-balancing correlation-dependent policies, and observe that although the latter perform better, the performance difference is rather small.
{"title":"Multi-sensor event detection under temporal correlations with renewable energy sources","authors":"Neeraj Jaggi, K. Kar","doi":"10.1109/WIOPT.2009.5291634","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291634","url":null,"abstract":"Sensor networks have major applications in environmental monitoring, relief operations, surveillance, health-care and defense. Future sensor networks would comprise of sensing devices with energy harvesting capabilities from renewable energy sources such as solar power. Multiple sensor nodes deployed in the region of interest would collaborate to achieve a global objective, such as detection of application specific events. This paper focuses on the design of efficient algorithms for multi-sensor activation in order to optimize the overall event detection probability. The recharge-discharge dynamics of the individual rechargeable sensor nodes, along with temporally correlated nature of event occurrences makes the optimal multi-sensor event detection question very challenging. We formulate the dynamic multi-sensor event detection question in a stochastic optimization framework, and design efficient sensor activation algorithms. Particularly, we analyze certain classes of threshold activation policies and show that they achieve near-optimal performance when the threshold is chosen carefully. Specifically, we show that a time-invariant threshold policy, which attempts to maintain a fixed number (appropriately chosen) of sensors active at all times, is optimal in absence of temporal correlations. Moreover, the same energy-balancing time-invariant threshold policy approaches optimality in presence of temporal correlations as well, albeit under certain limiting assumptions. Through simulation studies, we compare the performance of this time-invariant policy with energy-balancing correlation-dependent policies, and observe that although the latter perform better, the performance difference is rather small.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121232200","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291570
Chi-Kin Chau
Random geometric graphs are widely-used for modelling wireless ad hoc networks, where nodes are randomly deployed with each covering a finite region. The fundamental properties of random geometric graphs are often studied in the literature, such as the probability of connectivity and random coverage area. While there are numerous asymptotic results that concern the related scaling laws in very large random geometric graphs, more accurate estimation for the finite cases with moderate-sized networks remains challenging. In this paper, we present a remarkably good approximation relationship for the probability of connectivity and random coverage area between the random geometric graphs induced by circular and square coverage models, under suitable normalisation. We also provide analytical results towards justifying the good approximation relationship. This relationship is then exploited, combining with the results from reliability studies, to obtain more accurate estimation for the probability of connectivity in finite random geometric graphs.
{"title":"Finite random geometric graphs by circular and square coverage","authors":"Chi-Kin Chau","doi":"10.1109/WIOPT.2009.5291570","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291570","url":null,"abstract":"Random geometric graphs are widely-used for modelling wireless ad hoc networks, where nodes are randomly deployed with each covering a finite region. The fundamental properties of random geometric graphs are often studied in the literature, such as the probability of connectivity and random coverage area. While there are numerous asymptotic results that concern the related scaling laws in very large random geometric graphs, more accurate estimation for the finite cases with moderate-sized networks remains challenging. In this paper, we present a remarkably good approximation relationship for the probability of connectivity and random coverage area between the random geometric graphs induced by circular and square coverage models, under suitable normalisation. We also provide analytical results towards justifying the good approximation relationship. This relationship is then exploited, combining with the results from reliability studies, to obtain more accurate estimation for the probability of connectivity in finite random geometric graphs.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125525148","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291614
J. Brehmer, W. Utschick
We consider the problem of bargaining over block fading interference channels, where interaction between players takes place over multiple channel realizations. Based on the assumption that the transmitters have conflicting objectives, we use axiomatic bargaining theory to derive optimal rate allocations in each block. In the setup under consideration, the Nash bargaining solution (NBS) is non-causal, i.e., cannot be implemented in a real-world system. We argue that the invariance axiom is superfluous when bargaining over a rate region. Without the invariance axiom, an equivalent solution follows from the maximization of a sum of utilities under minimum utility constraints. This alternative solution is also non-causal. We propose causal approximations to the optimal solutions. The sum utility solution allows for a more systematic approximation than the NBS. Thus, dropping the invariance axiom makes it possible to choose a solution which can be better approximated. We provide numerical results to illustrate the performance of the proposed solutions.
{"title":"Bargaining over fading interference channels","authors":"J. Brehmer, W. Utschick","doi":"10.1109/WIOPT.2009.5291614","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291614","url":null,"abstract":"We consider the problem of bargaining over block fading interference channels, where interaction between players takes place over multiple channel realizations. Based on the assumption that the transmitters have conflicting objectives, we use axiomatic bargaining theory to derive optimal rate allocations in each block. In the setup under consideration, the Nash bargaining solution (NBS) is non-causal, i.e., cannot be implemented in a real-world system. We argue that the invariance axiom is superfluous when bargaining over a rate region. Without the invariance axiom, an equivalent solution follows from the maximization of a sum of utilities under minimum utility constraints. This alternative solution is also non-causal. We propose causal approximations to the optimal solutions. The sum utility solution allows for a more systematic approximation than the NBS. Thus, dropping the invariance axiom makes it possible to choose a solution which can be better approximated. We provide numerical results to illustrate the performance of the proposed solutions.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117227028","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291639
M. Kodialam, W. Lau, T. Nandagopal
Given a large set of RFID tags, we are interested in determining the categories of tags that are present in the shortest time possible. Since there can be more than one tag present in a particular category, pure randomized strategies that rely on resolving individual tags are very inefficient. Instead, we rely on a pseudo-random strategy that utilizes a uniform hash function to accurately identify all t categories present among a given set of ψ tags with high probability. We propose two algorithms: (a) a single frame algorithm that determines the optimal frame size, and (b) a probabilistic version where the frame size is fixed, and we select the probability to minimize the number of frames needed for identification. Both of these algorithms run in time linear to the number of categories present, t. We show that our approach significantly outperforms existing algorithms for category identification. The performance of our algorithms is within a constant factor of the lower bound.
{"title":"Identifying RFID tag categories in linear time","authors":"M. Kodialam, W. Lau, T. Nandagopal","doi":"10.1109/WIOPT.2009.5291639","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291639","url":null,"abstract":"Given a large set of RFID tags, we are interested in determining the categories of tags that are present in the shortest time possible. Since there can be more than one tag present in a particular category, pure randomized strategies that rely on resolving individual tags are very inefficient. Instead, we rely on a pseudo-random strategy that utilizes a uniform hash function to accurately identify all t categories present among a given set of ψ tags with high probability. We propose two algorithms: (a) a single frame algorithm that determines the optimal frame size, and (b) a probabilistic version where the frame size is fixed, and we select the probability to minimize the number of frames needed for identification. Both of these algorithms run in time linear to the number of categories present, t. We show that our approach significantly outperforms existing algorithms for category identification. The performance of our algorithms is within a constant factor of the lower bound.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128443779","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291602
Yan Chen, V. Lau, Shunqing Zhang, Peiliang Qiu
Cognitive and cooperative technologies are two core components in the design of next generation wireless networks. One key issue associated with cognitive transmission is the inefficient spectrum sharing of the secondary system, especially for secondary communications separated by long distance. To boost the spectrum sharing efficiency, cognitive multi-relay system appears to be an attractive solution for the cognitive transmission systems. In this paper, we consider a cognitive multi-relay (CMR) system and propose a novel CMR buffered decode-and-forward protocol that exploit the buffers in the source and each relay node. Moreover, we derive the closed-form average end-to-end delay and the stability region by exploiting the birth-death nature of the queue dynamics and the methods of state aggregation and queue dominance. Comparing with the baseline protocols through analytical and numerical results, the proposed CMR-BDF scheme can dynamically adjust the cognitive transmission to exploit the spatial PU burstiness while simultaneously benefits from the advantage of double-sided selection diversity in both the source-relay and relay-destination interfaces.
{"title":"Exploiting buffers in cognitive multi-relay systems for delay-sensitive applications","authors":"Yan Chen, V. Lau, Shunqing Zhang, Peiliang Qiu","doi":"10.1109/WIOPT.2009.5291602","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291602","url":null,"abstract":"Cognitive and cooperative technologies are two core components in the design of next generation wireless networks. One key issue associated with cognitive transmission is the inefficient spectrum sharing of the secondary system, especially for secondary communications separated by long distance. To boost the spectrum sharing efficiency, cognitive multi-relay system appears to be an attractive solution for the cognitive transmission systems. In this paper, we consider a cognitive multi-relay (CMR) system and propose a novel CMR buffered decode-and-forward protocol that exploit the buffers in the source and each relay node. Moreover, we derive the closed-form average end-to-end delay and the stability region by exploiting the birth-death nature of the queue dynamics and the methods of state aggregation and queue dominance. Comparing with the baseline protocols through analytical and numerical results, the proposed CMR-BDF scheme can dynamically adjust the cognitive transmission to exploit the spatial PU burstiness while simultaneously benefits from the advantage of double-sided selection diversity in both the source-relay and relay-destination interfaces.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134090316","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291583
Pierre Coucheney, Corinne Touati, B. Gaujal
Most of recent mobile equipment now supports different network technologies (WiFi, WiMax, LTE, Bluetooth and such like). Meanwhile, network operators offer services through these different technologies. The superposition of the different technologies (using different frequency band) increases the potential throughput of the system and hence global performance.
{"title":"Different dynamics for optimal association in heterogeneous wireless networks","authors":"Pierre Coucheney, Corinne Touati, B. Gaujal","doi":"10.1109/WIOPT.2009.5291583","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291583","url":null,"abstract":"Most of recent mobile equipment now supports different network technologies (WiFi, WiMax, LTE, Bluetooth and such like). Meanwhile, network operators offer services through these different technologies. The superposition of the different technologies (using different frequency band) increases the potential throughput of the system and hence global performance.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127699470","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291585
D. Lucani, F. Fitzek, M. Médard, M. Stojanovic
We propose a linear network coding scheme to disseminate a finite number of data packets in arbitrary networks. The setup assumes a packet erasure channel, slotted time, and that nodes cannot transmit and receive information simultaneously. The dissemination process is completed when all terminals can decode the original data packets. We also assume a perfect knowledge of the information at each of the nodes, but not necessarily a perfect knowledge of the channel. A centralized controller decides which nodes should transmit, to what set of receiver nodes, and what information should be broadcasted. We show that the problem can be thought of as a scheduling problem, which is hard to solve. Thus, we consider the use of a greedy algorithm that only takes into account the current state of the system to make a decision. The proposed algorithm tries to maximize the impact on the network at each slot, i.e. maximize the number of nodes that will benefit from the coded packet sent by each active transmitter. We show that our scheme is considerably better, in terms of the number of slots to complete transmission, than schemes that choose the node with more information as the transmitter at every time slot.
{"title":"Network coding for data dissemination: it is not what you know, but what your neighbors don't know","authors":"D. Lucani, F. Fitzek, M. Médard, M. Stojanovic","doi":"10.1109/WIOPT.2009.5291585","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291585","url":null,"abstract":"We propose a linear network coding scheme to disseminate a finite number of data packets in arbitrary networks. The setup assumes a packet erasure channel, slotted time, and that nodes cannot transmit and receive information simultaneously. The dissemination process is completed when all terminals can decode the original data packets. We also assume a perfect knowledge of the information at each of the nodes, but not necessarily a perfect knowledge of the channel. A centralized controller decides which nodes should transmit, to what set of receiver nodes, and what information should be broadcasted. We show that the problem can be thought of as a scheduling problem, which is hard to solve. Thus, we consider the use of a greedy algorithm that only takes into account the current state of the system to make a decision. The proposed algorithm tries to maximize the impact on the network at each slot, i.e. maximize the number of nodes that will benefit from the coded packet sent by each active transmitter. We show that our scheme is considerably better, in terms of the number of slots to complete transmission, than schemes that choose the node with more information as the transmitter at every time slot.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116758805","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 : 2009-06-23DOI: 10.1109/WIOPT.2009.5291598
M. Elnaggar, A. Kempf
We define a generalized entropy that measures the evenness of the distribution of the real non-negative elements of a multiset X . The approach is to determine a comparison multiset R which is in a precise sense equivalent to X and which contains only one distinct positive element, whose multiplicity k then yields the desired measure. To this end, R and X are considered equivalent if their p− and q− norms coincide. Accordingly, we define k and its logarithm to be the effective cardinality and the generalized entropy of X respectively, of the order p,q . We show that the new entropy measure is a generalization of the Rényi entropy after proper normalization of the multiset elements. We also discuss some properties of the proposed measure.
{"title":"On a generic entropy measure in physics and information","authors":"M. Elnaggar, A. Kempf","doi":"10.1109/WIOPT.2009.5291598","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291598","url":null,"abstract":"We define a generalized entropy that measures the evenness of the distribution of the real non-negative elements of a multiset X . The approach is to determine a comparison multiset R which is in a precise sense equivalent to X and which contains only one distinct positive element, whose multiplicity k then yields the desired measure. To this end, R and X are considered equivalent if their p− and q− norms coincide. Accordingly, we define k and its logarithm to be the effective cardinality and the generalized entropy of X respectively, of the order p,q . We show that the new entropy measure is a generalization of the Rényi entropy after proper normalization of the multiset elements. We also discuss some properties of the proposed measure.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116862045","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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