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.2009.5291590
Sara Akbarzadeh, L. Cottatellucci, C. Bonnet
We considered a dense interference network with a large number (K → ∞) of transmitter-receiver pairs. Each transmitter is endowed with a finite buffer and accepts packets from an arrival process. Each transmitter-receiver link is a fading vector channel with N diversity paths whose statistics are described by a Markov chain. We investigate distributed algorithms for joint admission control, rate and power allocation aiming at maximizing the individual throughput defined as the average information rate successfully received. The decisions are based on the statistical knowledge of the channel and buffer states of the other communication pairs and on the exact knowledge of their own channel and buffer states. In the case of a finite number of communication pairs this problem is computationally extremely intensive with an exponential complexity in the number of users. Assuming that K,N → ∞ with constant ratio the algorithm complexity becomes substantially independent of the number of active communications and grows with the groups of users having distinct asymptotic channel statistics. The cross-layer design is investigated for different kind of decoders at the receiver. The benefits of a cross layer approach compared to a resource allocation ignoring the states of the queues are assessed. The performance loss due to the use of policies designed for asymptotic conditions and applied to networks with a finite number of active communications is studied.
{"title":"Low complexity cross-layer design for dense interference networks","authors":"Sara Akbarzadeh, L. Cottatellucci, C. Bonnet","doi":"10.1109/WIOPT.2009.5291590","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291590","url":null,"abstract":"We considered a dense interference network with a large number (K → ∞) of transmitter-receiver pairs. Each transmitter is endowed with a finite buffer and accepts packets from an arrival process. Each transmitter-receiver link is a fading vector channel with N diversity paths whose statistics are described by a Markov chain. We investigate distributed algorithms for joint admission control, rate and power allocation aiming at maximizing the individual throughput defined as the average information rate successfully received. The decisions are based on the statistical knowledge of the channel and buffer states of the other communication pairs and on the exact knowledge of their own channel and buffer states. In the case of a finite number of communication pairs this problem is computationally extremely intensive with an exponential complexity in the number of users. Assuming that K,N → ∞ with constant ratio the algorithm complexity becomes substantially independent of the number of active communications and grows with the groups of users having distinct asymptotic channel statistics. The cross-layer design is investigated for different kind of decoders at the receiver. The benefits of a cross layer approach compared to a resource allocation ignoring the states of the queues are assessed. The performance loss due to the use of policies designed for asymptotic conditions and applied to networks with a finite number of active communications is studied.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"163 8 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":"129281679","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.2009.5291593
C. Yeung, K. Y. Wong
We study a model of transportation networks with nonlinear elements which represent local shortage of resources. Frustration arises from competition among the nodes to become satisfied. When the initial resources are uniform, algorithmically hard regimes emerge when the average availability of resources increases. These regimes are characterized by discrete fractions of satisfied nodes, resembling the Devil's staircase. Behavior similar to those in the vertex cover or close packing problems are found. When initial resources are bimodally distributed, such algorithmically hard regimes also emerge when the fraction of rich nodes increases.
{"title":"Emergence of algorithmically hard phases in transportation networks","authors":"C. Yeung, K. Y. Wong","doi":"10.1109/WIOPT.2009.5291593","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291593","url":null,"abstract":"We study a model of transportation networks with nonlinear elements which represent local shortage of resources. Frustration arises from competition among the nodes to become satisfied. When the initial resources are uniform, algorithmically hard regimes emerge when the average availability of resources increases. These regimes are characterized by discrete fractions of satisfied nodes, resembling the Devil's staircase. Behavior similar to those in the vertex cover or close packing problems are found. When initial resources are bimodally distributed, such algorithmically hard regimes also emerge when the fraction of rich nodes increases.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"50 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":"130940234","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.2009.5291601
P. Simoens, B. Vankeirsbilck, F. Ali, L. Deboosere, F. Turck, B. Dhoedt, P. Demeester, R. T. Duran, C. Desset
In thin client computing, applications are executed on a network server instead of on the user terminal. Since the amount of processing at the terminal is reduced, thin clients are potentially energy efficient devices. However, a network connection between client and server is required for the transmission of user input and display updates. The energy needed for this intense network communication might undo or even exceed the power savings achieved by the reduction in client-side processing. In this paper, we present experimental results on power efficiency of the wireless platform on the thin client in case of thin client traffic. The discussion is focused on VNC-RFB, a widespread thin client protocol, over an IEEE 802.11 link in three typical user scenarios. The results indicate that a cross-layer approach between application and wireless link layer could potentially lead to important power savings.
{"title":"Characterization of power consumption in thin clients due to protocol data transmission over IEEE 802.11","authors":"P. Simoens, B. Vankeirsbilck, F. Ali, L. Deboosere, F. Turck, B. Dhoedt, P. Demeester, R. T. Duran, C. Desset","doi":"10.1109/WIOPT.2009.5291601","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291601","url":null,"abstract":"In thin client computing, applications are executed on a network server instead of on the user terminal. Since the amount of processing at the terminal is reduced, thin clients are potentially energy efficient devices. However, a network connection between client and server is required for the transmission of user input and display updates. The energy needed for this intense network communication might undo or even exceed the power savings achieved by the reduction in client-side processing. In this paper, we present experimental results on power efficiency of the wireless platform on the thin client in case of thin client traffic. The discussion is focused on VNC-RFB, a widespread thin client protocol, over an IEEE 802.11 link in three typical user scenarios. The results indicate that a cross-layer approach between application and wireless link layer could potentially lead to important power savings.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"3 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":"114475696","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.2009.5291637
Honghai Zhang, S. Rangarajan
We consider the problem of maximizing the weighted sum data rate in multi-cell and multi-carrier wireless data systems in the presence of interference. We present a scheme that jointly considers load balancing, user scheduling, and interference mitigation to improve the system performance. Our proposed scheme iteratively applies two processes. The first process solves the sub-problem of load balancing and user scheduling while fixing the power allocation of each BS (and thus fixing the interference). We prove that this sub-problem is NP-hard, and devise a 1/2-approximation algorithm to solve the problem. We also consider an extended model capturing finite queue size and propose a 1/2-approximation algorithm under this model. The second process solves the problem of interference mitigation assuming fixed load balancing and user scheduling. We develop a local-improvement based algorithm to solve this problem. Via simulations, we demonstrate that our joint scheme improves both average system throughput and fairness significantly. Compared to the scheme with fixed user-BS association and 1/3 frequency reuse, the lowest 10% cell-edge users obtain more than 60% performance improvement and 90%of users enjoy more than 30%throughput improvement.
{"title":"Joint load balancing, scheduling, and interference mitigation in multi-cell and multi-carrier wireless data systems","authors":"Honghai Zhang, S. Rangarajan","doi":"10.1109/WIOPT.2009.5291637","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291637","url":null,"abstract":"We consider the problem of maximizing the weighted sum data rate in multi-cell and multi-carrier wireless data systems in the presence of interference. We present a scheme that jointly considers load balancing, user scheduling, and interference mitigation to improve the system performance. Our proposed scheme iteratively applies two processes. The first process solves the sub-problem of load balancing and user scheduling while fixing the power allocation of each BS (and thus fixing the interference). We prove that this sub-problem is NP-hard, and devise a 1/2-approximation algorithm to solve the problem. We also consider an extended model capturing finite queue size and propose a 1/2-approximation algorithm under this model. The second process solves the problem of interference mitigation assuming fixed load balancing and user scheduling. We develop a local-improvement based algorithm to solve this problem. Via simulations, we demonstrate that our joint scheme improves both average system throughput and fairness significantly. Compared to the scheme with fixed user-BS association and 1/3 frequency reuse, the lowest 10% cell-edge users obtain more than 60% performance improvement and 90%of users enjoy more than 30%throughput improvement.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"23 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":"114222408","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.2009.5291616
Xusheng Sun, E. Coyle
In clustered networks of wireless sensor motes, each mote collects noisy observations of the environment, quantizes these observations into a local estimate of finite length, and forwards them through one or more noisy wireless channels to the Cluster Head (CH). The measurement noise is assumed to be zero-mean and have finite variance. Each wireless hop is assumed to be a Binary Symmetric Channel (BSC) with a known crossover probability. We propose a novel scheme that uses dithered quantization and channel compensation to ensure that each motes' local estimate received by the CH is unbiased. The CH then fuses these unbiased local estimates into a global one using a Best Linear Unbiased Estimator (BLUE). The energy allocation problem at each mote and among different sensor motes are also discussed. Simulation results show that the proposed scheme can achieve much smaller mean square error (MSE) than two other common schemes while using the same amount of energy. The sensitivity of the proposed scheme to errors in estimates of the crossover probability of the BSC channel is studied by both analysis and simulation.
{"title":"Quantization, channel compensation, and energy allocation for estimation in wireless sensor networks","authors":"Xusheng Sun, E. Coyle","doi":"10.1109/WIOPT.2009.5291616","DOIUrl":"https://doi.org/10.1109/WIOPT.2009.5291616","url":null,"abstract":"In clustered networks of wireless sensor motes, each mote collects noisy observations of the environment, quantizes these observations into a local estimate of finite length, and forwards them through one or more noisy wireless channels to the Cluster Head (CH). The measurement noise is assumed to be zero-mean and have finite variance. Each wireless hop is assumed to be a Binary Symmetric Channel (BSC) with a known crossover probability. We propose a novel scheme that uses dithered quantization and channel compensation to ensure that each motes' local estimate received by the CH is unbiased. The CH then fuses these unbiased local estimates into a global one using a Best Linear Unbiased Estimator (BLUE). The energy allocation problem at each mote and among different sensor motes are also discussed. Simulation results show that the proposed scheme can achieve much smaller mean square error (MSE) than two other common schemes while using the same amount of energy. The sensitivity of the proposed scheme to errors in estimates of the crossover probability of the BSC channel is studied by both analysis and simulation.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"31 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":"114279324","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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