Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601034
M. Zoffoli, J. Gibson, M. Chiani
We consider strategies for the lossy transmission of a zero mean Gaussian source over multiple channels. In one strategy, we employ single description coding of the source and duplicate this description over two independent channels. We also consider optimal, no excess joint rate, and no excess marginal rate multiple description coding over two independent channels. These strategies are compared to the traditional approach where a single description is sent over a single channel. The performance measure used for comparison is expected distortion at the receiver, evaluated as a function of the outage probability. We also consider the transmission of a full rate single description over a standard 2times2 MIMO channel using spatial multiplexing and a time-sharing approach to using MD coding over a 2times2 MIMO channel.
{"title":"Source coding diversity and multiplexing strategies for a 2X2 MIMO system","authors":"M. Zoffoli, J. Gibson, M. Chiani","doi":"10.1109/ITA.2008.4601034","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601034","url":null,"abstract":"We consider strategies for the lossy transmission of a zero mean Gaussian source over multiple channels. In one strategy, we employ single description coding of the source and duplicate this description over two independent channels. We also consider optimal, no excess joint rate, and no excess marginal rate multiple description coding over two independent channels. These strategies are compared to the traditional approach where a single description is sent over a single channel. The performance measure used for comparison is expected distortion at the receiver, evaluated as a function of the outage probability. We also consider the transmission of a full rate single description over a standard 2times2 MIMO channel using spatial multiplexing and a time-sharing approach to using MD coding over a 2times2 MIMO channel.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126494890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601033
R. Zakhour, D. Gesbert
An adaptive scheme was introduced in view of optimizing the overall spectral efficiency of a multiuser MIMO wireless broadcast channel where the channel state information at the transmitting base station (CSIT), to be used for user scheduling and beamforming, is acquired over a limited-rate feedback channel. In this scheme, the feedback rate is no longer constant per scheduling period but rather optimized as a function of the time-dependent channel quality seen at the user side. The present paper further refines this idea and elaborates on some of the associated practical concerns.
{"title":"Adaptive feedback rate control in MIMO broadcast systems with user scheduling","authors":"R. Zakhour, D. Gesbert","doi":"10.1109/ITA.2008.4601033","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601033","url":null,"abstract":"An adaptive scheme was introduced in view of optimizing the overall spectral efficiency of a multiuser MIMO wireless broadcast channel where the channel state information at the transmitting base station (CSIT), to be used for user scheduling and beamforming, is acquired over a limited-rate feedback channel. In this scheme, the feedback rate is no longer constant per scheduling period but rather optimized as a function of the time-dependent channel quality seen at the user side. The present paper further refines this idea and elaborates on some of the associated practical concerns.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130493777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601090
Z. Kong, E. Yeh
We study the problem of wireless network resilience to node failures from a percolation-based perspective. In practical wireless networks, it is often the case that nodes with larger degrees (i.e., more neighbors) are more likely to fail. We model this phenomenon as a degree-dependent site percolation process on random geometric graphs. In particular, we obtain analytical conditions for the existence of phase transitions within this model. Furthermore, in networks carrying traffic load, the failure of one node can result in redistribution of the load onto other nearby nodes. If these nodes fail due to excessive load, then this process can result in cascading failure. We analyze this cascading failures problem in large-scale wireless networks, and show that it is equivalent to a degree-dependent site percolation on random geometric graphs. We obtain analytical conditions for cascades in this model.
{"title":"Percolation processes and wireless network resilience","authors":"Z. Kong, E. Yeh","doi":"10.1109/ITA.2008.4601090","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601090","url":null,"abstract":"We study the problem of wireless network resilience to node failures from a percolation-based perspective. In practical wireless networks, it is often the case that nodes with larger degrees (i.e., more neighbors) are more likely to fail. We model this phenomenon as a degree-dependent site percolation process on random geometric graphs. In particular, we obtain analytical conditions for the existence of phase transitions within this model. Furthermore, in networks carrying traffic load, the failure of one node can result in redistribution of the load onto other nearby nodes. If these nodes fail due to excessive load, then this process can result in cascading failure. We analyze this cascading failures problem in large-scale wireless networks, and show that it is equivalent to a degree-dependent site percolation on random geometric graphs. We obtain analytical conditions for cascades in this model.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132951878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601044
Bo Zhou, Li Zhang, Jingyu Kang, Qin Huang, Y. Tai, Shu Lin, Meina Xu
This paper investigates the potential of non-binary LDPC codes to replace widely used Reed-Solomon (RS) codes for applications in communication and storage systems for combating mixed types of noise and interferences. The investigation begins with presentation of four algebraic constructions of RS-based non-binary quasi-cyclic (QC)-LDPC codes. Then, the performances of some codes constructed based on the proposed methods with iterative decoding are compared with those of RS codes of the same lengths and rates decoded with the hard-decision Berlekamp-Massey (BM)-algorithm and the algebraic soft-decision Kotter-Vardy (KV)-algorithm over both the AWGN and a Rayleigh fading channels. Comparison shows that the constructed non-binary QC-LDPC codes significantly outperform their corresponding RS codes decoded with either the BM-algorithm or the KV-algorithm. Most impressively, the orders of decoding computational complexity of the constructed non-binary QC-LDPC codes decoded with 5 and 50 iterations of a Fast Fourier Transform based sum-product algorithm are much smaller than those of their corresponding RS codes decoded with the KV-algorithm, while achieve 1:5 to 3 dB coding gains. The comparison shows that well designed non-binary LDPC codes have a great potential to replace RS codes for some applications in communication or storage systems, at least before a very efficient algorithm for decoding RS codes is devised.
{"title":"Non-binary LDPC codes vs. Reed-Solomon codes","authors":"Bo Zhou, Li Zhang, Jingyu Kang, Qin Huang, Y. Tai, Shu Lin, Meina Xu","doi":"10.1109/ITA.2008.4601044","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601044","url":null,"abstract":"This paper investigates the potential of non-binary LDPC codes to replace widely used Reed-Solomon (RS) codes for applications in communication and storage systems for combating mixed types of noise and interferences. The investigation begins with presentation of four algebraic constructions of RS-based non-binary quasi-cyclic (QC)-LDPC codes. Then, the performances of some codes constructed based on the proposed methods with iterative decoding are compared with those of RS codes of the same lengths and rates decoded with the hard-decision Berlekamp-Massey (BM)-algorithm and the algebraic soft-decision Kotter-Vardy (KV)-algorithm over both the AWGN and a Rayleigh fading channels. Comparison shows that the constructed non-binary QC-LDPC codes significantly outperform their corresponding RS codes decoded with either the BM-algorithm or the KV-algorithm. Most impressively, the orders of decoding computational complexity of the constructed non-binary QC-LDPC codes decoded with 5 and 50 iterations of a Fast Fourier Transform based sum-product algorithm are much smaller than those of their corresponding RS codes decoded with the KV-algorithm, while achieve 1:5 to 3 dB coding gains. The comparison shows that well designed non-binary LDPC codes have a great potential to replace RS codes for some applications in communication or storage systems, at least before a very efficient algorithm for decoding RS codes is devised.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133033741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601013
M. Alanyali, M. Dashouk
A low-complexity guiding principle is considered for transmission scheduling from n homogeneous queues whose channel states fluctuate independently. The scheduler transmits from a longest queue within d randomly chosen queues with eligible channel states. A Markovian model is studied where mean packet transmission time is n-1 and packet arrival rate is lambda < 1 per queue. Equilibrium distribution of queue occupancy is obtained in the limit as n rarr infin and it is shown to have tails that decay as Theta((lambda/d)k). If transmissions are scheduled from a longest eligible queue in the entire system then almost all queues are empty in equilibrium; the number of queues with one packet is Theta(1) and the number of queues with more than one packet is o(1) as n rarr infin. Equilibrium distribution of the total number of packets in the system is also characterized in this latter case.
{"title":"On power-of-choice in downlink transmission scheduling","authors":"M. Alanyali, M. Dashouk","doi":"10.1109/ITA.2008.4601013","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601013","url":null,"abstract":"A low-complexity guiding principle is considered for transmission scheduling from n homogeneous queues whose channel states fluctuate independently. The scheduler transmits from a longest queue within d randomly chosen queues with eligible channel states. A Markovian model is studied where mean packet transmission time is n-1 and packet arrival rate is lambda < 1 per queue. Equilibrium distribution of queue occupancy is obtained in the limit as n rarr infin and it is shown to have tails that decay as Theta((lambda/d)k). If transmissions are scheduled from a longest eligible queue in the entire system then almost all queues are empty in equilibrium; the number of queues with one packet is Theta(1) and the number of queues with more than one packet is o(1) as n rarr infin. Equilibrium distribution of the total number of packets in the system is also characterized in this latter case.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125142239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601014
L. Azzam, E. Ayanoglu
In this paper, we discuss three applications of the QR decomposition algorithm to decoding in a number of Multi-Input Multi-Output (MIMO) systems. In the first application, we propose a new structure for MIMO Sphere Decoding (SD). We show that the new approach achieves 80% reduction in the overall complexity compared to conventional SD for a 2 times 2 system, and almost 50% reduction for the 4 times 4 and 6 times 6 cases. In the second application, we propose a low complexity Maximum Likelihood Decoding (MLD) algorithm for quasi-orthogonal space-time block codes (QOSTBCs). We show that for N = 8 transmit antennas and 16-QAM modulation scheme, the new approach achieves > 97% reduction in the overall complexity compared to conventional MLD, and > 89% reduction compared to the most competitive reported algorithms in the literature. This complexity gain becomes greater when the number of transmit antennas (N) or the constellation size (L) becomes larger. In the third application, we propose a low complexity Maximum Likelihood Decoding (MLD) algorithm for orthogonal space-time block codes (OSTBCs) based on the real-valued lattice representation and QR decomposition. For a system employing the well-known Alamouti OSTBC and 16-QAM modulation scheme, the new approach achieves > 87% reduction in the overall complexity compared to conventional MLD. Moreover, we show that for square L-QAM constellations, the proposed algorithm reduces the decoding computational complexity from O(LN/2) for conventional MLD to O(L) for systems employing QOSTBCs and from O(L) for conventional MLD to O(radicL) for those employing OSTBCs without sacrificing the performance.
{"title":"Reduction of ML decoding complexity for MIMO Sphere Decoding, QOSTBC, and OSTBC","authors":"L. Azzam, E. Ayanoglu","doi":"10.1109/ITA.2008.4601014","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601014","url":null,"abstract":"In this paper, we discuss three applications of the QR decomposition algorithm to decoding in a number of Multi-Input Multi-Output (MIMO) systems. In the first application, we propose a new structure for MIMO Sphere Decoding (SD). We show that the new approach achieves 80% reduction in the overall complexity compared to conventional SD for a 2 times 2 system, and almost 50% reduction for the 4 times 4 and 6 times 6 cases. In the second application, we propose a low complexity Maximum Likelihood Decoding (MLD) algorithm for quasi-orthogonal space-time block codes (QOSTBCs). We show that for N = 8 transmit antennas and 16-QAM modulation scheme, the new approach achieves > 97% reduction in the overall complexity compared to conventional MLD, and > 89% reduction compared to the most competitive reported algorithms in the literature. This complexity gain becomes greater when the number of transmit antennas (N) or the constellation size (L) becomes larger. In the third application, we propose a low complexity Maximum Likelihood Decoding (MLD) algorithm for orthogonal space-time block codes (OSTBCs) based on the real-valued lattice representation and QR decomposition. For a system employing the well-known Alamouti OSTBC and 16-QAM modulation scheme, the new approach achieves > 87% reduction in the overall complexity compared to conventional MLD. Moreover, we show that for square L-QAM constellations, the proposed algorithm reduces the decoding computational complexity from O(LN/2) for conventional MLD to O(L) for systems employing QOSTBCs and from O(L) for conventional MLD to O(radicL) for those employing OSTBCs without sacrificing the performance.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"385 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125507543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601079
T. Stoenescu, J. Ledyard
We provide a mechanism that solves the engineering and economic rate allocation problems in the presence of production when agents behave in a way that produces a Nash Equilibrium. The mechanism works for a range of utility functions, wider than just quasi-linear functions. The mechanism produces a Pareto-optimal allocation at Nash equilibrium. The mechanism is balanced in equilibrium and satisfies voluntary participation.
{"title":"Nash implementation for resource allocation network problems with production","authors":"T. Stoenescu, J. Ledyard","doi":"10.1109/ITA.2008.4601079","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601079","url":null,"abstract":"We provide a mechanism that solves the engineering and economic rate allocation problems in the presence of production when agents behave in a way that produces a Nash Equilibrium. The mechanism works for a range of utility functions, wider than just quasi-linear functions. The mechanism produces a Pareto-optimal allocation at Nash equilibrium. The mechanism is balanced in equilibrium and satisfies voluntary participation.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124076889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601066
S. Sarkar, Chanan Singh, Anurag Kumar
We consider a setting in which several operators offer downlink wireless data access services in a certain geographical region. Each operator deploys several base stations or access points, and registers some subscribers. In such a situation, if operators pool their infrastructure, and permit the possibility of subscribers being served by any of the cooperating operators, then there can be overall better user satisfaction, and increased operator revenue. We use coalitional game theory to investigate such resource pooling and cooperation between operators.We use utility functions to model user satisfaction, and show that the resulting coalitional game has the property that if all operators cooperate (i.e., form a grand coalition) then there is an operating point that maximizes the sum utility over the operators while providing the operators revenues such that no subset of operators has an incentive to break away from the coalition. We investigate whether such operating points can result in utility unfairness between users of the various operators. We also study other revenue sharing concepts, namely, the nucleolus and the Shapely value. Such investigations throw light on criteria for operators to accept or reject subscribers, based on the service level agreements proposed by them. We also investigate the situation in which only certain subsets of operators may be willing to cooperate.
{"title":"A coalitional game model for spectrum pooling in wireless data access networks","authors":"S. Sarkar, Chanan Singh, Anurag Kumar","doi":"10.1109/ITA.2008.4601066","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601066","url":null,"abstract":"We consider a setting in which several operators offer downlink wireless data access services in a certain geographical region. Each operator deploys several base stations or access points, and registers some subscribers. In such a situation, if operators pool their infrastructure, and permit the possibility of subscribers being served by any of the cooperating operators, then there can be overall better user satisfaction, and increased operator revenue. We use coalitional game theory to investigate such resource pooling and cooperation between operators.We use utility functions to model user satisfaction, and show that the resulting coalitional game has the property that if all operators cooperate (i.e., form a grand coalition) then there is an operating point that maximizes the sum utility over the operators while providing the operators revenues such that no subset of operators has an incentive to break away from the coalition. We investigate whether such operating points can result in utility unfairness between users of the various operators. We also study other revenue sharing concepts, namely, the nucleolus and the Shapely value. Such investigations throw light on criteria for operators to accept or reject subscribers, based on the service level agreements proposed by them. We also investigate the situation in which only certain subsets of operators may be willing to cooperate.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130238136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601094
Andrew. Brzezinski, Andrew. Brzezinski, G. Zussman, E. Modiano
A major challenge in the design and operation of wireless networks is to jointly route packets and schedule transmissions to efficiently share the common spectrum among links in the same area. Due to the lack of central control in wireless networks, these algorithms have to be decentralized. It was recently shown that distributed (greedy) algorithms can usually guarantee only fractional throughput. It was also recently shown that if a set of conditions regarding the network topology (known as Local Pooling) is satisfied, simple distributed maximal weight (greedy) scheduling algorithms achieve 100% throughput. In this paper, we focus on networks in which packets have to undergo multihop routing and derive multihop local pooling conditions for that setting. In networks satisfying these conditions, a backpressure-based joint routing and scheduling algorithm employing maximal weight scheduling achieves 100% throughput.
{"title":"Local pooling conditions for joint routing and scheduling","authors":"Andrew. Brzezinski, Andrew. Brzezinski, G. Zussman, E. Modiano","doi":"10.1109/ITA.2008.4601094","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601094","url":null,"abstract":"A major challenge in the design and operation of wireless networks is to jointly route packets and schedule transmissions to efficiently share the common spectrum among links in the same area. Due to the lack of central control in wireless networks, these algorithms have to be decentralized. It was recently shown that distributed (greedy) algorithms can usually guarantee only fractional throughput. It was also recently shown that if a set of conditions regarding the network topology (known as Local Pooling) is satisfied, simple distributed maximal weight (greedy) scheduling algorithms achieve 100% throughput. In this paper, we focus on networks in which packets have to undergo multihop routing and derive multihop local pooling conditions for that setting. In networks satisfying these conditions, a backpressure-based joint routing and scheduling algorithm employing maximal weight scheduling achieves 100% throughput.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127784255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-08-15DOI: 10.1109/ITA.2008.4601018
Daniel Vainsencher, A. Bruckstein
In the plane, the way to enclose the most area with a given perimeter and to use the shortest perimeter to enclose a given area, is to use a circle. If we replace the plane by a regular tiling of it, and construct polyforms i.e. shapes as sets of tiles, things become more complicated. We need to redefine the area and perimeter measures, and study the consequences carefully. In this paper we characterize all shapes that have both shortest boundaries and maximal areas for one particular boundary measure on the hexagon tiling. We show this set of Pareto optimal shapes is the same as that induced by a different boundary measure that was studied in the context of theoretical chemistry.
{"title":"Isoperimetrically Pareto-optimal shapes on the hexagonal grid","authors":"Daniel Vainsencher, A. Bruckstein","doi":"10.1109/ITA.2008.4601018","DOIUrl":"https://doi.org/10.1109/ITA.2008.4601018","url":null,"abstract":"In the plane, the way to enclose the most area with a given perimeter and to use the shortest perimeter to enclose a given area, is to use a circle. If we replace the plane by a regular tiling of it, and construct polyforms i.e. shapes as sets of tiles, things become more complicated. We need to redefine the area and perimeter measures, and study the consequences carefully. In this paper we characterize all shapes that have both shortest boundaries and maximal areas for one particular boundary measure on the hexagon tiling. We show this set of Pareto optimal shapes is the same as that induced by a different boundary measure that was studied in the context of theoretical chemistry.","PeriodicalId":345196,"journal":{"name":"2008 Information Theory and Applications Workshop","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115539529","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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