Pub Date : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797714
S. Puducheri, T. Fuja
This paper considers two simple wireless network configurations in which the links making up the network do not interfere with one another and the assumed link loss mechanisms are erasures. The first configuration is the M-source multiple access relay channel (MARC), in which M different sources convey information to a single destination with the help of a single relay. The second configuration is the two-fold multi-relay channel (MRC), in which a pair of relays help a single source convey information to a single destination. Cut set bounds are established for these configurations, and linear programming is then employed to formulate closed-form solutions for the capacity regions as a function of the link parameters; moreover, it is shown that easily-implemented capacity-approaching codes such as LDPC or Tornado codes can be used at the link level to achieve any point in the capacity region. For the erasure MARC, the results indicate that the relay should help only those sources that have a weaker direct channel to the destination than the relay itself does - regardless of the quality of the source-to-relay channels. For the erasure MRC, the solution is not as intuitive, but it displays a structure in which the relative quality of the various links determine which relays are used - and, when both are used, which relay is ldquoprimaryrdquo and which is ldquosecondaryrdquo.
{"title":"Capacity results for certain wireless relay networks with erasure links","authors":"S. Puducheri, T. Fuja","doi":"10.1109/ALLERTON.2008.4797714","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797714","url":null,"abstract":"This paper considers two simple wireless network configurations in which the links making up the network do not interfere with one another and the assumed link loss mechanisms are erasures. The first configuration is the M-source multiple access relay channel (MARC), in which M different sources convey information to a single destination with the help of a single relay. The second configuration is the two-fold multi-relay channel (MRC), in which a pair of relays help a single source convey information to a single destination. Cut set bounds are established for these configurations, and linear programming is then employed to formulate closed-form solutions for the capacity regions as a function of the link parameters; moreover, it is shown that easily-implemented capacity-approaching codes such as LDPC or Tornado codes can be used at the link level to achieve any point in the capacity region. For the erasure MARC, the results indicate that the relay should help only those sources that have a weaker direct channel to the destination than the relay itself does - regardless of the quality of the source-to-relay channels. For the erasure MRC, the solution is not as intuitive, but it displays a structure in which the relative quality of the various links determine which relays are used - and, when both are used, which relay is ldquoprimaryrdquo and which is ldquosecondaryrdquo.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133443788","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797721
P. Venkitasubramaniam, V. Anantharam
The analysis of a multi-source single-destination network of mixes is considered under strict latency constraints at each mix. Mixes are relay nodes that accept packets arriving from multiple sources and release them after variable delays to prevent an eavesdropper from perfectly identifying the sources of outgoing packets (also, the contents of the packets are encrypted to prevent these from being used to correlate the arrivals to the mix with its departures). Using an entropy-based measure to quantify anonymity, the anonymity provided by such a single-destination network of mixes is analyzed, with the focus on light traffic conditions. A general upper bound is presented that bounds the anonymity of a single-destination mix network in terms of a linear combination of the anonymity of two-stage networks. By using a specific mixing strategy, a lower bound is provided on the light traffic derivative of the anonymity of single-destination mix networks. The light traffic derivative of the upper bound coincides with the lower bound for the case of mix-cascades (linear single-destination mix networks). Thus, the optimal light traffic derivative of the anonymity is characterized for mix cascades.
{"title":"Anonymity under light traffic conditions using a network of mixes","authors":"P. Venkitasubramaniam, V. Anantharam","doi":"10.1109/ALLERTON.2008.4797721","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797721","url":null,"abstract":"The analysis of a multi-source single-destination network of mixes is considered under strict latency constraints at each mix. Mixes are relay nodes that accept packets arriving from multiple sources and release them after variable delays to prevent an eavesdropper from perfectly identifying the sources of outgoing packets (also, the contents of the packets are encrypted to prevent these from being used to correlate the arrivals to the mix with its departures). Using an entropy-based measure to quantify anonymity, the anonymity provided by such a single-destination network of mixes is analyzed, with the focus on light traffic conditions. A general upper bound is presented that bounds the anonymity of a single-destination mix network in terms of a linear combination of the anonymity of two-stage networks. By using a specific mixing strategy, a lower bound is provided on the light traffic derivative of the anonymity of single-destination mix networks. The light traffic derivative of the upper bound coincides with the lower bound for the case of mix-cascades (linear single-destination mix networks). Thus, the optimal light traffic derivative of the anonymity is characterized for mix cascades.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132114014","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797630
G. Caire, S. Ramprashad, H. Papadopoulos, C. Pépin, C. Sundberg
We consider a realistic albeit simplified scenario for wireless cellular systems of the next generation (4G and beyond), where MIMO-OFDM, opportunistic scheduling, channel state information at the transmitter and limited base-station cooperation are envisaged. We propose two strategies with limited base-station cooperation that can be easily implemented with today's technology and achieve an approximate form of inter-cell interference alignment. The first strategy consists of imposing a ldquopower maskrdquo in frequency such that adjacent cooperative clusters of base stations generate different interference levels in different frequency subchannels. The second strategy consists of switching between different cooperative clusters such that no user is in a permanently disadvantaged location.We compare single-user and multiuser MIMO systems in terms of average throughput as a function of the user location.
{"title":"Multiuser MIMO downlink with limited inter-cell cooperation: Approximate interference alignment in time, frequency and space","authors":"G. Caire, S. Ramprashad, H. Papadopoulos, C. Pépin, C. Sundberg","doi":"10.1109/ALLERTON.2008.4797630","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797630","url":null,"abstract":"We consider a realistic albeit simplified scenario for wireless cellular systems of the next generation (4G and beyond), where MIMO-OFDM, opportunistic scheduling, channel state information at the transmitter and limited base-station cooperation are envisaged. We propose two strategies with limited base-station cooperation that can be easily implemented with today's technology and achieve an approximate form of inter-cell interference alignment. The first strategy consists of imposing a ldquopower maskrdquo in frequency such that adjacent cooperative clusters of base stations generate different interference levels in different frequency subchannels. The second strategy consists of switching between different cooperative clusters such that no user is in a permanently disadvantaged location.We compare single-user and multiuser MIMO systems in terms of average throughput as a function of the user location.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133879883","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797726
J. Kliewer, K. Zigangirov, D. J. Costello
We consider the ensemble of codes formed by a serial concatenation of a repetition code with two accumulators through uniform random interleavers. For this ensemble, asymptotic expressions for the normalized minimum trapping distance are derived. We employ a variant of the Gallager-Zyablov-Pinsker bit flipping decoding algorithm on a binary symmetric channel, where the analysis is based on the factor graph of the code. In particular, we show that the minimum trapping distance can be determined by solving a non-linear optimization problem. As a result we find that the minimum trapping distance grows linearly with block length for code rates of 1/3 and smaller, albeit with very small growth rate coefficients.
{"title":"On the minimum trapping distance of repeat accumulate accumulate codes","authors":"J. Kliewer, K. Zigangirov, D. J. Costello","doi":"10.1109/ALLERTON.2008.4797726","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797726","url":null,"abstract":"We consider the ensemble of codes formed by a serial concatenation of a repetition code with two accumulators through uniform random interleavers. For this ensemble, asymptotic expressions for the normalized minimum trapping distance are derived. We employ a variant of the Gallager-Zyablov-Pinsker bit flipping decoding algorithm on a binary symmetric channel, where the analysis is based on the factor graph of the code. In particular, we show that the minimum trapping distance can be determined by solving a non-linear optimization problem. As a result we find that the minimum trapping distance grows linearly with block length for code rates of 1/3 and smaller, albeit with very small growth rate coefficients.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"283 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124522592","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797716
S. Puducheri, T. Fuja
We study the tradeoffs in employing two different approaches - coding and feedback - for reliable communication over packet erasure channels. Results are shown for a scheme that combines both approaches. Inspired by this scheme, we use rate distortion results to characterize the best achievable tradeoffs for a class of joint coding-and-feedback schemes.
{"title":"Trading off coding complexity and feedback requirements for the packet erasure channel","authors":"S. Puducheri, T. Fuja","doi":"10.1109/ALLERTON.2008.4797716","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797716","url":null,"abstract":"We study the tradeoffs in employing two different approaches - coding and feedback - for reliable communication over packet erasure channels. Results are shown for a scheme that combines both approaches. Inspired by this scheme, we use rate distortion results to characterize the best achievable tradeoffs for a class of joint coding-and-feedback schemes.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115767118","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797671
Sungho Yun, C. Caramanis
We consider a system-level approach to interference management in a cellular broadband system operating in an interference-limited and highly dynamic regime, as put forth. Here, base stations in neighboring cells (partially) coordinate their transmission schedules in an attempt to avoid simultaneous transmission to their mutual cell edge. Limits on communication overhead and use of the backhaul require base station coordination to occur at a slower time scale than the arriving customers. Depending on the overhead restrictions, the slower time scale could be on the scale of minutes or even hours. Thus base stations coordinate using only the statistics of customer arrival, while they serve users based on the actual realizations. The central challenge is to properly structure coordination decisions at the slow time scale, as these subsequently restrict the actions of each base station until the next coordination period. A further challenge comes from the fact that over longer coordination intervals, the statistics of the arriving customers, e.g., the load, may themselves vary or be only approximately known. Indeed, we show through simulation that while the approach is effective for a broad range of arriving load, performance rapidly degrades as the variation of the arriving load from the nominal (or assured) arriving load grows. We show this is true even when the variations are neutral, namely when the aggregate load is fixed, but there are local variations. In this paper we show that a two-stage robust optimization framework is a natural way to model two time-scale decision problems. We provide tractable formulations for the base- station coordination problem, and show that our formulation is robust to fluctuations (uncertainties) in the arriving load. This tolerance to load fluctuation also serves to reduce the need for frequent re-optimization across base stations, thus helping minimize the communication overhead required for system level interference reduction. Building in robustness to load variation comes at the potential cost of somewhat degraded performance when variations happen to be very small. Our robust optimization formulations are flexible, allowing us to control the conservatism of the solution. Our simulations show that we can build in robustness without significant degradation of nominal performance.
{"title":"System level optimization in wireless networks with uncertain customer arrival rates","authors":"Sungho Yun, C. Caramanis","doi":"10.1109/ALLERTON.2008.4797671","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797671","url":null,"abstract":"We consider a system-level approach to interference management in a cellular broadband system operating in an interference-limited and highly dynamic regime, as put forth. Here, base stations in neighboring cells (partially) coordinate their transmission schedules in an attempt to avoid simultaneous transmission to their mutual cell edge. Limits on communication overhead and use of the backhaul require base station coordination to occur at a slower time scale than the arriving customers. Depending on the overhead restrictions, the slower time scale could be on the scale of minutes or even hours. Thus base stations coordinate using only the statistics of customer arrival, while they serve users based on the actual realizations. The central challenge is to properly structure coordination decisions at the slow time scale, as these subsequently restrict the actions of each base station until the next coordination period. A further challenge comes from the fact that over longer coordination intervals, the statistics of the arriving customers, e.g., the load, may themselves vary or be only approximately known. Indeed, we show through simulation that while the approach is effective for a broad range of arriving load, performance rapidly degrades as the variation of the arriving load from the nominal (or assured) arriving load grows. We show this is true even when the variations are neutral, namely when the aggregate load is fixed, but there are local variations. In this paper we show that a two-stage robust optimization framework is a natural way to model two time-scale decision problems. We provide tractable formulations for the base- station coordination problem, and show that our formulation is robust to fluctuations (uncertainties) in the arriving load. This tolerance to load fluctuation also serves to reduce the need for frequent re-optimization across base stations, thus helping minimize the communication overhead required for system level interference reduction. Building in robustness to load variation comes at the potential cost of somewhat degraded performance when variations happen to be very small. Our robust optimization formulations are flexible, allowing us to control the conservatism of the solution. Our simulations show that we can build in robustness without significant degradation of nominal performance.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114854383","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797627
E. Larsson, D. Danev, Eduard Axel Jorswieck
We consider the interference channel with multiple antennas at the transmitter. We prove that at high signal-to-noise ratio (SNR), the zero-forcing transmit scheme is optimal in the sum-rate sense. Furthermore we prove that at low SNR, maximum-ratio transmission is optimal in the sum-rate sense. We also provide a discussion of the connection to classical results on spectral efficiency in the wideband regime. Finally, we propose a non-convex optimization approach based on monotonic optimization to solve the sum rate maximization problem.
{"title":"Asymptotically optimal transmit strategies for the multiple antenna interference channel","authors":"E. Larsson, D. Danev, Eduard Axel Jorswieck","doi":"10.1109/ALLERTON.2008.4797627","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797627","url":null,"abstract":"We consider the interference channel with multiple antennas at the transmitter. We prove that at high signal-to-noise ratio (SNR), the zero-forcing transmit scheme is optimal in the sum-rate sense. Furthermore we prove that at low SNR, maximum-ratio transmission is optimal in the sum-rate sense. We also provide a discussion of the connection to classical results on spectral efficiency in the wideband regime. Finally, we propose a non-convex optimization approach based on monotonic optimization to solve the sum rate maximization problem.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"282 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126916090","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797699
P. Tague, R. Poovendran
We formalize a model for node capture attacks in which an adversary collects information about the network via eavesdropping on the wireless medium and captures nodes based on the learned information. We show that attacks in this adversary model correspond to NP-hard optimization problems and discuss the behavior of a reasonable heuristic algorithm. We show that the goals of node capture attacks can be decomposed into a collection of primitive events, the impact of which can be evaluated and recombined to yield an overall evaluation of the attack. We demonstrate the use of the attack decomposition model for derivation of attack metrics and discuss the potential use of this decomposition technique for the purposes of defense against node capture attacks.
{"title":"Modeling node capture attacks in wireless sensor networks","authors":"P. Tague, R. Poovendran","doi":"10.1109/ALLERTON.2008.4797699","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797699","url":null,"abstract":"We formalize a model for node capture attacks in which an adversary collects information about the network via eavesdropping on the wireless medium and captures nodes based on the learned information. We show that attacks in this adversary model correspond to NP-hard optimization problems and discuss the behavior of a reasonable heuristic algorithm. We show that the goals of node capture attacks can be decomposed into a collection of primitive events, the impact of which can be evaluated and recombined to yield an overall evaluation of the attack. We demonstrate the use of the attack decomposition model for derivation of attack metrics and discuss the potential use of this decomposition technique for the purposes of defense against node capture attacks.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127055960","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797704
C. Kelley
Over the past few years several constructions of protograph codes have been proposed that are based on random lifts of suitably chosen base graphs. More recently, an algebraic analog of this approach was introduced using the theory of voltage graphs. The strength of the voltage graph framework is the ability to analyze the resulting derived graph algebraically, even when the voltages themselves are assigned randomly. Moreover, the theory of voltage graphs provides insight to designing lifts of graphs with particular properties. In this paper we illustrate how the properties of the derived graphs and the corresponding codes relate to the voltage assignments. In particular, we present a construction of LDPC codes by giving an algebraic method of choosing the permutation voltages and illustrate the usefulness of the proposed technique via simulation results.
{"title":"On codes designed via algebraic lifts of graphs","authors":"C. Kelley","doi":"10.1109/ALLERTON.2008.4797704","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797704","url":null,"abstract":"Over the past few years several constructions of protograph codes have been proposed that are based on random lifts of suitably chosen base graphs. More recently, an algebraic analog of this approach was introduced using the theory of voltage graphs. The strength of the voltage graph framework is the ability to analyze the resulting derived graph algebraically, even when the voltages themselves are assigned randomly. Moreover, the theory of voltage graphs provides insight to designing lifts of graphs with particular properties. In this paper we illustrate how the properties of the derived graphs and the corresponding codes relate to the voltage assignments. In particular, we present a construction of LDPC codes by giving an algebraic method of choosing the permutation voltages and illustrate the usefulness of the proposed technique via simulation results.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"161 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127307889","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 : 2008-09-01DOI: 10.1109/ALLERTON.2008.4797609
R. Nowak
This paper studies a generalization of the classic binary search problem of locating a desired value within a sorted list. The classic problem can be viewed as determining the correct one-dimensional, binary-valued threshold function from a finite class of such functions based on queries taking the form of point samples of the function. The classic problem is also equivalent to a simple binary encoding of the threshold location. This paper extends binary search to learning more general binary-valued functions. Specifically, if the set of target functions and queries satisfy certain geometrical relationships, then an algorithm, based on selecting a query that is maximally discriminating at each step, will determine the correct function in a number of steps that is logarithmic in the number of functions under consideration. Examples of classes satisfying the geometrical relationships include linear separators in multiple dimensions. Extensions to handle noise are also discussed. Possible applications include machine learning, channel coding, and sequential experimental design.
{"title":"Generalized binary search","authors":"R. Nowak","doi":"10.1109/ALLERTON.2008.4797609","DOIUrl":"https://doi.org/10.1109/ALLERTON.2008.4797609","url":null,"abstract":"This paper studies a generalization of the classic binary search problem of locating a desired value within a sorted list. The classic problem can be viewed as determining the correct one-dimensional, binary-valued threshold function from a finite class of such functions based on queries taking the form of point samples of the function. The classic problem is also equivalent to a simple binary encoding of the threshold location. This paper extends binary search to learning more general binary-valued functions. Specifically, if the set of target functions and queries satisfy certain geometrical relationships, then an algorithm, based on selecting a query that is maximally discriminating at each step, will determine the correct function in a number of steps that is logarithmic in the number of functions under consideration. Examples of classes satisfying the geometrical relationships include linear separators in multiple dimensions. Extensions to handle noise are also discussed. Possible applications include machine learning, channel coding, and sequential experimental design.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122955738","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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