Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282937
Y. Steinberg
It is well known that cooperation between users in a communication network can lead to significant performance gains relative to the same network without cooperation. One common model which has been studied recently is the two users degraded broadcast channel (BC) with cooperating decoders. It can be viewed as a special case of the relay-broadcast channel (RBC), where the link from the relay to the other user is a noiseless channel (bit-pipe), that does not interact with the main channel. In this work two extensions of this basic model are suggested and studied: the BC with conferencing and degraded message sets, and the degraded BC with parallel conferencing, where there are parallel relays whose data streams are received by all the users in the channel. Since the data stream of each relay is also received by the other, one relay can allocate part of its rate to help the other relay to distribute its data stream. The capacity region is characterized for the two models.
{"title":"Instances of the relay-broadcast channel and cooperation strategies","authors":"Y. Steinberg","doi":"10.1109/ISIT.2015.7282937","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282937","url":null,"abstract":"It is well known that cooperation between users in a communication network can lead to significant performance gains relative to the same network without cooperation. One common model which has been studied recently is the two users degraded broadcast channel (BC) with cooperating decoders. It can be viewed as a special case of the relay-broadcast channel (RBC), where the link from the relay to the other user is a noiseless channel (bit-pipe), that does not interact with the main channel. In this work two extensions of this basic model are suggested and studied: the BC with conferencing and degraded message sets, and the degraded BC with parallel conferencing, where there are parallel relays whose data streams are received by all the users in the channel. Since the data stream of each relay is also received by the other, one relay can allocate part of its rate to help the other relay to distribute its data stream. The capacity region is characterized for the two models.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129621550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282558
Javad Heydari, A. Tajer
Linear search arises in many application domains. The problem of linear search over multiple sequences in order to identify one sequence with a desired statistical feature is considered. The quickest linear search optimizes a balance between two opposing performance measures, one being the delay in detecting a desirable sequence, and the other one being the quality of the decision. The existing approaches in the quickest search literature rely on the assumption that the sequences are statistically independent. In many applications, however, due to the underlying physical couplings, generations of available sequences are not necessarily independent. Driven by such underlying couplings, this paper considers searching over correlated sequences, in which the distribution of each sequence depends on the distribution of its preceding one. The closed-form characterization of the sampling process for the optimal search is delineated. The analysis reveals that depending on the correlation structure, the optimal search strategy can be similar to (in spirit) or dramatically different from the optimal search strategy over independent sequences.
{"title":"Quickest linear search over correlated sequences","authors":"Javad Heydari, A. Tajer","doi":"10.1109/ISIT.2015.7282558","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282558","url":null,"abstract":"Linear search arises in many application domains. The problem of linear search over multiple sequences in order to identify one sequence with a desired statistical feature is considered. The quickest linear search optimizes a balance between two opposing performance measures, one being the delay in detecting a desirable sequence, and the other one being the quality of the decision. The existing approaches in the quickest search literature rely on the assumption that the sequences are statistically independent. In many applications, however, due to the underlying physical couplings, generations of available sequences are not necessarily independent. Driven by such underlying couplings, this paper considers searching over correlated sequences, in which the distribution of each sequence depends on the distribution of its preceding one. The closed-form characterization of the sampling process for the optimal search is delineated. The analysis reveals that depending on the correlation structure, the optimal search strategy can be similar to (in spirit) or dramatically different from the optimal search strategy over independent sequences.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129039663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282772
Yuanming Shi, Jun Zhang, K. Letaief
This paper considers the topological interference management problem in a partially connected K-user interference channel, where no channel state information at transmitters (CSIT) is available beyond the network topology knowledge. Due to the practical CSI assumption, this problem has recently received enough attention. In particular, it has been established that the topological interference management problem, in terms of degrees of freedom (DoF), is equivalent to the index coding problem with linear schemes. However, so far only a few index coding problems have been solved, and thus there is a lack of a systematic way to characterize optimal DoF of an arbitrary network topology. In this paper, we present a low-rank matrix completion (LRMC) approach to find linear solutions to maximize the achievable symmetric DoF for any given network topology. To decode the desired messages at each receiver, we also propose an LRMC based channel acquisition scheme, which can obtain interference-free measurements of the desired channel at each receiver while minimizing the pilot training length. To address the NP-hardness of the non-convex rank objective function in the resulting LRMC problem, we further present a Riemannian pursuit (RP) algorithm to solve it efficiently. This algorithm alternatively performs fixed-rank optimization using Riemannian optimization and rank increase by exploiting the manifold structure of the fixed-rank matrices. The LRMC approach aided by the RP algorithms not only recovers the existing optimal DoF results but also provides insights for general network topologies.
{"title":"Low-rank matrix completion via Riemannian pursuit for topological interference management","authors":"Yuanming Shi, Jun Zhang, K. Letaief","doi":"10.1109/ISIT.2015.7282772","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282772","url":null,"abstract":"This paper considers the topological interference management problem in a partially connected K-user interference channel, where no channel state information at transmitters (CSIT) is available beyond the network topology knowledge. Due to the practical CSI assumption, this problem has recently received enough attention. In particular, it has been established that the topological interference management problem, in terms of degrees of freedom (DoF), is equivalent to the index coding problem with linear schemes. However, so far only a few index coding problems have been solved, and thus there is a lack of a systematic way to characterize optimal DoF of an arbitrary network topology. In this paper, we present a low-rank matrix completion (LRMC) approach to find linear solutions to maximize the achievable symmetric DoF for any given network topology. To decode the desired messages at each receiver, we also propose an LRMC based channel acquisition scheme, which can obtain interference-free measurements of the desired channel at each receiver while minimizing the pilot training length. To address the NP-hardness of the non-convex rank objective function in the resulting LRMC problem, we further present a Riemannian pursuit (RP) algorithm to solve it efficiently. This algorithm alternatively performs fixed-rank optimization using Riemannian optimization and rank increase by exploiting the manifold structure of the fixed-rank matrices. The LRMC approach aided by the RP algorithms not only recovers the existing optimal DoF results but also provides insights for general network topologies.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"46 45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132403367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282814
Muhammed Faruk Gencel, M. Rasekh, Upamanyu Madhow
Distributed transmit beamforming with N cooperating nodes, each with fixed transmit power, provides a received power scaling with N2, corresponding to a “power pooling” gain of N and a beamforming gain of N. Prior work has shown that the optimal beamforming solution can be attained using a decentralized, iterative algorithm based on one bit (per iteration) feedback broadcast from the receiver to the transmitters. The algorithm is provably convergent in a noiseless setting, and is the basis for several successful prototypes. In this paper, we develop a framework for providing analytical insight into the effect of receiver noise, with the following key question in mind: can we bootstrap the algorithm from the incoherent power-pooled solution to operate in a regime in which the received SNR per node can be made arbitrarily small as we scale up the number of nodes N? Our analytical computations, validated by simulations, yield a somewhat negative answer: while the power-pooling gain guarantees a linear increase in received power with N, the per-node SNR cannot be scaled down with N if we wish to attain a quadratic increase in received power. Specifically, the fraction of the ideal beamforming gain attained using the one-bit algorithm is asymptotically independent of N, and depends only on the per-node SNR. However, the one-bit algorithm provides significant performance gains in practical regimes with a moderate number of cooperating nodes: the per-node SNR required for attaining a substantial fraction of the beamforming gain is low enough (e.g., - 5dB for 65% of the beamforming gain) to provide significant extension in operation regimes, while providing aggregate SNRs which permit reliable communication at high spectral efficiency: for example, starting from -5 dB per-node SNR, we obtain about 11 dB aggregate SNR with 10 cooperating nodes, and 17 dB SNR with 20 cooperating nodes.
{"title":"Distributed transmit beamforming with one bit feedback revisited: How noise limits scaling","authors":"Muhammed Faruk Gencel, M. Rasekh, Upamanyu Madhow","doi":"10.1109/ISIT.2015.7282814","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282814","url":null,"abstract":"Distributed transmit beamforming with N cooperating nodes, each with fixed transmit power, provides a received power scaling with N2, corresponding to a “power pooling” gain of N and a beamforming gain of N. Prior work has shown that the optimal beamforming solution can be attained using a decentralized, iterative algorithm based on one bit (per iteration) feedback broadcast from the receiver to the transmitters. The algorithm is provably convergent in a noiseless setting, and is the basis for several successful prototypes. In this paper, we develop a framework for providing analytical insight into the effect of receiver noise, with the following key question in mind: can we bootstrap the algorithm from the incoherent power-pooled solution to operate in a regime in which the received SNR per node can be made arbitrarily small as we scale up the number of nodes N? Our analytical computations, validated by simulations, yield a somewhat negative answer: while the power-pooling gain guarantees a linear increase in received power with N, the per-node SNR cannot be scaled down with N if we wish to attain a quadratic increase in received power. Specifically, the fraction of the ideal beamforming gain attained using the one-bit algorithm is asymptotically independent of N, and depends only on the per-node SNR. However, the one-bit algorithm provides significant performance gains in practical regimes with a moderate number of cooperating nodes: the per-node SNR required for attaining a substantial fraction of the beamforming gain is low enough (e.g., - 5dB for 65% of the beamforming gain) to provide significant extension in operation regimes, while providing aggregate SNRs which permit reliable communication at high spectral efficiency: for example, starting from -5 dB per-node SNR, we obtain about 11 dB aggregate SNR with 10 cooperating nodes, and 17 dB SNR with 20 cooperating nodes.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114226740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282887
Haiyang Liu, Daeyeoul Kim, Yang Li, A. Z. Jia
Separating redundancy, proposed by Abdel-Ghaffar and Weber, is an important concept in the analysis of the error and erasure decoding of a linear block code using a parity-check matrix of the code. In this paper, we investigate the second and third separating redundancies of extended Hamming codes. For an extended Hamming code, we establish two binary integer linear program problems, the optima of which give lower and upper bounds on the second/third separating redundancy of the code. Numerical results suggest that our bounds might improve the known bounds of the second and third separating redundancies of extended Hamming codes.
{"title":"On the separating redundancy of extended Hamming codes","authors":"Haiyang Liu, Daeyeoul Kim, Yang Li, A. Z. Jia","doi":"10.1109/ISIT.2015.7282887","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282887","url":null,"abstract":"Separating redundancy, proposed by Abdel-Ghaffar and Weber, is an important concept in the analysis of the error and erasure decoding of a linear block code using a parity-check matrix of the code. In this paper, we investigate the second and third separating redundancies of extended Hamming codes. For an extended Hamming code, we establish two binary integer linear program problems, the optima of which give lower and upper bounds on the second/third separating redundancy of the code. Numerical results suggest that our bounds might improve the known bounds of the second and third separating redundancies of extended Hamming codes.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115254465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282923
Dong Yin, Kangwook Lee, Ramtin Pedarsani, K. Ramchandran
In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a K-sparse complex signal s ∈ ℂn, from a set of m noisy quadratic measurements: yi = |aiHs|2 + wi; where aiH ∈ ℂn is the ith row of the measurement matrix A ∈ ℂm×n, and wi is the additive noise to the ith measurement. We consider the regime where K = βnδ, δ ∈ (0; 1). We use the architecture of PhaseCode algorithm [1], and robustify it using two schemes: the almost-linear scheme and the sublinear scheme. We prove that with high probability, the almost-linear scheme recovers s with sample complexity1 Θ(K log(n)) and computational complexity Θ(n log(n)), and the sublinear scheme recovers s with sample complexity Θ(K log3(n)) and computational complexity Θ(K log3(n)). To the best of our knowledge, this is the first scheme that achieves sublinear computational complexity for compressive phase retrieval problem. Finally, we provide simulation results that support our theoretical contributions.
{"title":"Fast and robust compressive phase retrieval with sparse-graph codes","authors":"Dong Yin, Kangwook Lee, Ramtin Pedarsani, K. Ramchandran","doi":"10.1109/ISIT.2015.7282923","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282923","url":null,"abstract":"In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a K-sparse complex signal s ∈ ℂ<sup>n</sup>, from a set of m noisy quadratic measurements: y<sub>i</sub> = |a<sub>i</sub><sup>H</sup>s|<sup>2</sup> + w<sub>i</sub>; where a<sub>i</sub><sup>H</sup> ∈ ℂ<sup>n</sup> is the ith row of the measurement matrix A ∈ ℂ<sup>m×n</sup>, and w<sub>i</sub> is the additive noise to the ith measurement. We consider the regime where K = βn<sup>δ</sup>, δ ∈ (0; 1). We use the architecture of PhaseCode algorithm [1], and robustify it using two schemes: the almost-linear scheme and the sublinear scheme. We prove that with high probability, the almost-linear scheme recovers s with sample complexity<sup>1</sup> Θ(K log(n)) and computational complexity Θ(n log(n)), and the sublinear scheme recovers s with sample complexity Θ(K log<sup>3</sup>(n)) and computational complexity Θ(K log<sup>3</sup>(n)). To the best of our knowledge, this is the first scheme that achieves sublinear computational complexity for compressive phase retrieval problem. Finally, we provide simulation results that support our theoretical contributions.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125020606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282650
Chuili Kong, C. Zhong, Anastasios K. Papazafeiropoulos, M. Matthaiou, Zhaoyang Zhang
This paper investigates the achievable sum-rate of uplink massive multiple-input multiple-output (MIMO) systems considering a practical channel impairment, namely, aged channel state information (CSI). Taking into account both maximum ratio combining (MRC) and zero-forcing (ZF) receivers at the base station, we present tight closed-form lower bounds on the sum-rate for both receivers, which provide efficient means to evaluate the sum-rate of the system. More importantly, we characterize the impact of channel aging on the power scaling law. Specifically, we show that the transmit power of each user can be scaled down by 1/√(M), which indicates that aged CSI does not affect the power scaling law; instead, it causes only a reduction on the sum rate by reducing the effective signal-to-interference-and-noise ratio (SINR).
{"title":"Effect of channel aging on the sum rate of uplink massive MIMO systems","authors":"Chuili Kong, C. Zhong, Anastasios K. Papazafeiropoulos, M. Matthaiou, Zhaoyang Zhang","doi":"10.1109/ISIT.2015.7282650","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282650","url":null,"abstract":"This paper investigates the achievable sum-rate of uplink massive multiple-input multiple-output (MIMO) systems considering a practical channel impairment, namely, aged channel state information (CSI). Taking into account both maximum ratio combining (MRC) and zero-forcing (ZF) receivers at the base station, we present tight closed-form lower bounds on the sum-rate for both receivers, which provide efficient means to evaluate the sum-rate of the system. More importantly, we characterize the impact of channel aging on the power scaling law. Specifically, we show that the transmit power of each user can be scaled down by 1/√(M), which indicates that aged CSI does not affect the power scaling law; instead, it causes only a reduction on the sum rate by reducing the effective signal-to-interference-and-noise ratio (SINR).","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121353162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282586
Farzad Farnoud, Moshe Schwartz, Jehoshua Bruck
Mutation processes such as point mutation, insertion, deletion, and duplication (including tandem and interspersed duplication) have an important role in evolution, as they lead to genomic diversity, and thus to phenotypic variation. In this work, we study the expressive power of interspersed duplication, i.e., its ability to generate diversity, via a simple but fundamental stochastic model, where the length and the location of the substring that is duplicated and the point of insertion of the copy are chosen randomly. We investigate the properties of the set of high-probability sequences in these stochastic systems. In particular we provide results regarding the asymptotic behavior of frequencies of symbols and strings in a sequence evolving through interspersed duplication. The study of such systems is an important step towards the design and analysis of more realistic and sophisticated models of genomic mutation processes.
{"title":"A stochastic model for genomic interspersed duplication","authors":"Farzad Farnoud, Moshe Schwartz, Jehoshua Bruck","doi":"10.1109/ISIT.2015.7282586","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282586","url":null,"abstract":"Mutation processes such as point mutation, insertion, deletion, and duplication (including tandem and interspersed duplication) have an important role in evolution, as they lead to genomic diversity, and thus to phenotypic variation. In this work, we study the expressive power of interspersed duplication, i.e., its ability to generate diversity, via a simple but fundamental stochastic model, where the length and the location of the substring that is duplicated and the point of insertion of the copy are chosen randomly. We investigate the properties of the set of high-probability sequences in these stochastic systems. In particular we provide results regarding the asymptotic behavior of frequencies of symbols and strings in a sequence evolving through interspersed duplication. The study of such systems is an important step towards the design and analysis of more realistic and sophisticated models of genomic mutation processes.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133575472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282550
Mitsugu Iwamoto, Junji Shikata
Constructions of symmetric-key encryption with guessing secrecy are discussed. In the previous works, only a construction of symmetric-key encryption with average guessing secrecy is proposed for one-bit plaintexts. In this paper, we analyze a symmetric-key encryption with average guessing secrecy through OTP (one-time pad) constructions for a wide class of probability distributions of plaintexts and keys. As a result, we show a necessary and sufficient condition that such class of distributions satisfies average guessing secrecy in OTP constructions. On the other hand, we prove that optimal guessing secrecy is essentially equivalent to perfect secrecy under several natural restrictions. Therefore, only average guessing secrecy is meaningful for considering guessing secrecy other than perfect secrecy.
{"title":"Constructions of symmetric-key encryption with guessing secrecy","authors":"Mitsugu Iwamoto, Junji Shikata","doi":"10.1109/ISIT.2015.7282550","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282550","url":null,"abstract":"Constructions of symmetric-key encryption with guessing secrecy are discussed. In the previous works, only a construction of symmetric-key encryption with average guessing secrecy is proposed for one-bit plaintexts. In this paper, we analyze a symmetric-key encryption with average guessing secrecy through OTP (one-time pad) constructions for a wide class of probability distributions of plaintexts and keys. As a result, we show a necessary and sufficient condition that such class of distributions satisfies average guessing secrecy in OTP constructions. On the other hand, we prove that optimal guessing secrecy is essentially equivalent to perfect secrecy under several natural restrictions. Therefore, only average guessing secrecy is meaningful for considering guessing secrecy other than perfect secrecy.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121798596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-14DOI: 10.1109/ISIT.2015.7282561
P. Moulin, Patrick R. Johnstone
Exact asymptotics are derived for composite hypothesis testing between two product probability measures Pn vs Qn, subject to a type-I error-probability constraint ε. Here P is known but Q is an unknown element of a given d-dimensional regular exponential family. We study the Rao score test, which is a quadratic approximation to the GLRT. The type-II error probability is shown to vanish as equation where D and V are respectively the Kullback-Leibler divergence and the variance of information divergence between P and Q; τ(ε; d) is the 1 - ε quantile for the χd2 distribution; and the constants βd > 0 and γd are explicitly identified. The asymptotic regret relative to the Neyman-Pearson test (which knows Q) is reflected in the coefficient τ(ε; d), as is the cost of dimensionality. Looser asymptotics (with O(1) in place of εd) are obtained for the GLRT.
对于两个乘积概率度量Pn vs Qn之间的复合假设检验，导出了精确渐近性，并受到i型误差概率约束ε的约束。这里P是已知的，而Q是给定的d维正则指数族的未知元素。我们研究了Rao分数检验，它是GLRT的二次逼近。ii型误差概率以方程形式消失，其中D和V分别为Kullback-Leibler散度和P与Q之间的信息散度方差;τ(ε;D)为χd2分布的1 - ε分位数;常数βd > 0和γd是明确确定的。相对于Neyman-Pearson检验(它知道Q)的渐近后悔反映在系数τ(ε;D)维度的成本也是如此。对于GLRT，得到了更宽松的渐近性(用O(1)代替εd)。
{"title":"Strong large deviations for Rao test score and GLRT in exponential families","authors":"P. Moulin, Patrick R. Johnstone","doi":"10.1109/ISIT.2015.7282561","DOIUrl":"https://doi.org/10.1109/ISIT.2015.7282561","url":null,"abstract":"Exact asymptotics are derived for composite hypothesis testing between two product probability measures P<sup>n</sup> vs Q<sup>n</sup>, subject to a type-I error-probability constraint ε. Here P is known but Q is an unknown element of a given d-dimensional regular exponential family. We study the Rao score test, which is a quadratic approximation to the GLRT. The type-II error probability is shown to vanish as equation where D and V are respectively the Kullback-Leibler divergence and the variance of information divergence between P and Q; τ(ε; d) is the 1 - ε quantile for the χ<sub>d</sub><sup>2</sup> distribution; and the constants β<sub>d</sub> > 0 and γ<sub>d</sub> are explicitly identified. The asymptotic regret relative to the Neyman-Pearson test (which knows Q) is reflected in the coefficient τ(ε; d), as is the cost of dimensionality. Looser asymptotics (with O(1) in place of ε<sub>d</sub>) are obtained for the GLRT.","PeriodicalId":272313,"journal":{"name":"2015 IEEE International Symposium on Information Theory (ISIT)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128035075","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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