Pub Date : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834893
Zilong Wang, Qian Chen, G. Gong
The set of perfect sequences with optimal cross-correlation has applications in communication and radar systems. Many different constructions, which are called optimal sets of perfect sequences according to Sarwate bound, have been studied in the literature. However, Song et al. and Zhang et al. recently showed that the set size of these constructions can be improved, since the term related to size vanishes for perfect sequences in Sarwate bound. Until now, we don’t know whether the set size of these constructions is optimal, though they are all called optimal sets. We studied the problem of the set size of perfect sequences with optimal cross-correlation, and showed that the set size must be upper bounded by the length of the perfect sequences in this paper.
{"title":"An Upper Bound of the Set Size of Perfect Sequences with Optimal Cross-correlation","authors":"Zilong Wang, Qian Chen, G. Gong","doi":"10.1109/ISIT50566.2022.9834893","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834893","url":null,"abstract":"The set of perfect sequences with optimal cross-correlation has applications in communication and radar systems. Many different constructions, which are called optimal sets of perfect sequences according to Sarwate bound, have been studied in the literature. However, Song et al. and Zhang et al. recently showed that the set size of these constructions can be improved, since the term related to size vanishes for perfect sequences in Sarwate bound. Until now, we don’t know whether the set size of these constructions is optimal, though they are all called optimal sets. We studied the problem of the set size of perfect sequences with optimal cross-correlation, and showed that the set size must be upper bounded by the length of the perfect sequences in this paper.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128435334","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834365
Sagnik Bhattacharya, P. Narayan
Shared information is a measure of mutual dependence among m ≥ 2 jointly distributed discrete random variables. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. When the joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance.
{"title":"Shared Information for a Markov Chain on a Tree","authors":"Sagnik Bhattacharya, P. Narayan","doi":"10.1109/ISIT50566.2022.9834365","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834365","url":null,"abstract":"Shared information is a measure of mutual dependence among m ≥ 2 jointly distributed discrete random variables. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. When the joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129155888","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834663
Jie Li, Xiaohu Tang, Hanxu Hou, Y. Han, B. Bai, Gong Zhang
Partial maximum distance separable (PMDS) codes are a kind of erasure codes where the storage nodes are divided into multiple groups with each forming an MDS code of a smaller code length. They allow repairing a failed node by contacting only a few helper nodes and can correct all erasure patterns which are information-theoretically correctable. However, the repair of a failed node of PMDS codes still requires a large amount of communication if the group size is large. Recently, PMDS array codes with each local code being an MSR code were introduced to further reduce the repair bandwidth, but codes over small finite fields only exist for two global parities, and require large rebuilding access and unavoidably a large sub-packetization level. In this paper, we propose two constructions of PMDS array codes with two and three global parities, respectively. Both have a small sub-packetization level, small repair bandwidth, and much smaller finite fields than existing ones.
PMDS (Partial maximum distance分离式部分最大距离可分离码)是将存储节点分成多组，每组组成一个较小码长的MDS码的一种擦除码。它们允许通过仅联系几个辅助节点来修复故障节点，并且可以纠正所有在信息理论上可纠正的擦除模式。但是，在组规模较大的情况下，PMDS码的故障节点修复仍然需要大量的通信。近年来，为了进一步减少修复带宽，引入了每个局部码都是MSR码的PMDS阵列码，但小有限域上的码只存在两个全局对，需要大量的重建访问，并且不可避免地需要很大的子分组级别。本文提出了两种具有两个和三个全局对的PMDS阵列码结构。两者都具有小的子分组级别、小的修复带宽和比现有的小得多的有限域。
{"title":"PMDS Array Codes With Small Sub-packetization Level and Small Repair Bandwidth","authors":"Jie Li, Xiaohu Tang, Hanxu Hou, Y. Han, B. Bai, Gong Zhang","doi":"10.1109/ISIT50566.2022.9834663","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834663","url":null,"abstract":"Partial maximum distance separable (PMDS) codes are a kind of erasure codes where the storage nodes are divided into multiple groups with each forming an MDS code of a smaller code length. They allow repairing a failed node by contacting only a few helper nodes and can correct all erasure patterns which are information-theoretically correctable. However, the repair of a failed node of PMDS codes still requires a large amount of communication if the group size is large. Recently, PMDS array codes with each local code being an MSR code were introduced to further reduce the repair bandwidth, but codes over small finite fields only exist for two global parities, and require large rebuilding access and unavoidably a large sub-packetization level. In this paper, we propose two constructions of PMDS array codes with two and three global parities, respectively. Both have a small sub-packetization level, small repair bandwidth, and much smaller finite fields than existing ones.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130527077","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834768
Yonglong Li, C. Hirche, M. Tomamichel
We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in expectation or with high probability. We show that, by using adaptive strategies for the discrimination problem, both types of error probabilities decrease to zero exponentially fast and the rates are characterized by the measured relative entropy between two quantum channels. Allowing for quantum memory, we see that the optimal rates are given by the regularized channel relative entropy. We also characterize the error exponents in the discrimination problem if non-adaptive strategies are used.
{"title":"Sequential Quantum Channel Discrimination","authors":"Yonglong Li, C. Hirche, M. Tomamichel","doi":"10.1109/ISIT50566.2022.9834768","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834768","url":null,"abstract":"We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in expectation or with high probability. We show that, by using adaptive strategies for the discrimination problem, both types of error probabilities decrease to zero exponentially fast and the rates are characterized by the measured relative entropy between two quantum channels. Allowing for quantum memory, we see that the optimal rates are given by the regularized channel relative entropy. We also characterize the error exponents in the discrimination problem if non-adaptive strategies are used.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130656562","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834858
Farzad Pourkamali, N. Macris
We consider the estimation of a n×m matrix u∗v∗T observed through an additive Gaussian noise channel, a problem that frequently arises in statistics and machine learning. We investigate a scenario involving mismatched Bayesian inference in which the statistician is unaware of true prior and uses an assumed prior. We derive the exact analytic expression for the asymptotic mean squared error (MSE) in the large system size limit for the particular case of Gaussian priors and additive noise. Our formulas demonstrate that in the mismatched case, estimation is still possible. Additionally, the minimum MSE (MMSE) can be obtained by selecting a non-trivial set of parameters beyond the matched parameters. Our technique is based on the asymptotic behavior of spherical integrals for rectangular matrices. Our method can be extended to non-rotation-invariant distributions for the true prior but requires rotation invariance for the statistician’s assumed prior.
{"title":"Mismatched Estimation of Non-Symmetric Rank-One Matrices Under Gaussian Noise","authors":"Farzad Pourkamali, N. Macris","doi":"10.1109/ISIT50566.2022.9834858","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834858","url":null,"abstract":"We consider the estimation of a n×m matrix u∗v∗T observed through an additive Gaussian noise channel, a problem that frequently arises in statistics and machine learning. We investigate a scenario involving mismatched Bayesian inference in which the statistician is unaware of true prior and uses an assumed prior. We derive the exact analytic expression for the asymptotic mean squared error (MSE) in the large system size limit for the particular case of Gaussian priors and additive noise. Our formulas demonstrate that in the mismatched case, estimation is still possible. Additionally, the minimum MSE (MMSE) can be obtained by selecting a non-trivial set of parameters beyond the matched parameters. Our technique is based on the asymptotic behavior of spherical integrals for rectangular matrices. Our method can be extended to non-rotation-invariant distributions for the true prior but requires rotation invariance for the statistician’s assumed prior.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130768014","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834592
A. Khina, A. Yeredor, R. Zamir
It is common to assess the "memory strength" of a stationary process by looking at how fast the normalized log– determinant of its covariance submatrices (i.e., entropy rate) decreases. In this work, we propose an alternative characterization in terms of the normalized trace–inverse of the covariance submatrices. We show that this sequence is monotonically non-decreasing and is constant if and only if the process is white. Furthermore, while the entropy rate is associated with one-sided prediction errors (present from past), the new measure is associated with two-sided prediction errors (present from past and future). Minimizing this measure is then used as an alternative to Burg’s maximum-entropy principle for spectral estimation.
{"title":"Monotonicity of the Trace–Inverse of Covariance Submatrices and Two-Sided Prediction","authors":"A. Khina, A. Yeredor, R. Zamir","doi":"10.1109/ISIT50566.2022.9834592","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834592","url":null,"abstract":"It is common to assess the \"memory strength\" of a stationary process by looking at how fast the normalized log– determinant of its covariance submatrices (i.e., entropy rate) decreases. In this work, we propose an alternative characterization in terms of the normalized trace–inverse of the covariance submatrices. We show that this sequence is monotonically non-decreasing and is constant if and only if the process is white. Furthermore, while the entropy rate is associated with one-sided prediction errors (present from past), the new measure is associated with two-sided prediction errors (present from past and future). Minimizing this measure is then used as an alternative to Burg’s maximum-entropy principle for spectral estimation.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132886193","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834669
Suayb S. Arslan, Massoud Pourmandi, Elif Haytaoglu
We consider a novel distributed data storage/caching scenario in a cellular network, where multiple nodes may fail/depart simultaneously To meet reliability, we allow cooperative regeneration of lost nodes with the help of base stations allocated in a set of hierarchical layers1. Due to this layered structure, a symbol download from each base station has a different cost, while the link capacities between the nodes of the cellular system and the base stations are also constrained. Under such a setting, we formulate the fundamental trade-off with closed form expressions between repair bandwidth cost and the storage space per node. Particularly, the minimum storage as well as bandwidth cost points are formulated. Finally, we provide an explicit optimal code construction for the minimum storage regeneration point for a special set of system parameters.
{"title":"Base Station-Assisted Cooperative Network Coding for Cellular Systems with Link Constraints","authors":"Suayb S. Arslan, Massoud Pourmandi, Elif Haytaoglu","doi":"10.1109/ISIT50566.2022.9834669","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834669","url":null,"abstract":"We consider a novel distributed data storage/caching scenario in a cellular network, where multiple nodes may fail/depart simultaneously To meet reliability, we allow cooperative regeneration of lost nodes with the help of base stations allocated in a set of hierarchical layers1. Due to this layered structure, a symbol download from each base station has a different cost, while the link capacities between the nodes of the cellular system and the base stations are also constrained. Under such a setting, we formulate the fundamental trade-off with closed form expressions between repair bandwidth cost and the storage space per node. Particularly, the minimum storage as well as bandwidth cost points are formulated. Finally, we provide an explicit optimal code construction for the minimum storage regeneration point for a special set of system parameters.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132958470","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834754
Keshav Goyal, H. M. Kiah
We revisit the well-known Gilbert-Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be determined via the solution of some optimization problem. Later, Marcus and Roth (1992) modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and hence, compute the bounds. We then show the procedures can be further simplified when we plot the respective curves.
{"title":"Evaluating the Gilbert-Varshamov Bound for Constrained Systems","authors":"Keshav Goyal, H. M. Kiah","doi":"10.1109/ISIT50566.2022.9834754","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834754","url":null,"abstract":"We revisit the well-known Gilbert-Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be determined via the solution of some optimization problem. Later, Marcus and Roth (1992) modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and hence, compute the bounds. We then show the procedures can be further simplified when we plot the respective curves.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131967525","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834701
Jiachun Pan, Yonglong Li, V. Tan
In this paper, we formulate the sequential binary hypothesis testing problem in which an adversary is active under both hypotheses. This problem is formulated as a sequential adversarial hypothesis testing game played between the decision maker and the adversary and it is a zero-sum and strategic one. The goal of the decision maker is to minimize the expectation of stopping time to make the test more efficient, while the adversary’s goal is to maximize it. We obtain the pair of strategies under which the asymptotic Nash equilibrium of the game is attained.
{"title":"Asymptotic Nash Equilibrium for the Sequential Adversarial Hypothesis Testing Game","authors":"Jiachun Pan, Yonglong Li, V. Tan","doi":"10.1109/ISIT50566.2022.9834701","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834701","url":null,"abstract":"In this paper, we formulate the sequential binary hypothesis testing problem in which an adversary is active under both hypotheses. This problem is formulated as a sequential adversarial hypothesis testing game played between the decision maker and the adversary and it is a zero-sum and strategic one. The goal of the decision maker is to minimize the expectation of stopping time to make the test more efficient, while the adversary’s goal is to maximize it. We obtain the pair of strategies under which the asymptotic Nash equilibrium of the game is attained.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132031025","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834461
T. Wadayama, Satoshi Takabe
Chebyshev-periodical successive over-relaxation was recently proposed as a method of accelerating the convergence speed of fixed-point iterations. If a PSOR iteration is influenced by stochastic disturbances, such as Gaussian noise, then the behavior of the PSOR iteration deviates from the predicted behavior of the noiseless iterations, i.e., the convergence behavior of the Chebyshev-PSOR is highly sensitive to the noises. This paper presents a concise formula for the asymptotic mean squared error (AMSE) of the noisy PSOR iterations. A PSOR iteration can be regarded as a stochastic difference equation and spectral decomposition plays a key role to reveal the asymptotic behaviors of the error covariance. Based on the AMSE formula, a noise mitigation method is developed to reduce the effects of the stochastic disturbance.
{"title":"Asymptotic Mean Squared Error of Noisy Periodical Successive Over-Relaxation","authors":"T. Wadayama, Satoshi Takabe","doi":"10.1109/ISIT50566.2022.9834461","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834461","url":null,"abstract":"Chebyshev-periodical successive over-relaxation was recently proposed as a method of accelerating the convergence speed of fixed-point iterations. If a PSOR iteration is influenced by stochastic disturbances, such as Gaussian noise, then the behavior of the PSOR iteration deviates from the predicted behavior of the noiseless iterations, i.e., the convergence behavior of the Chebyshev-PSOR is highly sensitive to the noises. This paper presents a concise formula for the asymptotic mean squared error (AMSE) of the noisy PSOR iterations. A PSOR iteration can be regarded as a stochastic difference equation and spectral decomposition plays a key role to reveal the asymptotic behaviors of the error covariance. Based on the AMSE formula, a noise mitigation method is developed to reduce the effects of the stochastic disturbance.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130459773","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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