Pub Date : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174362
Farzin Salek, A. Winter
The tasks of converting noisy multipartite quantum correlations into noiseless classical and quantum ones using local operations and classical communications (LOCC) are studied. For the former, known as common randomness (CR) distillation, two novel lower bounds on the "distillable common randomness", an operational measure of the total genuine (classical) correlations in a quantum state, are obtained. Our proof relies on a generalization of communication for omniscience (CO) [Csiszár and Narayan, IEEE Trans. Inf. Theory 50: 3047-3061, 2004]. For the latter, we derive two lower bounds on the rate at which Greenberger-Horne-Zeilinger (GHZ) states can be asymptotically distilled from any given pure state under LOCC. Our approach consists in "making coherent" the proposed CR distillation protocols and recycling of resources [Devetak, Harrow and Winter, IEEE Trans. Inf. Theory 54:4587-4618, 2008]. The first lower bound is identical to a recent result by Vrana and Christandl [IEEE Trans. Inf. Theory 65:5945-5958, 2019], which is based on a combinatorial approach to achieve the same rate. Our second lower bound generalises and improves upon this result, and unifies a number of other known lower bounds on GHZ distillation. Full details in the long version [1].
{"title":"Multi-User Distillation of Common Randomness and Entanglement from Quantum States","authors":"Farzin Salek, A. Winter","doi":"10.1109/ISIT44484.2020.9174362","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174362","url":null,"abstract":"The tasks of converting noisy multipartite quantum correlations into noiseless classical and quantum ones using local operations and classical communications (LOCC) are studied. For the former, known as common randomness (CR) distillation, two novel lower bounds on the \"distillable common randomness\", an operational measure of the total genuine (classical) correlations in a quantum state, are obtained. Our proof relies on a generalization of communication for omniscience (CO) [Csiszár and Narayan, IEEE Trans. Inf. Theory 50: 3047-3061, 2004]. For the latter, we derive two lower bounds on the rate at which Greenberger-Horne-Zeilinger (GHZ) states can be asymptotically distilled from any given pure state under LOCC. Our approach consists in \"making coherent\" the proposed CR distillation protocols and recycling of resources [Devetak, Harrow and Winter, IEEE Trans. Inf. Theory 54:4587-4618, 2008]. The first lower bound is identical to a recent result by Vrana and Christandl [IEEE Trans. Inf. Theory 65:5945-5958, 2019], which is based on a combinatorial approach to achieve the same rate. Our second lower bound generalises and improves upon this result, and unifies a number of other known lower bounds on GHZ distillation. Full details in the long version [1].","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129069967","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174355
Ertan Kazıklı, S. Gezici, S. Yüksel
We consider a privacy-signaling game problem in which a transmitter with privacy concerns and a receiver, which does not pay attention to these privacy concerns, communicate. In this communication scenario, the transmitter observes a pair of correlated random variables which are modeled as jointly Gaussian. The transmitter constructs its message based on these random variables with the aim to hide one of them and convey the other one. In contrast, the objective of the receiver is to accurately estimate both of the random variables so as to gather as much information as possible. These conflicting objectives are analyzed in a game theoretic framework where depending on the commitment conditions (of the sender), we consider Nash or Stackelberg equilibria. We show that a payoff dominant (i.e., most desirable for both players) Nash equilibrium is attained by affine policies and we explicitly characterize these policies. In addition, the strategies at the characterized Nash equilibrium is shown to form also a Stackelberg equilibrium. Furthermore, we show that there always exists an informative Stackelberg equilibrium for the multidimensional parameter setup. We also revisit the information bottleneck problem within our Stackelberg framework under the mean squared error distortion criterion where the information bottleneck setup has a further restriction that only one of the parameters is observed at the sender. We fully characterize the Stackelberg equilibria under certain conditions and when these conditions are not met we establish the existence of informative equilibria.
{"title":"Quadratic Privacy-Signaling Games and Payoff Dominant Equilibria","authors":"Ertan Kazıklı, S. Gezici, S. Yüksel","doi":"10.1109/ISIT44484.2020.9174355","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174355","url":null,"abstract":"We consider a privacy-signaling game problem in which a transmitter with privacy concerns and a receiver, which does not pay attention to these privacy concerns, communicate. In this communication scenario, the transmitter observes a pair of correlated random variables which are modeled as jointly Gaussian. The transmitter constructs its message based on these random variables with the aim to hide one of them and convey the other one. In contrast, the objective of the receiver is to accurately estimate both of the random variables so as to gather as much information as possible. These conflicting objectives are analyzed in a game theoretic framework where depending on the commitment conditions (of the sender), we consider Nash or Stackelberg equilibria. We show that a payoff dominant (i.e., most desirable for both players) Nash equilibrium is attained by affine policies and we explicitly characterize these policies. In addition, the strategies at the characterized Nash equilibrium is shown to form also a Stackelberg equilibrium. Furthermore, we show that there always exists an informative Stackelberg equilibrium for the multidimensional parameter setup. We also revisit the information bottleneck problem within our Stackelberg framework under the mean squared error distortion criterion where the information bottleneck setup has a further restriction that only one of the parameters is observed at the sender. We fully characterize the Stackelberg equilibria under certain conditions and when these conditions are not met we establish the existence of informative equilibria.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129126097","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174519
X. Chang, Zhilong Chen, Yingzi Xu
Estimating the integer parameter vector in a linear model with additive Gaussian noise arises from many applications, including communications. The optimal approach is to solve an integer least squares (ILS) problem, which is unfortunately NP-hard. Recently Klein’s randomized algorithm, which finds a sub-optimal solution to the ILS problem, to be referred to as the randomized Babai point, has attracted much attention. This paper presents a formula of the success probability of the randomized Babai point and some interesting properties, and compares it with the deterministic Babai point.
{"title":"On the Randomized Babai Point","authors":"X. Chang, Zhilong Chen, Yingzi Xu","doi":"10.1109/ISIT44484.2020.9174519","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174519","url":null,"abstract":"Estimating the integer parameter vector in a linear model with additive Gaussian noise arises from many applications, including communications. The optimal approach is to solve an integer least squares (ILS) problem, which is unfortunately NP-hard. Recently Klein’s randomized algorithm, which finds a sub-optimal solution to the ILS problem, to be referred to as the randomized Babai point, has attracted much attention. This paper presents a formula of the success probability of the randomized Babai point and some interesting properties, and compares it with the deterministic Babai point.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114229008","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174065
A. Thangaraj, H. Pfister
Reed–Muller (RM) codes, a classical family of codes known for their elegant algebraic structure, have recently been shown to achieve capacity under maximum-likelihood (ML) decoding on the binary erasure channel and this has rekindled interest in their efficient decoding. We consider the code family RM(m−3,m) and develop a new ML decoder, for transmission over the binary symmetric channel, that exploits their large symmetry group. The new decoder has lower complexity than an earlier method introduced by Seroussi and Lempel in 1983.
{"title":"Efficient Maximum-Likelihood Decoding of Reed–Muller RM(m−3,m) Codes","authors":"A. Thangaraj, H. Pfister","doi":"10.1109/ISIT44484.2020.9174065","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174065","url":null,"abstract":"Reed–Muller (RM) codes, a classical family of codes known for their elegant algebraic structure, have recently been shown to achieve capacity under maximum-likelihood (ML) decoding on the binary erasure channel and this has rekindled interest in their efficient decoding. We consider the code family RM(m−3,m) and develop a new ML decoder, for transmission over the binary symmetric channel, that exploits their large symmetry group. The new decoder has lower complexity than an earlier method introduced by Seroussi and Lempel in 1983.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114528789","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174522
Jari Lietzén, R. Vehkalahti, O. Tirkkonen
Two-way quantum key distribution (QKD) protocols can provide positive secret key rates for considerably higher quantum bit error rates (QBER) than one-way protocols. However, when QBER is low, only modest key rate gains have been achieved. This is one of the major obstacles for using two-way protocols. In this paper we introduce a new two-way QKD protocol which is a step towards overcoming this shortcoming. Under the assumption that the eavesdropper can only perform individual symmetric quantum attacks, our protocol performs quantum key distribution with a secret key rate that is higher than the information theoretical bound limiting the performance of any one-way protocol. This holds true also for very low QBER values.
{"title":"A Two-way QKD Protocol Outperforming One-way Protocols at Low QBER","authors":"Jari Lietzén, R. Vehkalahti, O. Tirkkonen","doi":"10.1109/ISIT44484.2020.9174522","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174522","url":null,"abstract":"Two-way quantum key distribution (QKD) protocols can provide positive secret key rates for considerably higher quantum bit error rates (QBER) than one-way protocols. However, when QBER is low, only modest key rate gains have been achieved. This is one of the major obstacles for using two-way protocols. In this paper we introduce a new two-way QKD protocol which is a step towards overcoming this shortcoming. Under the assumption that the eavesdropper can only perform individual symmetric quantum attacks, our protocol performs quantum key distribution with a secret key rate that is higher than the information theoretical bound limiting the performance of any one-way protocol. This holds true also for very low QBER values.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"279 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114622662","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174238
B. M. Zaidel, O. Shental, S. Shamai
Non-orthogonal multiple access (NOMA) is a promising technology in the design of efficient state-of-the-art communication, particularly 5G and beyond cellular systems. Understanding its fundamental information-theoretic limits is hence of paramount interest. This paper focuses on regular sparse NOMA (where only a fixed and finite number of orthogonal resources is allocated to any designated user, and vice versa), and extends a previous analysis by the authors to a setting where the system comprises two classes of users with different power constraints. Explicit rigorous closed-form analytical inner and outer bounds on the achievable rate (total class throughput) region in the large-system limit are derived. The inner bound is based on the conditional vector entropy power inequality (EPI), while the outer bound relies on a recent strengthened version of the EPI by Courtade. The closed-form bounds provide valuable insights into the potential performance gains of regular sparse NOMA in practically oriented settings, comprising, e.g., a combination of low-complexity devices and broadband users with higher transmit power capabilities, or combinations of cell-edge users with users located close to the cell center. Conditions are identified where superior performance over dense code-domain NOMA is guaranteed, and a relatively small gap to the ultimate performance limits is attainable. The bounds may also serve as a useful tool for future analyses involving interference networks, as, e.g., Wyner-type cellular models.
{"title":"Bounding the Achievable Region of Sparse NOMA","authors":"B. M. Zaidel, O. Shental, S. Shamai","doi":"10.1109/ISIT44484.2020.9174238","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174238","url":null,"abstract":"Non-orthogonal multiple access (NOMA) is a promising technology in the design of efficient state-of-the-art communication, particularly 5G and beyond cellular systems. Understanding its fundamental information-theoretic limits is hence of paramount interest. This paper focuses on regular sparse NOMA (where only a fixed and finite number of orthogonal resources is allocated to any designated user, and vice versa), and extends a previous analysis by the authors to a setting where the system comprises two classes of users with different power constraints. Explicit rigorous closed-form analytical inner and outer bounds on the achievable rate (total class throughput) region in the large-system limit are derived. The inner bound is based on the conditional vector entropy power inequality (EPI), while the outer bound relies on a recent strengthened version of the EPI by Courtade. The closed-form bounds provide valuable insights into the potential performance gains of regular sparse NOMA in practically oriented settings, comprising, e.g., a combination of low-complexity devices and broadband users with higher transmit power capabilities, or combinations of cell-edge users with users located close to the cell center. Conditions are identified where superior performance over dense code-domain NOMA is guaranteed, and a relatively small gap to the ultimate performance limits is attainable. The bounds may also serve as a useful tool for future analyses involving interference networks, as, e.g., Wyner-type cellular models.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114718327","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174008
Tugcan Aktas, P. Sen
This paper studies the detection problem for the Gaussian random access channels, in which only a randomly chosen αK out of K senders wish to convey their messages to a receiver that has the side information of which sender is actively transmitting. A novel coding scheme, referred to as L-interleaved block coding, based on interleaving L single-user codes and successive cancellation decoding is proposed for the symmetric rate tuples in the capacity region of this channel. L-interleaved block coding with L sufficiently large is shown to achieve arbitrarily close to the symmetric capacity. Therefore, it replaces the efforts of finding capacity achieving codes for the Gaussian random access channels with selecting L off-the-shelf codes for Gaussian point-to-point channels for L sufficiently large. An example illustrates that this scheme with a small number of blocks (L = 16) achieves more than 0.95 of the symmetric capacity when two senders are active.
{"title":"Interleaved Block Coding for Achieving Gaussian Random Access Channel Capacity","authors":"Tugcan Aktas, P. Sen","doi":"10.1109/ISIT44484.2020.9174008","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174008","url":null,"abstract":"This paper studies the detection problem for the Gaussian random access channels, in which only a randomly chosen αK out of K senders wish to convey their messages to a receiver that has the side information of which sender is actively transmitting. A novel coding scheme, referred to as L-interleaved block coding, based on interleaving L single-user codes and successive cancellation decoding is proposed for the symmetric rate tuples in the capacity region of this channel. L-interleaved block coding with L sufficiently large is shown to achieve arbitrarily close to the symmetric capacity. Therefore, it replaces the efforts of finding capacity achieving codes for the Gaussian random access channels with selecting L off-the-shelf codes for Gaussian point-to-point channels for L sufficiently large. An example illustrates that this scheme with a small number of blocks (L = 16) achieves more than 0.95 of the symmetric capacity when two senders are active.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127781093","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174028
Praveen Venkatesh, Sanghamitra Dutta, P. Grover
Recently, we developed a systematic framework for defining and inferring flows of information about a specific message in neural circuits [2], [3]. We defined a computational model of a neural circuit consisting of computational nodes and transmissions being sent between these nodes over time. We then gave a formal definition of information flow pertaining to a specific message, which was capable of identifying paths along which information flowed in such a system. However, this definition also had some non-intuitive properties, such as the existence of "orphans"—nodes from which information flowed out, even though no information flowed in. In part, these non-intuitive properties arose because we restricted our attention to measures that were functions of transmissions at a single time instant, and measures that were observational rather than counterfactual. In this paper, we consider alternative definitions, including one that is a function of transmissions at multiple time instants, one that is counterfactual, and a new observational definition. We show that a definition of information flow based on counterfactual causal influence (CCI) guarantees the existence of information paths while also having no orphans. We also prove that no observational definition of information flow that satisfies the information path property can match CCI in every instance. Furthermore, each of the definitions we examine (including CCI) is shown to have examples in which the information flow can take a non-intuitive path. Nevertheless, we believe our framework remains more amenable to drawing clear interpretations than classical tools used in neuroscience, such as Granger Causality.The full version of this paper is available online [1].
{"title":"How else can we define Information Flow in Neural Circuits?","authors":"Praveen Venkatesh, Sanghamitra Dutta, P. Grover","doi":"10.1109/ISIT44484.2020.9174028","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174028","url":null,"abstract":"Recently, we developed a systematic framework for defining and inferring flows of information about a specific message in neural circuits [2], [3]. We defined a computational model of a neural circuit consisting of computational nodes and transmissions being sent between these nodes over time. We then gave a formal definition of information flow pertaining to a specific message, which was capable of identifying paths along which information flowed in such a system. However, this definition also had some non-intuitive properties, such as the existence of \"orphans\"—nodes from which information flowed out, even though no information flowed in. In part, these non-intuitive properties arose because we restricted our attention to measures that were functions of transmissions at a single time instant, and measures that were observational rather than counterfactual. In this paper, we consider alternative definitions, including one that is a function of transmissions at multiple time instants, one that is counterfactual, and a new observational definition. We show that a definition of information flow based on counterfactual causal influence (CCI) guarantees the existence of information paths while also having no orphans. We also prove that no observational definition of information flow that satisfies the information path property can match CCI in every instance. Furthermore, each of the definitions we examine (including CCI) is shown to have examples in which the information flow can take a non-intuitive path. Nevertheless, we believe our framework remains more amenable to drawing clear interpretations than classical tools used in neuroscience, such as Granger Causality.The full version of this paper is available online [1].","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126416170","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174042
Utkarsh Gupta, H. M. Kiah, A. Vardy, Hanwen Yao
The imbalance of a binary word refers to the absolute difference between the number of ones and zeros in the word. Motivated by applications in DNA-based data storage and the success of polar codes, we study the problem of reducing imbalance in the codewords of a polar code. To this end, we adapt the technique of Mazumdar, Roth, and Vontobel by considering balancing sets that correspond to low-order Reed-Muller (RM) codes. Such balancing sets are likely to be included as subcodes in polar codes.Specifically, using the first-order RM code, we show that any message can be encoded into a length-n polar codeword with imbalance at most o(n) in O(nlogn)-time. We then reduce the imbalance even further using two methods. First, we constrain the ambient space $mathbb{X}$ and analyze the imbalance that the first-order RM code can achieve for words in $mathbb{X}$. We demonstrate that for codelengths up to 128, the first-order RM code achieves zero imbalance for appropriate choices of $mathbb{X}$ that sacrifice only a few message bits. Second, we augment the balancing set by considering higher order RM codes. We give a simple recursive upper bound for the guaranteed imbalance of RM codes. We also prove that the second-order RM code $mathbb{R}mathbb{M}left( {2,m} right)$ balances all even-weight words for m ⩽ 5, while the RM code of order m − 3 balances all even-weight words for m ⩾ 5.
{"title":"Polar Codes with Balanced Codewords","authors":"Utkarsh Gupta, H. M. Kiah, A. Vardy, Hanwen Yao","doi":"10.1109/ISIT44484.2020.9174042","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174042","url":null,"abstract":"The imbalance of a binary word refers to the absolute difference between the number of ones and zeros in the word. Motivated by applications in DNA-based data storage and the success of polar codes, we study the problem of reducing imbalance in the codewords of a polar code. To this end, we adapt the technique of Mazumdar, Roth, and Vontobel by considering balancing sets that correspond to low-order Reed-Muller (RM) codes. Such balancing sets are likely to be included as subcodes in polar codes.Specifically, using the first-order RM code, we show that any message can be encoded into a length-n polar codeword with imbalance at most o(n) in O(nlogn)-time. We then reduce the imbalance even further using two methods. First, we constrain the ambient space $mathbb{X}$ and analyze the imbalance that the first-order RM code can achieve for words in $mathbb{X}$. We demonstrate that for codelengths up to 128, the first-order RM code achieves zero imbalance for appropriate choices of $mathbb{X}$ that sacrifice only a few message bits. Second, we augment the balancing set by considering higher order RM codes. We give a simple recursive upper bound for the guaranteed imbalance of RM codes. We also prove that the second-order RM code $mathbb{R}mathbb{M}left( {2,m} right)$ balances all even-weight words for m ⩽ 5, while the RM code of order m − 3 balances all even-weight words for m ⩾ 5.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125674564","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174081
Aristomenis Tsopelakos, Georgios Fellouris
The problem of sequential anomaly detection is considered under sampling constraints and generalized error control. It is assumed that there is no prior information on the number of anomalies. It is required to control the probability at least k errors, of any kind, upon stopping, where k is a user specified integer. It is possible to sample only a fixed number of processes at each sampling instance. The processes to be sampled are determined based on the already acquired observations. The goal is to find a procedure that consists of a stopping rule and a decision rule and a sampling rule that satisfy the sampling and error constraints, and have as small as possible average sample size for every possible scenario regarding the subset of anomalous processes. We characterize the optimal expected sample size for this problem to a first order approximation as the error probability vanishes to zero, and we propose procedures that achieve it. The performance of those procedures is compared in a simulation study for different values of k.
{"title":"Sequential anomaly detection with observation control under a generalized error metric","authors":"Aristomenis Tsopelakos, Georgios Fellouris","doi":"10.1109/ISIT44484.2020.9174081","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174081","url":null,"abstract":"The problem of sequential anomaly detection is considered under sampling constraints and generalized error control. It is assumed that there is no prior information on the number of anomalies. It is required to control the probability at least k errors, of any kind, upon stopping, where k is a user specified integer. It is possible to sample only a fixed number of processes at each sampling instance. The processes to be sampled are determined based on the already acquired observations. The goal is to find a procedure that consists of a stopping rule and a decision rule and a sampling rule that satisfy the sampling and error constraints, and have as small as possible average sample size for every possible scenario regarding the subset of anomalous processes. We characterize the optimal expected sample size for this problem to a first order approximation as the error probability vanishes to zero, and we propose procedures that achieve it. The performance of those procedures is compared in a simulation study for different values of k.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131366920","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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