Pub Date : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174169
Mangqing Guo, M. C. Gursoy, P. Varshney
We investigate the sparse activity detection problem in cell-free massive multiple-input multiple-output (MIMO) systems in this paper. With the approximate message passing (AMP) algorithm, the received pilot signals at the access points (APs) are decomposed into independent circularly symmetric complex Gaussian noise corrupted components. By using the minimum mean-squared error (MMSE) denoiser during the AMP procedure, we obtain a threshold detection rule, and analytically describe the noise covariance matrix of the corrupted components via the state evolution equations, which is helpful for the performance analysis of the detection rule. Using the law of large numbers, it can be shown that the error probability of this threshold detection rule tends to zero when the number of APs, pilots and users tend to infinity while the ratio of the number of pilots and users is kept constant. Numerical results show that the error probability decreases while the number of APs increases, corroborating our theoretical analysis. In addition, we investigate the relationship between the error probability of the threshold detection rule and the number of symbols used for pilot transmissions during each channel coherence interval via numerical results.
{"title":"Sparse Activity Detection in Cell-Free Massive MIMO systems","authors":"Mangqing Guo, M. C. Gursoy, P. Varshney","doi":"10.1109/ISIT44484.2020.9174169","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174169","url":null,"abstract":"We investigate the sparse activity detection problem in cell-free massive multiple-input multiple-output (MIMO) systems in this paper. With the approximate message passing (AMP) algorithm, the received pilot signals at the access points (APs) are decomposed into independent circularly symmetric complex Gaussian noise corrupted components. By using the minimum mean-squared error (MMSE) denoiser during the AMP procedure, we obtain a threshold detection rule, and analytically describe the noise covariance matrix of the corrupted components via the state evolution equations, which is helpful for the performance analysis of the detection rule. Using the law of large numbers, it can be shown that the error probability of this threshold detection rule tends to zero when the number of APs, pilots and users tend to infinity while the ratio of the number of pilots and users is kept constant. Numerical results show that the error probability decreases while the number of APs increases, corroborating our theoretical analysis. In addition, we investigate the relationship between the error probability of the threshold detection rule and the number of symbols used for pilot transmissions during each channel coherence interval via numerical results.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"59 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":"126239251","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/ISIT44484.2020.9174380
Hao Lou, Farzad Farnoud
Data deduplication saves storage space by identifying and removing repeats in the data stream. In this paper, we provide an information-theoretic analysis of the performance of deduplication algorithms with data streams where repeats are not exact. We introduce a source model in which probabilistic substitutions are considered. Two modified versions of fixed-length deduplication are studied and proven to have performance within a constant factor of optimal with the knowledge of repeat length. We also study the variable-length scheme and show that as entropy becomes smaller, the size of the compressed string vanishes relative to the length of the uncompressed string.
{"title":"Data Deduplication with Random Substitutions","authors":"Hao Lou, Farzad Farnoud","doi":"10.1109/ISIT44484.2020.9174380","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174380","url":null,"abstract":"Data deduplication saves storage space by identifying and removing repeats in the data stream. In this paper, we provide an information-theoretic analysis of the performance of deduplication algorithms with data streams where repeats are not exact. We introduce a source model in which probabilistic substitutions are considered. Two modified versions of fixed-length deduplication are studied and proven to have performance within a constant factor of optimal with the knowledge of repeat length. We also study the variable-length scheme and show that as entropy becomes smaller, the size of the compressed string vanishes relative to the length of the uncompressed string.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"6 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":"126042463","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/ISIT44484.2020.9174021
Meng-Che Chang, M. Bloch
We consider an active hypothesis testing scenario in which an adversary obtains observations while legitimate parties engage in a sequential adaptive control policy to estimate an unknown parameter. The objective is for the legitimate parties to evade the adversary by controlling the risk of their test while minimizing the detection ability of the adversary, measured in terms of its error exponent. We develop bounds on the adversary’s error exponent that offer insight into how legitimate adversaries can best evade the adversary’s detection. We illustrate the results in a wireless transmission detection example.
{"title":"Evasive Active Hypothesis Testing","authors":"Meng-Che Chang, M. Bloch","doi":"10.1109/ISIT44484.2020.9174021","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174021","url":null,"abstract":"We consider an active hypothesis testing scenario in which an adversary obtains observations while legitimate parties engage in a sequential adaptive control policy to estimate an unknown parameter. The objective is for the legitimate parties to evade the adversary by controlling the risk of their test while minimizing the detection ability of the adversary, measured in terms of its error exponent. We develop bounds on the adversary’s error exponent that offer insight into how legitimate adversaries can best evade the adversary’s detection. We illustrate the results in a wireless transmission detection example.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"129 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":"128245916","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/ISIT44484.2020.9173977
Roni Con, Amir Shpilka
In the binary deletion channel with parameter p (BDCp) every bit is deleted independently with probability p. [1] proved a lower bound of (1−p)/9 on the capacity of the BDCp, yet currently no explicit construction achieves this rate. In this work we give an explicit family of codes of rate (1 −p)/16, for every p. This improves upon the work of Guruswami and Li [2] that gave a construction of rate (1−p)/120. The codes in our family have polynomial time encoding and decoding algorithms.
{"title":"Explicit and Efficient Constructions of Coding Schemes for the Binary Deletion Channel","authors":"Roni Con, Amir Shpilka","doi":"10.1109/ISIT44484.2020.9173977","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9173977","url":null,"abstract":"In the binary deletion channel with parameter p (BDCp) every bit is deleted independently with probability p. [1] proved a lower bound of (1−p)/9 on the capacity of the BDCp, yet currently no explicit construction achieves this rate. In this work we give an explicit family of codes of rate (1 −p)/16, for every p. This improves upon the work of Guruswami and Li [2] that gave a construction of rate (1−p)/120. The codes in our family have polynomial time encoding and decoding algorithms.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"15 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":"124561540","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/ISIT44484.2020.9174389
Ajaykrishnan Nageswaran, P. Narayan
A user generates n independent and identically distributed data random variables with a probability mass function that must be guarded from a querier. The querier must recover, with a prescribed accuracy, a given function of the data from each of n independent and identically distributed user-devised query responses. The user chooses the data pmf and the random query responses to maximize distribution privacy as gauged by the divergence between the pmf and the querier's best estimate of it based on the n query responses. A general lower bound is provided for distribution privacy; and, for the case of binaryvalued functions, upper and lower bounds that converge to said bound as n grows. Explicit strategies for the user and querier are identified.
{"title":"Distribution Privacy Under Function Recoverability","authors":"Ajaykrishnan Nageswaran, P. Narayan","doi":"10.1109/ISIT44484.2020.9174389","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174389","url":null,"abstract":"A user generates n independent and identically distributed data random variables with a probability mass function that must be guarded from a querier. The querier must recover, with a prescribed accuracy, a given function of the data from each of n independent and identically distributed user-devised query responses. The user chooses the data pmf and the random query responses to maximize distribution privacy as gauged by the divergence between the pmf and the querier's best estimate of it based on the n query responses. A general lower bound is provided for distribution privacy; and, for the case of binaryvalued functions, upper and lower bounds that converge to said bound as n grows. Explicit strategies for the user and querier are identified.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"124 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":"124632022","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/ISIT44484.2020.9173982
Hirosuke Yamamoto, Koki Imaeda, Kengo Hashimoto, K. Iwata
In the entropy coding, AIVF (almost instantaneous variable-to-fixed length) codes using multiple parsing trees can attain a better compression rate than the Tunstall code, which attains the best compression rate in the class of VF codes with a single parsing tree. Furthermore, the multiple parsing trees of an AIVF code can be multiplexed into a single parsing tree. In this paper, we propose a new universal data compression code based on the techniques of the AIVF code. The proposed universal code can also be considered as an improvement of the LZW code (Welch code). We explain how the AIVF coding techniques can be applied to universal coding by growing dynamically a single parsing tree, and we evaluate the compression rate of the proposed universal code theoretically and using several corpora.
{"title":"A Universal Data Compression Scheme based on the AIVF Coding Techniques","authors":"Hirosuke Yamamoto, Koki Imaeda, Kengo Hashimoto, K. Iwata","doi":"10.1109/ISIT44484.2020.9173982","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9173982","url":null,"abstract":"In the entropy coding, AIVF (almost instantaneous variable-to-fixed length) codes using multiple parsing trees can attain a better compression rate than the Tunstall code, which attains the best compression rate in the class of VF codes with a single parsing tree. Furthermore, the multiple parsing trees of an AIVF code can be multiplexed into a single parsing tree. In this paper, we propose a new universal data compression code based on the techniques of the AIVF code. The proposed universal code can also be considered as an improvement of the LZW code (Welch code). We explain how the AIVF coding techniques can be applied to universal coding by growing dynamically a single parsing tree, and we evaluate the compression rate of the proposed universal code theoretically and using several corpora.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"10 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":"124958109","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/ISIT44484.2020.9174235
Anna Frank
For streaming applications, we consider parallel burst erasure channels in the presence of an eavesdropper. The legitimate receiver must perfectly recover each source symbol subject to a decoding delay constraint without the eavesdropper gaining any information from his observation. For a certain class of code parameters, we propose delay-optimal M-link codes that recover multiple bursts of erasures of a limited length, and where the codes provide perfect security even if the eavesdropper can observe a link of his choice. Our codes achieve the maximum secrecy rate for the channel model.
{"title":"Delay-Optimal Coding for Secure Transmission over Parallel Burst Erasure Channels with an Eavesdropper","authors":"Anna Frank","doi":"10.1109/ISIT44484.2020.9174235","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174235","url":null,"abstract":"For streaming applications, we consider parallel burst erasure channels in the presence of an eavesdropper. The legitimate receiver must perfectly recover each source symbol subject to a decoding delay constraint without the eavesdropper gaining any information from his observation. For a certain class of code parameters, we propose delay-optimal M-link codes that recover multiple bursts of erasures of a limited length, and where the codes provide perfect security even if the eavesdropper can observe a link of his choice. Our codes achieve the maximum secrecy rate for the channel model.","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":"131137381","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/ISIT44484.2020.9174173
Aditya Narayan Ravi, S. R. Pillai, V. Prabhakaran, M. Wigger
Feedback is known to enlarge the capacity region of a Gaussian Broadcast Channel (GBC) with independent noise realizations at the receivers, and an average power constraint at the transmitter. The capacity enlargement may occur even when there is noisy feedback from only one of the two receivers. However, recent results show the existence of a feedback noise threshold, beyond which one-sided feedback from only the stronger receiver is futile in enlarging the capacity region. The current paper presents a tight characterization of the feedback noise threshold, which separates the regimes where feedback from only the stronger receiver enlarges the capacity or leaves it unchanged. The scheme used to prove this result also leads to some interesting observations on noisy feedback from only the weak receiver.
{"title":"When does Partial Noisy Feedback Enlarge the Capacity of a Gaussian Broadcast Channel?","authors":"Aditya Narayan Ravi, S. R. Pillai, V. Prabhakaran, M. Wigger","doi":"10.1109/ISIT44484.2020.9174173","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174173","url":null,"abstract":"Feedback is known to enlarge the capacity region of a Gaussian Broadcast Channel (GBC) with independent noise realizations at the receivers, and an average power constraint at the transmitter. The capacity enlargement may occur even when there is noisy feedback from only one of the two receivers. However, recent results show the existence of a feedback noise threshold, beyond which one-sided feedback from only the stronger receiver is futile in enlarging the capacity region. The current paper presents a tight characterization of the feedback noise threshold, which separates the regimes where feedback from only the stronger receiver enlarges the capacity or leaves it unchanged. The scheme used to prove this result also leads to some interesting observations on noisy feedback from only the weak receiver.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"14 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":"128873818","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/ISIT44484.2020.9174261
Maciej Obremski, M. Skorski
Estimating entropy of random processes is one of the fundamental problems of machine learning and property testing. It has numerous applications to anything from DNA testing and predictability of human behaviour to modeling neural activity and cryptography. We investigate the problem of Renyi entropy estimation for sources that form Markov chains.Kamath and Verd (ISIT’16) showed that good mixing properties are essential for that task. We prove that even with very good mixing time, estimation of entropy of order α > 1 requires Ω(K2−1/α) samples, where K is the size of the alphabet; particularly min-entropy requires Ω(K2) sample size and collision entropy requires Ω(K3/2) samples. Our results hold both in asymptotic and non-asymptotic regimes (under mild restrictions). The analysis is completed by the upper complexity bound of O(K2) for the standard plug-in estimator. This leads to an interesting open question how to improve upon a plugin estimator, which looks much more challenging than for IID sources (which tensorize nicely).We achieve the results by applying Le Cam’s method to two Markov chains which differ by an appropriately chosen sparse perturbation; the discrepancy between these chains is estimated with help of perturbation theory. Our techniques might be of independent interest.
{"title":"Complexity of Estimating Rényi Entropy of Markov Chains","authors":"Maciej Obremski, M. Skorski","doi":"10.1109/ISIT44484.2020.9174261","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174261","url":null,"abstract":"Estimating entropy of random processes is one of the fundamental problems of machine learning and property testing. It has numerous applications to anything from DNA testing and predictability of human behaviour to modeling neural activity and cryptography. We investigate the problem of Renyi entropy estimation for sources that form Markov chains.Kamath and Verd (ISIT’16) showed that good mixing properties are essential for that task. We prove that even with very good mixing time, estimation of entropy of order α > 1 requires Ω(K2−1/α) samples, where K is the size of the alphabet; particularly min-entropy requires Ω(K2) sample size and collision entropy requires Ω(K3/2) samples. Our results hold both in asymptotic and non-asymptotic regimes (under mild restrictions). The analysis is completed by the upper complexity bound of O(K2) for the standard plug-in estimator. This leads to an interesting open question how to improve upon a plugin estimator, which looks much more challenging than for IID sources (which tensorize nicely).We achieve the results by applying Le Cam’s method to two Markov chains which differ by an appropriately chosen sparse perturbation; the discrepancy between these chains is estimated with help of perturbation theory. Our techniques might be of independent interest.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"59 1-3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120992410","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/ISIT44484.2020.9174294
N. Merhav, I. Sason
We explore known integral representations of the logarithmic and power functions, and demonstrate their usefulness for information-theoretic analyses. We obtain compact, easily–computable exact formulas for several source and channel coding problems that involve expectations and higher moments of the logarithm of a positive random variable and the moment of order ρ>0 of a non-negative random variable (or the sum of i.i.d. positive random variables). These integral representations are used in a variety of applications, including the calculation of the degradation in mutual information between the channel input and output as a result of jamming, universal lossless data compression, Shannon and Rényi entropy evaluations, and the ergodic capacity evaluation of the single-input, multiple–output (SIMO) Gaussian channel with random parameters (known to both transmitter and receiver). The integral representation of the logarithmic function and its variants are anticipated to serve as a rigorous alternative to the popular (but non–rigorous) replica method (at least in some situations).
{"title":"Exact Expressions in Source and Channel Coding Problems Using Integral Representations","authors":"N. Merhav, I. Sason","doi":"10.1109/ISIT44484.2020.9174294","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174294","url":null,"abstract":"We explore known integral representations of the logarithmic and power functions, and demonstrate their usefulness for information-theoretic analyses. We obtain compact, easily–computable exact formulas for several source and channel coding problems that involve expectations and higher moments of the logarithm of a positive random variable and the moment of order ρ>0 of a non-negative random variable (or the sum of i.i.d. positive random variables). These integral representations are used in a variety of applications, including the calculation of the degradation in mutual information between the channel input and output as a result of jamming, universal lossless data compression, Shannon and Rényi entropy evaluations, and the ergodic capacity evaluation of the single-input, multiple–output (SIMO) Gaussian channel with random parameters (known to both transmitter and receiver). The integral representation of the logarithmic function and its variants are anticipated to serve as a rigorous alternative to the popular (but non–rigorous) replica method (at least in some situations).","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":"122356417","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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