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  Subjects -> ELECTRONICS (Total: 207 journals)
Showing 1 - 200 of 277 Journals sorted by number of followers
IEEE Transactions on Aerospace and Electronic Systems     Hybrid Journal   (Followers: 283)
Control Systems     Hybrid Journal   (Followers: 238)
IEEE Transactions on Geoscience and Remote Sensing     Hybrid Journal   (Followers: 174)
Journal of Guidance, Control, and Dynamics     Hybrid Journal   (Followers: 167)
Electronic Design     Partially Free   (Followers: 125)
Electronics     Open Access   (Followers: 125)
Advances in Electronics     Open Access   (Followers: 122)
Electronics For You     Partially Free   (Followers: 114)
IEEE Antennas and Propagation Magazine     Hybrid Journal   (Followers: 112)
IEEE Power Electronics Magazine     Full-text available via subscription   (Followers: 90)
IEEE Antennas and Wireless Propagation Letters     Hybrid Journal   (Followers: 88)
IEEE Transactions on Power Electronics     Hybrid Journal   (Followers: 87)
IEEE Transactions on Industrial Electronics     Hybrid Journal   (Followers: 85)
IEEE Transactions on Software Engineering     Hybrid Journal   (Followers: 84)
IEEE Transactions on Antennas and Propagation     Full-text available via subscription   (Followers: 79)
IET Power Electronics     Open Access   (Followers: 76)
IEEE Transactions on Automatic Control     Hybrid Journal   (Followers: 65)
Selected Topics in Applied Earth Observations and Remote Sensing, IEEE Journal of     Hybrid Journal   (Followers: 62)
IEEE Embedded Systems Letters     Hybrid Journal   (Followers: 60)
IEEE Transactions on Industry Applications     Hybrid Journal   (Followers: 57)
Advances in Power Electronics     Open Access   (Followers: 56)
IEEE Journal of Emerging and Selected Topics in Power Electronics     Hybrid Journal   (Followers: 52)
Canadian Journal of Remote Sensing     Full-text available via subscription   (Followers: 50)
IEEE Nanotechnology Magazine     Hybrid Journal   (Followers: 45)
IEEE Transactions on Consumer Electronics     Hybrid Journal   (Followers: 45)
Journal of Electrical and Electronics Engineering Research     Open Access   (Followers: 41)
IET Microwaves, Antennas & Propagation     Open Access   (Followers: 35)
IEEE Transactions on Biomedical Engineering     Hybrid Journal   (Followers: 35)
IEEE Transactions on Circuits and Systems for Video Technology     Hybrid Journal   (Followers: 31)
International Journal of Power Electronics     Hybrid Journal   (Followers: 30)
Bell Labs Technical Journal     Hybrid Journal   (Followers: 27)
IEEE Transactions on Information Theory     Hybrid Journal   (Followers: 27)
Microelectronics and Solid State Electronics     Open Access   (Followers: 27)
American Journal of Electrical and Electronic Engineering     Open Access   (Followers: 26)
Journal of Sensors     Open Access   (Followers: 25)
Electronics Letters     Open Access   (Followers: 25)
International Journal of Aerospace Innovations     Full-text available via subscription   (Followers: 23)
International Journal of Image, Graphics and Signal Processing     Open Access   (Followers: 22)
Journal of Power Electronics & Power Systems     Full-text available via subscription   (Followers: 19)
IEEE Reviews in Biomedical Engineering     Hybrid Journal   (Followers: 19)
IEEE/OSA Journal of Optical Communications and Networking     Hybrid Journal   (Followers: 19)
Journal of Artificial Intelligence     Open Access   (Followers: 18)
IEEE Transactions on Electron Devices     Hybrid Journal   (Followers: 18)
IET Wireless Sensor Systems     Open Access   (Followers: 17)
Circuits and Systems     Open Access   (Followers: 16)
International Journal of Microwave and Wireless Technologies     Hybrid Journal   (Followers: 16)
IEEE Transactions on Signal and Information Processing over Networks     Hybrid Journal   (Followers: 14)
Journal of Low Power Electronics     Full-text available via subscription   (Followers: 14)
International Journal of Advanced Research in Computer Science and Electronics Engineering     Open Access   (Followers: 14)
Archives of Electrical Engineering     Open Access   (Followers: 14)
International Journal of Control     Hybrid Journal   (Followers: 13)
International Journal of Sensors, Wireless Communications and Control     Hybrid Journal   (Followers: 13)
Advances in Microelectronic Engineering     Open Access   (Followers: 12)
IEEE Transactions on Learning Technologies     Full-text available via subscription   (Followers: 12)
International Journal of Wireless and Microwave Technologies     Open Access   (Followers: 12)
International Journal of Advances in Telecommunications, Electrotechnics, Signals and Systems     Open Access   (Followers: 12)
Intelligent Transportation Systems Magazine, IEEE     Full-text available via subscription   (Followers: 12)
IEEE Solid-State Circuits Magazine     Hybrid Journal   (Followers: 11)
IEICE - Transactions on Electronics     Full-text available via subscription   (Followers: 11)
IEEE Women in Engineering Magazine     Hybrid Journal   (Followers: 11)
IEEE Transactions on Broadcasting     Hybrid Journal   (Followers: 11)
Journal of Electromagnetic Waves and Applications     Hybrid Journal   (Followers: 10)
International Journal of Advanced Electronics and Communication Systems     Open Access   (Followers: 10)
International Journal of Antennas and Propagation     Open Access   (Followers: 10)
IETE Journal of Research     Open Access   (Followers: 10)
Journal of Low Power Electronics and Applications     Open Access   (Followers: 9)
IETE Technical Review     Open Access   (Followers: 9)
Batteries     Open Access   (Followers: 8)
IEEE Journal of the Electron Devices Society     Open Access   (Followers: 8)
IEEE Transactions on Autonomous Mental Development     Hybrid Journal   (Followers: 8)
Journal of Power Electronics     Hybrid Journal   (Followers: 8)
China Communications     Full-text available via subscription   (Followers: 8)
International Journal of Electronics and Telecommunications     Open Access   (Followers: 8)
Open Journal of Antennas and Propagation     Open Access   (Followers: 8)
Metrology and Measurement Systems     Open Access   (Followers: 8)
APSIPA Transactions on Signal and Information Processing     Open Access   (Followers: 8)
Journal of Microwave Power and Electromagnetic Energy     Hybrid Journal   (Followers: 8)
Progress in Quantum Electronics     Full-text available via subscription   (Followers: 8)
Electronics and Communications in Japan     Hybrid Journal   (Followers: 8)
Solid-State Electronics     Hybrid Journal   (Followers: 7)
Nanotechnology, Science and Applications     Open Access   (Followers: 7)
Universal Journal of Electrical and Electronic Engineering     Open Access   (Followers: 7)
International Journal of Electronics     Hybrid Journal   (Followers: 7)
IEEE Magnetics Letters     Hybrid Journal   (Followers: 7)
Foundations and Trends® in Signal Processing     Full-text available via subscription   (Followers: 7)
Journal of Electromagnetic Analysis and Applications     Open Access   (Followers: 6)
Foundations and Trends® in Communications and Information Theory     Full-text available via subscription   (Followers: 6)
Annals of Telecommunications     Hybrid Journal   (Followers: 6)
Electronic Markets     Hybrid Journal   (Followers: 6)
International Journal of Systems, Control and Communications     Hybrid Journal   (Followers: 6)
Advances in Biosensors and Bioelectronics     Open Access   (Followers: 6)
Research & Reviews : Journal of Embedded System & Applications     Full-text available via subscription   (Followers: 6)
IEICE - Transactions on Information and Systems     Full-text available via subscription   (Followers: 5)
Kinetik : Game Technology, Information System, Computer Network, Computing, Electronics, and Control     Open Access   (Followers: 5)
Journal of Electronics (China)     Hybrid Journal   (Followers: 5)
Journal of Field Robotics     Hybrid Journal   (Followers: 5)
Energy Storage Materials     Full-text available via subscription   (Followers: 5)
IEEE Pulse     Hybrid Journal   (Followers: 5)
International Journal of Computational Vision and Robotics     Hybrid Journal   (Followers: 5)
Advances in Electrical and Electronic Engineering     Open Access   (Followers: 5)
Batteries & Supercaps     Hybrid Journal   (Followers: 5)
IEEE Transactions on Services Computing     Hybrid Journal   (Followers: 5)
Journal of Electrical Engineering & Electronic Technology     Hybrid Journal   (Followers: 4)
Wireless and Mobile Technologies     Open Access   (Followers: 4)
Superconductivity     Full-text available via subscription   (Followers: 4)
IEEE Transactions on Haptics     Hybrid Journal   (Followers: 4)
Synthesis Lectures on Power Electronics     Full-text available via subscription   (Followers: 4)
Journal of Biosensors & Bioelectronics     Open Access   (Followers: 4)
Networks: an International Journal     Hybrid Journal   (Followers: 4)
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields     Hybrid Journal   (Followers: 4)
Electronic Materials Letters     Hybrid Journal   (Followers: 4)
Journal of Circuits, Systems, and Computers     Hybrid Journal   (Followers: 4)
Journal of Energy Storage     Full-text available via subscription   (Followers: 4)
Journal of Optoelectronics Engineering     Open Access   (Followers: 4)
Sensors International     Open Access   (Followers: 3)
Nature Electronics     Hybrid Journal   (Followers: 3)
IJEIS (Indonesian Journal of Electronics and Instrumentation Systems)     Open Access   (Followers: 3)
EPE Journal : European Power Electronics and Drives     Hybrid Journal   (Followers: 3)
Machine Learning with Applications     Full-text available via subscription   (Followers: 3)
International Journal of Applied Electronics in Physics & Robotics     Open Access   (Followers: 3)
Informatik-Spektrum     Hybrid Journal   (Followers: 3)
IETE Journal of Education     Open Access   (Followers: 3)
International Transaction of Electrical and Computer Engineers System     Open Access   (Followers: 2)
IEEE Journal on Exploratory Solid-State Computational Devices and Circuits     Hybrid Journal   (Followers: 2)
Power Electronics and Drives     Open Access   (Followers: 2)
Security and Communication Networks     Hybrid Journal   (Followers: 2)
Journal of Microelectronics and Electronic Packaging     Hybrid Journal   (Followers: 2)
Advancing Microelectronics     Hybrid Journal   (Followers: 2)
Transactions on Electrical and Electronic Materials     Hybrid Journal   (Followers: 2)
Energy Storage     Hybrid Journal   (Followers: 2)
Journal of Information and Telecommunication     Open Access   (Followers: 2)
Sensing and Imaging : An International Journal     Hybrid Journal   (Followers: 2)
Radiophysics and Quantum Electronics     Hybrid Journal   (Followers: 2)
TELKOMNIKA (Telecommunication, Computing, Electronics and Control)     Open Access   (Followers: 2)
Advanced Materials Technologies     Hybrid Journal   (Followers: 2)
EPJ Quantum Technology     Open Access   (Followers: 2)
e-Prime : Advances in Electrical Engineering, Electronics and Energy     Open Access   (Followers: 2)
Journal of Intelligent Procedures in Electrical Technology     Open Access   (Followers: 2)
IET Smart Grid     Open Access   (Followers: 2)
International Journal of Review in Electronics & Communication Engineering     Open Access   (Followers: 2)
Journal of Nuclear Cardiology     Hybrid Journal   (Followers: 1)
Transactions on Cryptographic Hardware and Embedded Systems     Open Access   (Followers: 1)
ACS Applied Electronic Materials     Open Access   (Followers: 1)
Frontiers in Electronics     Open Access   (Followers: 1)
IEEE Letters on Electromagnetic Compatibility Practice and Applications     Hybrid Journal   (Followers: 1)
Semiconductors and Semimetals     Full-text available via subscription   (Followers: 1)
International Journal of Granular Computing, Rough Sets and Intelligent Systems     Hybrid Journal   (Followers: 1)
IET Energy Systems Integration     Open Access   (Followers: 1)
ECTI Transactions on Electrical Engineering, Electronics, and Communications     Open Access   (Followers: 1)
International Journal of Hybrid Intelligence     Hybrid Journal   (Followers: 1)
Open Electrical & Electronic Engineering Journal     Open Access   (Followers: 1)
Ural Radio Engineering Journal     Open Access   (Followers: 1)
Frontiers of Optoelectronics     Hybrid Journal   (Followers: 1)
Електротехніка і Електромеханіка     Open Access   (Followers: 1)
Edu Elektrika Journal     Open Access   (Followers: 1)
Journal of Computational Intelligence and Electronic Systems     Full-text available via subscription   (Followers: 1)
Majalah Ilmiah Teknologi Elektro : Journal of Electrical Technology     Open Access   (Followers: 1)
Journal of Advanced Dielectrics     Open Access   (Followers: 1)
IET Cyber-Physical Systems : Theory & Applications     Open Access   (Followers: 1)
Automatika : Journal for Control, Measurement, Electronics, Computing and Communications     Open Access  
npj Flexible Electronics     Open Access  
Elektronika ir Elektortechnika     Open Access  
Emitor : Jurnal Teknik Elektro     Open Access  
IEEE Solid-State Circuits Letters     Hybrid Journal  
IEEE Open Journal of Industry Applications     Open Access  
IEEE Open Journal of the Industrial Electronics Society     Open Access  
IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology     Hybrid Journal  
IEEE Open Journal of Circuits and Systems     Open Access  
Journal of Electronic Science and Technology     Open Access  
Australian Journal of Electrical and Electronics Engineering     Hybrid Journal  
Solid State Electronics Letters     Open Access  
Industrial Technology Research Journal Phranakhon Rajabhat University     Open Access  
Journal of Engineered Fibers and Fabrics     Open Access  
Jurnal Teknologi Elektro     Open Access  
IET Nanodielectrics     Open Access  
Elkha : Jurnal Teknik Elektro     Open Access  
JAREE (Journal on Advanced Research in Electrical Engineering)     Open Access  
Jurnal Teknik Elektro     Open Access  
IACR Transactions on Symmetric Cryptology     Open Access  
Acta Electronica Malaysia     Open Access  
Bioelectronics in Medicine     Hybrid Journal  
Chinese Journal of Electronics     Open Access  
Problemy Peredachi Informatsii     Full-text available via subscription  
Technical Report Electronics and Computer Engineering     Open Access  
Jurnal Rekayasa Elektrika     Open Access  
Facta Universitatis, Series : Electronics and Energetics     Open Access  
Visión Electrónica : algo más que un estado sólido     Open Access  
Telematique     Open Access  
International Journal of Nanoscience     Hybrid Journal  
International Journal of High Speed Electronics and Systems     Hybrid Journal  

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Similar Journals
Journal Cover
IEEE Transactions on Information Theory
Journal Prestige (SJR): 1.162
Citation Impact (citeScore): 3
Number of Followers: 27  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0018-9448
Published by IEEE Homepage  [228 journals]
  • IEEE Transactions on Information Theory publication information

    • Free pre-print version: Loading...

      Abstract: Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • IEEE Transactions on Information Theory information for authors

    • Free pre-print version: Loading...

      Abstract: These instructions give guidelines for preparing papers for this publication. Presents information for authors publishing in this journal.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Decoder Ties Do Not Affect the Error Exponent of the Memoryless Binary
           Symmetric Channel

    • Free pre-print version: Loading...

      Authors: Ling-Hua Chang;Po-Ning Chen;Fady Alajaji;Yunghsiang S. Han;
      Pages: 3501 - 3510
      Abstract: The generalized Poor-Verdú error lower bound established by Chang et al. (2020) for multihypothesis testing is studied in the classical channel coding context. It is proved that for any sequence of block codes sent over the memoryless binary symmetric channel (BSC), the minimum probability of error (under maximum likelihood decoding) has a relative deviation from the generalized bound that grows at most linearly in blocklength. This result directly implies that for arbitrary codes used over the BSC, decoder ties can only affect the subexponential behavior of the minimum probability of error.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Nearest Neighbor Density Functional Estimation From Inverse Laplace
           Transform

    • Free pre-print version: Loading...

      Authors: J. Jon Ryu;Shouvik Ganguly;Young-Han Kim;Yung-Kyun Noh;Daniel D. Lee;
      Pages: 3511 - 3551
      Abstract: A new approach to $L_{2}$ -consistent estimation of a general density functional using $k$ -nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities at each point. The estimator is designed to be asymptotically unbiased, using the convergence of the normalized volume of a $k$ -nearest neighbor ball to a Gamma distribution in the large-sample limit, and naturally involves the inverse Laplace transform of a scaled version of the function $f$ . Some instantiations of the proposed estimator recover existing $k$ -nearest neighbor based estimators of Shannon and Rényi entropies and Kullback–Leibler and Rényi divergences, and discover new consistent estimators for many other functionals such as logarithmic entropies and divergences. The $L_{2}$ -consistency of the proposed estimator is established for a broad class of densities for general functionals, and the convergence rate in mean squared error is established as a function of the sample size for smooth, bounded densities.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • A Second-Order Converse Bound for the Multiple-Access Channel via Wringing
           Dependence

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      Authors: Oliver Kosut;
      Pages: 3552 - 3584
      Abstract: A new converse bound is presented for the two-user multiple-access channel under the average probability of error constraint. This bound shows that for most channels of interest, the second-order coding rate—that is, the difference between the best achievable rates and the asymptotic capacity region as a function of blocklength $n$ with fixed probability of error—is $O(1/sqrt {n})$ bits per channel use. The principal tool behind this converse proof is a new measure of dependence between two random variables called wringing dependence, as it is inspired by Ahlswede’s wringing technique. The $O(1/sqrt {n})$ gap is shown to hold for any channel satisfying certain regularity conditions, which includes all discrete-memoryless channels and the Gaussian multiple-access channel. Exact upper bounds as a function of the probability of error are proved for the coefficient in the $O(1/sqrt {n})$ term, although for most channels they do not match existing achievable bounds.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Second-Order Asymptotically Optimal Outlier Hypothesis Testing

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      Authors: Lin Zhou;Yun Wei;Alfred O. Hero;
      Pages: 3585 - 3607
      Abstract: We revisit the outlier hypothesis testing framework of Li et al. (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are generated i.i.d. from a nominal distribution. The task is to discern the set of outlying sequences that are generated from anomalous distributions. The nominal and anomalous distributions are unknown. We study the tradeoff among the probabilities of misclassification error, false alarm and false reject for tests that satisfy weak conditions on the rate of decrease of these error probabilities as a function of sequence length. Specifically, we propose a threshold-based test that ensures exponential decay of misclassification error and false alarm probabilities. We study two constraints on the false reject probability, with one constraint being that it is a non-vanishing constant and the other being that it has an exponential decay rate. For both cases, we characterize bounds on the false reject probability, as a function of the threshold, for each pair of nominal and anomalous distributions and demonstrate the optimality of our test under the generalized Neyman-Pearson criterion. We first consider the case of at most one outlying sequence and then generalize our results to the case of multiple outlying sequences where the number of outlying sequences is unknown and each outlying sequence can follow a different anomalous distribution.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Multiple Access Channel Resolvability Codes From Source Resolvability
           Codes

    • Free pre-print version: Loading...

      Authors: Rumia Sultana;Rémi A. Chou;
      Pages: 3608 - 3619
      Abstract: We show that the problem of code construction for multiple access channel (MAC) resolvability can be reduced to the simpler problem of code construction for source resolvability. Specifically, we propose a MAC resolvability code construction that relies on a combination of multiple source resolvability codes, used in a black-box manner, and leverages randomness recycling implemented via distributed hashing and block-Markov coding. Since explicit source resolvability codes are known, our results also yield the first explicit coding schemes that achieve the entire MAC resolvability region for any discrete memoryless multiple-access channel with binary input alphabets.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Secure List Decoding and its Application to Bit-String Commitment

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      Authors: Masahito Hayashi;
      Pages: 3620 - 3642
      Abstract: We propose a new concept of secure list decoding, which is related to bit-string commitment. While the conventional list decoding requires that the list contains the transmitted message, secure list decoding requires the following additional security conditions to work as a modification of bit-string commitment. The first additional security condition is the receiver’s uncertainty for the transmitted message, which is stronger than the impossibility of the correct decoding, even though the transmitted message is contained in the list. The other additional security condition is the impossibility for the sender to estimate another element of the decoded list except for the transmitted message. The first condition is evaluated by the equivocation rate. The asymptotic property is evaluated by three parameters, the rates of the message and list sizes, and the equivocation rate. We derive the capacity region of this problem. We show that the combination of hash function and secure list decoding yields the conventional bit-string commitment. Our results hold even when the input and output systems are general probability spaces including continuous systems. When the input system is a general probability space, we formulate the abilities of the honest sender and the dishonest sender in a different way.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • The Subfield Codes of Some [q + 1, 2,
           q] MDS Codes

    • Free pre-print version: Loading...

      Authors: Ziling Heng;Cunsheng Ding;
      Pages: 3643 - 3656
      Abstract: Recently, subfield codes of geometric codes over large finite fields ${mathrm {GF}}(q)$ with dimension 3 and 4 were studied and distance-optimal subfield codes over ${mathrm {GF}}(p)$ were obtained, where $q=p^{m}$ . The key idea for obtaining very good subfield codes over small fields is to choose very good linear codes over an extension field with small dimension. This paper first presents a general construction of $[q+1, 2, q]$ MDS codes over ${mathrm {GF}}(q)$ , and then studies the subfield codes over ${mathrm {GF}}(p)$ of some of the $[q+1, 2,q]$ MDS codes over ${mathrm {GF}}(q)$ . Two families of dimension-optimal codes over ${mathrm {GF}}(p)$ are obtained, and several families of nearly optimal codes over ${mathrm {GF}}(p)$ are produced. Several open problems are also proposed in this paper.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Hierarchical Coding for Cloud Storage: Topology-Adaptivity, Scalability,
           and Flexibility

    • Free pre-print version: Loading...

      Authors: Siyi Yang;Ahmed Hareedy;Robert Calderbank;Lara Dolecek;
      Pages: 3657 - 3680
      Abstract: In order to accommodate the ever-growing data from various, possibly independent, sources and the dynamic nature of data usage rates in practical applications, modern cloud data storage systems are required to be scalable, flexible, and heterogeneous. The recent rise of the blockchain technology is also moving various information systems towards decentralization to achieve high privacy at low costs. While codes with hierarchical locality have been intensively studied in the context of centralized cloud storage due to their effectiveness in reducing the average reading time, those for decentralized storage networks (DSNs) have not yet been discussed. In this paper, we propose a joint coding scheme where each node receives extra protection through the cooperation with nodes in its neighborhood in a heterogeneous DSN with any given topology. This work extends and subsumes our prior work on coding for centralized cloud storage. In particular, our proposed construction not only preserves desirable properties such as scalability and flexibility, which are critical in dynamic networks, but also adapts to arbitrary topologies, a property that is essential in DSNs but has been overlooked in existing works.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Recoverable Systems

    • Free pre-print version: Loading...

      Authors: Ohad Elishco;Alexander Barg;
      Pages: 3681 - 3699
      Abstract: Motivated by the established notion of storage codes, we consider sets of infinite sequences over a finite alphabet such that every $k$ -tuple of consecutive entries is uniquely recoverable from its $l$ -neighborhood in the sequence. We address the problem of finding the maximum growth rate of the set, which we term capacity, as well as constructions of explicit families that approach the optimal rate. The techniques that we employ rely on the connection of this problem with constrained systems. In the second part of the paper we consider a modification of the problem wherein the entries in the sequence are viewed as random variables over a finite alphabet that follow some joint distribution, and the recovery condition requires that the Shannon entropy of the $k$ -tuple conditioned on its $l$ -neighborhood be bounded above by some $epsilon>0$ . We study properties of measures on infinite sequences that maximize the metric entropy under the recoverability condition. Drawing on tools from ergodic theory, we prove some properties of entropy-maximizing measures. We also suggest a procedure of constructing an $epsilon $ -recoverable measure from a corresponding deterministic system.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • On the Decoding Performance of Spatially Coupled LDPC Codes With Sub-Block
           Access

    • Free pre-print version: Loading...

      Authors: Eshed Ram;Yuval Cassuto;
      Pages: 3700 - 3718
      Abstract: We study spatially coupled LDPC codes that allow access to sub-blocks much smaller than the full code block. Sub-block access is realized by a semi-global decoder that decodes a chosen target sub-block by only accessing the target, plus a prescribed number of helper sub-blocks adjacent in the code chain. This paper develops a theoretical methodology for analyzing the semi-global decoding performance of spatially coupled LDPC codes constructed from protographs. The main result shows that semi-global decoding thresholds can be derived from certain thresholds we define for the single-sub-block graph. These characterizing thresholds are also used for deriving lower bounds on the decoder’s performance over channels with variability across sub-blocks, which are motivated by applications in data storage.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Improved Rank-Modulation Codes for DNA Storage With Shotgun Sequencing

    • Free pre-print version: Loading...

      Authors: Niv Beeri;Moshe Schwartz;
      Pages: 3719 - 3730
      Abstract: A common method for reading information stored in DNA molecules is shotgun sequencing. This method outputs a histogram of the frequencies of all the molecules’ substrings of a given length $ell $ . To protect against noisy readings, the rank-modulation scheme encodes the information in the relative ranking of the substring frequencies, instead of their absolute values. However, the best rank-modulation codes for shotgun sequencing have low rates which are asymptotically vanishing. In this paper we propose new constructions of rank-modulation codes for shotgun sequencing. The first code construction is systematic, allowing the user to arbitrarily set the frequencies of a large subset of the substrings, which the encoder then completes to a permutation that may be realized by a DNA molecule. The construction is then improved by allowing the user to set the frequencies of additional substrings, at the cost of imposing constraints on the frequencies. The resulting codes have higher, non-vanishing rates, compared with previously known codes. As an example, for histograms of substrings of length $ell =2$ , and an alphabet of size 4 (as in DNA molecules), we are able to construct a code with rate $approx 0.909$ , whereas previously, the best construction resulted in a code with rate $approx 0.654$ . Additionally, the encoded information in our construction may be written to shorter DNA molecules than possible before. We also prove that the systematic codes constructed in this paper are the largest possible among all systematic codes.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Coding With Noiseless Feedback Over the Z-Channel

    • Free pre-print version: Loading...

      Authors: Christian Deppe;Vladimir Lebedev;Georg Maringer;Nikita Polyanskii;
      Pages: 3731 - 3739
      Abstract: In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze the combinatorial setting where the maximum number of errors inflicted by an adversary is proportional to the number of transmissions, which goes to infinity. Without feedback, it is known that the rate of optimal asymmetric-error-correcting codes for the error fraction $tau ge 1/4$ vanishes as the blocklength grows. In this paper, we give an efficient feedback encoding scheme with $n$ transmissions that achieves a positive rate for any fraction of errors $tau < 1$ and $nto infty $ . Additionally, we state an upper bound on the rate of asymptotically long feedback asymmetric error-correcting codes.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Base Field Extension of AG Codes for Decoding

    • Free pre-print version: Loading...

      Authors: Kwankyu Lee;
      Pages: 3740 - 3743
      Abstract: Previous algorithms for decoding AG codes up to the designed distance all assumed existence of an extra rational place on the base algebraic curve. The place is used to solve the decoding problem by linear algebra over the base field of the curve. The rationality of the place is essential, and therefore AG codes supported by all rational places on the curve are excluded from the domain of applicability of the decoding algorithms. This paper presents a decoding algorithm for those AG codes using an extra place of higher degree. Hence finally all AG codes, as Goppa defined 40 years ago, are equipped with a fast decoding algorithm.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • CRC-Aided List Decoding of Convolutional Codes in the Short Blocklength
           Regime

    • Free pre-print version: Loading...

      Authors: Hengjie Yang;Ethan Liang;Minghao Pan;Richard D. Wesel;
      Pages: 3744 - 3766
      Abstract: We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use of serial list Viterbi decoding (SLVD) to achieve maximum-likelihood decoding. The convolutional encoder of interest is of rate- $1/omega $ and the convolutional code is either zero-terminated (ZT) or tail-biting (TB). The resulting CRC-aided convolutional code is called a CRC-ZTCC or a CRC-TBCC. To design a good CRC-aided convolutional code, we propose the distance-spectrum optimal (DSO) CRC polynomial. A DSO CRC search algorithm for the TBCC is provided. Our analysis reveals that the complexity of SLVD is governed by the expected list rank which converges to 1 at high SNR. This allows a good performance to be achieved with a small increase in complexity. In this paper, we focus on transmitting 64 information bits with a rate-1/2 convolutional encoder. For a target error probability $10^{-4}$ , simulations show that the best CRC-ZTCC approaches the random-coding union (RCU) bound within 0.4 dB. Several CRC-TBCCs outperform the RCU bound at moderate SNR values.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Multiple Criss-Cross Insertion and Deletion Correcting Codes

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      Authors: Lorenz Welter;Rawad Bitar;Antonia Wachter-Zeh;Eitan Yaakobi;
      Pages: 3767 - 3779
      Abstract: This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of $n times n$ arrays affected by ${t}$ -criss-cross deletions defined as any combination of ${t_{mathrm {r}}}$ row and ${t_{mathrm {c}}}$ column deletions such that ${t_{mathrm {r}}}+ {t_{mathrm {c}}}= {t}$ for a given $t$ . We show an equivalence between correcting ${t}$ -criss-cross deletions and ${t}$ -criss-cross insertions and show that a code correcting ${t}$ -criss-cross insertions/deletions has redundancy at least ${t} n + {t}log n - log ({t}!)$ . Then, we present an existential construction of a ${t}$ -criss-cross insertion/deletion correcting code with redundancy bounded from above by ${t} n + mathcal {O}({t}^{2} log ^{2} n)$ . The main ingredients of the presented code construction are systematic binary ${t}$ -deletion correcting codes and Gabidulin codes. The first ingredient helps locating the indices of the inserted/deleted rows and columns, thus transfo-ming the insertion/deletion-correction problem into a row/column erasure-correction problem which is then solved using the second ingredient.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Shortened Linear Codes From APN and PN Functions

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      Authors: Can Xiang;Chunming Tang;Cunsheng Ding;
      Pages: 3780 - 3795
      Abstract: Linear codes generated by component functions of perfect nonlinear (PN for short) and almost perfect nonlinear (APN for short) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper is to investigate some binary shortened codes of two families of linear codes from APN functions and some $p$ -ary shortened codes associated with PN functions. The weight distributions of these shortened codes and the parameters of their duals are determined. The parameters of these binary codes and $p$ -ary codes are flexible. Many of the codes presented in this paper are optimal or almost optimal. The results of this paper show that the shortening technique is very promising for constructing good codes.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Determining When a Truncated Generalised Reed-Solomon Code Is Hermitian
           Self-Orthogonal

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      Authors: Simeon Ball;Ricard Vilar;
      Pages: 3796 - 3805
      Abstract: We prove that there is a Hermitian self-orthogonal $k$ -dimensional truncated generalised Reed-Solomon code of length $n leqslant q^{2}$ over ${mathbb F}_{q^{2}}$ if and only if there is a polynomial $g in {mathbb F}_{q^{2}}$ of degree at most $(q-k)q-1$ such that $g+g^{q}$ has $q^{2}-n$ distinct zeros. This allows us to determine the smallest $n$ for which there is a Hermitian self-orthogonal $k$ -dimensional truncated generalised Reed-Solomon code of length $n$ over ${mathbb F}_{q^{2}}$ , verifying a conjecture of Grassl and Rötteler. We also provide examples of Hermitian self-orthogonal $k$ -dimensional generalised Reed-Solomon codes of length $q^{2}+1$ over ${mathbb F}_{q^{2}}$ , for $k=q-1$ and $q$ an odd power of two.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Optimal Anticodes, MSRD Codes, and Generalized Weights in the Sum-Rank
           Metric

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      Authors: Eduardo Camps-Moreno;Elisa Gorla;Cristina Landolina;Elisa Lorenzo García;Umberto Martínez-Peñas;Flavio Salizzoni;
      Pages: 3806 - 3822
      Abstract: Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural generalization of both the Hamming metric and the rank metric. In this paper, we provide an Anticode Bound for the sum-rank metric, which extends the corresponding Hamming and rank-metric Anticode bounds. We classify then optimal anticodes, i.e., codes attaining the sum-rank metric Anticode Bound. We use these optimal anticodes to define generalized sum-rank weights and we study their main properties. In particular, we prove that the generalized weights of an MSRD code are determined by its parameters. As an application, in the Appendix we explain how generalized weights measure information leakage in multishot network coding.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • List-Decodability With Large Radius for Reed-Solomon Codes

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      Authors: Asaf Ferber;Matthew Kwan;Lisa Sauermann;
      Pages: 3823 - 3828
      Abstract: List-decodability of Reed–Solomon codes has received a lot of attention, but the best-possible dependence between the parameters is still not well-understood. In this work, we focus on the case where the list-decoding radius is of the form $r=1-varepsilon $ for $varepsilon $ tending to zero. Our main result states that there exist Reed–Solomon codes with rate $Omega (varepsilon)$ which are $(1-varepsilon, O(1/varepsilon))$ -list-decodable, meaning that any Hamming ball of radius $1-varepsilon $ contains at most $O(1/varepsilon)$ codewords. This trade-off between rate and list-decoding radius is best-possible for any code with list size less than exponential in the block length. By achieving this trade-off between rate and list-decoding radius we improve a recent result of Guo, Li, Shangguan, Tamo, and Wootters, and resolve the main motivating question of their work. Moreover, while their result requires the field to be exponentially large in the block length, we only need the field size to be polynomially large (and in fact, almost-linear suffices). We deduce our main result from a more general theorem, in which we prove good list-decodability properties of random puncturings of any given code with very large distance.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Compact and Flexible KEM From Ideal Lattice

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      Authors: Zhengzhong Jin;Shiyu Shen;Yunlei Zhao;
      Pages: 3829 - 3840
      Abstract: A remarkable breakthrough in mathematics in recent years is the proof of the long-standing conjecture: sphere packing in the $E_{8}$ lattice is optimal in the sense of the best density for sphere packing in $mathbb {R}^{8}$ . In this work, we design a mechanism for asymmetric key consensus from noise (AKCN), referred to as AKCN-E8, for error correction and key consensus. As a direct application, we present a practical key encapsulation mechanism (KEM) from the ideal lattice based on the ring learning with errors (RLWE) problem. Compared with NewHope-KEM that was the second round candidate of the National Institute of Standards and Technology (NIST) post-quantum cryptography (PQC) standardization, our AKCN-E8 KEM scheme overcomes some limitations and shortcomings of NewHope-KEM. Compared with some other dominating KEM schemes based on the variants of LWE, specifically Kyber and Saber, AKCN-E8 has a comparable performance but enjoys much flexible shared-key sizes. Specifically, the key encapsulated by AKCN-E8-512 (resp., 768, 1024) has the size of 256 (resp., 384, 512) bits. Flexible key size renders us stronger security against quantum attacks, more powerful and economic ability of key transportation, and better matches the demand in interactive protocols like TLS where parties need to negotiate the security parameters including the shared key length.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Transmit Correlation Diversity: Generalization, New Techniques, and
           Improved Bounds

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      Authors: Fan Zhang;Khac-Hoang Ngo;Sheng Yang;Aria Nosratinia;
      Pages: 3841 - 3869
      Abstract: When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted transmit correlation diversity. This idea was conceived for channels in which transmit correlation matrices have mutually exclusive eigenspaces, allowing non-interfering training and transmission. This paper broadens the scope of transmit correlation diversity to the case of partially and fully overlapping eigenspaces and introduces techniques to harvest these generalized gains. For the two-user MIMO broadcast channel, we derive achievable degrees of freedom (DoF) and achievable rate regions with/without channel state information at the receiver (CSIR). When CSIR is available, the proposed achievable DoF region is tight in some configurations of the number of receive antennas and the channel correlation ranks. We then extend the DoF results to the $K$ -user case by analyzing the interference graph that characterizes the overlapping structure of the eigenspaces. Our achievability results employ a combination of product superposition in the common part of the eigenspaces, and pre-beamforming (rate splitting) to create multiple data streams in non-overlapping parts of the eigenspaces. Massive MIMO is a natural example in which spatially correlated link gains are likely to occur. We study the achievable downlink sum rate for a frequency-division duplex massive MIMO system under transmit correlation diversity.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Iterative Message Passing Algorithm for Vertex-Disjoint Shortest Paths

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      Authors: Guowei Dai;Longkun Guo;Gregory Gutin;Xiaoyan Zhang;Zan-Bo Zhang;
      Pages: 3870 - 3878
      Abstract: As an algorithmic framework, message passing is extremely powerful and has wide applications in the context of different disciplines including communications, coding theory, statistics, signal processing, artificial intelligence and combinatorial optimization. In this paper, we investigate the performance of a message-passing algorithm called min-sum belief propagation (BP) for the vertex-disjoint shortest $k$ -path problem ( $k$ -VDSP) on weighted directed graphs, and derive the iterative message-passing update rules. As the main result of this paper, we prove that for a weighted directed graph $G$ of order $n$ , BP algorithm converges to the unique optimal solution of $k$ -VDSP on $G$ within $O(n^{2}w_{max})$ iterations, provided that the weight $w_{e}$ is nonnegative integral for each arc $ein E(G)$ , where $w_{max}=max {w_{e}: ein E(G)}$ . To the best of our knowledge, this is the first instance where BP algorithm is proved correct for NP-hard problems. Additionally, we establish the extensions of $k$ -VDSP to the case of multiple sources or sinks.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • The Langberg-Médard Multiple Unicast Conjecture for 3-Pair Networks

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      Authors: Kai Cai;Guangyue Han;
      Pages: 3879 - 3895
      Abstract: The Langberg-Médard multiple unicast conjecture claims that for a strongly reachable $k$ -pair network, there exists a feasible multi-flow with rate $(1,1, {dots },1)$ . In this paper, we confirm the conjecture for $k=3$ .
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Closed-Form Characterization of the MGF of AoI in Energy Harvesting Status
           Update Systems

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      Authors: Mohamed A. Abd-Elmagid;Harpreet S. Dhillon;
      Pages: 3896 - 3919
      Abstract: This paper considers a real-time status update system in which an energy harvesting (EH)-powered transmitter node observes some physical process, and sends its sensed measurements in the form of status updates to a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify the freshness of status updates when they reach the destination using the concept of Age of Information (AoI). Unlike most of the existing analyses of AoI focusing on the evaluation of its average value when the transmitter is not subject to energy constraints, our analysis is focused on understanding the distributional properties of AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and preemptive in service/waiting strategies. Using these MGF results, we further obtain closed-form expressions for the first and second moments of AoI in each queueing discipline. We demonstrate the generality of this analysis by recovering several existing results for the corresponding system with no energy constraints as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the necessity of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • On the Capacity of MISO Optical Intensity Channels With Per-Antenna
           Intensity Constraints

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      Authors: Ru-Han Chen;Longguang Li;Jian Zhang;Wenyi Zhang;Jing Zhou;
      Pages: 3920 - 3941
      Abstract: This paper investigates the capacity of general multiple-input single-output (MISO) optical intensity channels (OICs) under per-antenna peak- and average-intensity constraints. We first consider the MISO equal-cost constrained OIC (EC-OIC), where, apart from the peak-intensity constraint, average intensities of inputs are equal to arbitrarily preassigned constants. The second model of our interest is the MISO bounded-cost constrained OIC (BC-OIC), where, as compared with the EC-OIC, average intensities of inputs are no larger than arbitrarily preassigned constants. By leveraging tools from quantile functions, stop-loss transform and convex ordering of nonnegative random variables, we prove two decomposition theorems for bounded and nonnegative random variables, based on which we equivalently transform both the EC-OIC and the BC-OIC into respective single-input single-output channels under a peak-intensity and several stop-loss mean constraints. Capacity lower and upper bounds for both channels are established, based on which the asymptotic capacity at high and low signal-to-noise-ratio are determined.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Entropic Proofs of Singleton Bounds for Quantum Error-Correcting Codes

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      Authors: Markus Grassl;Felix Huber;Andreas Winter;
      Pages: 3942 - 3950
      Abstract: We show that a relatively simple reasoning using von Neumann entropy inequalities yields a robust proof of the quantum Singleton bound for quantum error-correcting codes (QECC). For entanglement-assisted quantum error-correcting codes (EAQECC) and catalytic codes (CQECC), a type of generalized quantum Singleton bound [Brun et al., IEEE Trans. Inf. Theory 60(6):3073–3089 (2014)] was believed to hold for many years until recently one of us found a counterexample [MG, Phys. Rev. A 103, 020601 (2021)]. Here, we rectify this state of affairs by proving the correct generalized quantum Singleton bound, extending the above-mentioned proof method for QECC; we also prove information-theoretically tight bounds on the entanglement-communication tradeoff for EAQECC. All of the bounds relate block length $n$ and code length $k$ for given minimum distance $d$ and we show that they are robust, in the sense that they hold with small perturbations for codes which only correct most of the erasure errors of less than $d$ letters. In contrast to the classical case, the bounds take on qualitatively different forms depending on whether the minimum distance is smaller or larger than half the block length. We also provide a propagation rule: any pure QECC yields an EAQECC with the same distance and dimension, but of shorter block length.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Learning Quantum Circuits of Some T Gates

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      Authors: Ching-Yi Lai;Hao-Chung Cheng;
      Pages: 3951 - 3964
      Abstract: In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$ -qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using $O(n^{2})$ queries to it. For decades, it has been unknown how to handle circuits beyond the Clifford group since the stabilizer formalism cannot be applied in this case. Herein, we study quantum circuits of $T$ -depth one on the computational basis. We show that the output state of a $T$ -depth one circuit can be represented by a stabilizer pseudomixture with a specific algebraic structure. Using Pauli and Bell measurements on copies of the output states, we can generate a hypothesis circuit that is equivalent to the unknown target circuit on computational basis states as input. If the number of $T$ gates of the target is of the order $O({log n})$ , our algorithm requires $O(n^{2})$ queries to it and produces its equivalent circuit representation on the computational basis in time $O(n^{3})$ . Using further additional $O(4^{3n})$ classical computations, we can derive an exact description of the target for arbitrary input states. Our results greatly extend the previously known facts that stabilizer states can be efficiently identified based on the stabilizer formalism.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • The Quantum Multiple-Access Channel With Cribbing Encoders

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      Authors: Uzi Pereg;Christian Deppe;Holger Boche;
      Pages: 3965 - 3988
      Abstract: Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2’s cribbing may inflict a “state collapse” for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input. Building on the analogy between the noisy cribbing model and the relay channel, a partial decode-forward region is derived for a quantum MAC with non-robust cribbing. For the classical-quantum MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing. In the special case of a classical-quantum MAC with a deterministic cribbing channel, the inner and outer bounds coincide.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Comments on and Corrections to “When Is the Chernoff Exponent for
           Quantum Operations Finite'”

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      Authors: Nengkun Yu;Li Zhou;
      Pages: 3989 - 3990
      Abstract: In the above article [1], we add some missing citations in the Notations and Preliminaries section. The new Notations and Preliminaries section is as follows.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Optimal High-Order Tensor SVD via Tensor-Train Orthogonal Iteration

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      Authors: Yuchen Zhou;Anru R. Zhang;Lili Zheng;Yazhen Wang;
      Pages: 3991 - 4019
      Abstract: This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estimate the low tensor-train rank structure from the noisy high-order tensor observation. The proposed TTOI consists of initialization via TT-SVD [Oseledets (2011)] and new iterative backward/forward updates. We develop the general upper bound on estimation error for TTOI with the support of several new representation lemmas on tensor matricizations. By developing a matching information-theoretic lower bound, we also prove that TTOI achieves the minimax optimality under the spiked tensor model. The merits of the proposed TTOI are illustrated through applications to estimation and dimension reduction of high-order Markov processes, numerical studies, and a real data example on New York City taxi travel records. The software of the proposed algorithm is available online (https://github.com/Lili-Zheng-stat/TTOI).
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Distances Between Probability Distributions of Different Dimensions

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      Authors: Yuhang Cai;Lek-Heng Lim;
      Pages: 4020 - 4031
      Abstract: Comparing probability distributions is an indispensable and ubiquitous task in machine learning and statistics. The most common way to compare a pair of Borel probability measures is to compute a metric between them, and by far the most widely used notions of metric are the Wasserstein metric and the total variation metric. The next most common way is to compute a divergence between them, and in this case almost every known divergences such as those of Kullback–Leibler, Jensen–Shannon, Rényi, and many more, are special cases of the $f$ -divergence. Nevertheless these metrics and divergences may only be computed, in fact, are only defined, when the pair of probability measures are on spaces of the same dimension. How would one quantify, say, a KL-divergence between the uniform distribution on the interval [−1, 1] and a Gaussian distribution on $mathbb {R}^{3}$ ' We show that these common notions of metrics and divergences give rise to natural distances between Borel probability measures defined on spaces of different dimensions, e.g., one on $mathbb {R}^{m}$ and another on $mathbb {R}^{n}$ where $m, n$ are distinct, so as to give a meaningful answer to the previous question.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Estimation of a Function of Low Local Dimensionality by Deep Neural
           Networks

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      Authors: Michael Kohler;Adam Krzyżak;Sophie Langer;
      Pages: 4032 - 4042
      Abstract: Deep neural networks (DNNs) achieve impressive results for complicated tasks like object detection on images and speech recognition. Motivated by this practical success, there is now a strong interest in showing good theoretical properties of DNNs. To describe for which tasks DNNs perform well and when they fail, it is a key challenge to understand their performance. The aim of this paper is to contribute to the current statistical theory of DNNs. We apply DNNs on high dimensional data and we show that the least squares regression estimates using DNNs are able to achieve dimensionality reduction in case that the regression function has locally low dimensionality. Consequently, the rate of convergence of the estimate does not depend on its input dimension $d$ , but on its local dimension $d^{*}$ and the DNNs are able to circumvent the curse of dimensionality in case that $d^{*}$ is much smaller than $d$ . In our simulation study we provide numerical experiments to support our theoretical result and we compare our estimate with other conventional nonparametric regression estimates. The performance of our estimates is also validated in experiments with real data.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • On a Phase Transition in General Order Spline Regression

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      Authors: Yandi Shen;Qiyang Han;Fang Han;
      Pages: 4043 - 4069
      Abstract: In the Gaussian sequence model $Y= theta _{0} + varepsilon $ in $mathbb {R}^{n}$ , we study the fundamental limit of statistical estimation when the signal $theta _{0}$ belongs to a class $Theta _{n}(d,d_{0},k)$ of (generalized) splines with free knots located at equally spaced design points. Here $d$ is the degree of the spline, $d_{0}$ is the order of differentiability at each inner knot, and $k$ is the maximal number of pieces. We show that, given any integer $dgeq 0$ and $d_{0}in {-1,0,ldots,d-1}$ , the minimax rate of estimation over $Theta _{n}(d,d_{0},k)$ exhibits the following phase transition: $begin{aligned} inf _{ widetilde {theta }}sup _{theta in Theta _{n}(d,d_{0}, k)} mathbb {E}_theta lVert widetilde {theta } - theta rVert _{}^{2} asymp _{d} begin{cases} klog log (16n/k), & 2leq kleq k_{0},\ klog (en/k), & k geq k_{0}+1. end{cases} end{aligned}$ The transition boundary $k_{0}$ , which takes the form $left lfloor{ (d+1)/(d-d_{0}) }right rfloor + 1$ , demonstrates the critical role of t-e regularity parameter $d_{0}$ in the separation between a faster $log log (16n)$ and a slower $log (en)$ rate. We further show that, once encouraging an additional ‘ $d$ -monotonicity’ shape constraint (including monotonicity for $d = 0$ and convexity for $d=1$ ), the above phase transition is removed and the faster $klog log (16n/k)$ rate can be achieved for all $k$ . These results provide theoretical support for developing $ell _{0}$ -penalized (shape-constrained) spline regression procedures as useful alternatives to $ell _{1}$ - and $ell _{2}$ -penalized ones.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Optimal Distributed Composite Testing in High-Dimensional Gaussian Models
           With 1-Bit Communication

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      Authors: Botond Szabó;Lasse Vuursteen;Harry Van Zanten;
      Pages: 4070 - 4084
      Abstract: In this paper we study the problem of signal detection in Gaussian noise in a distributed setting where the local machines in the star topology can communicate a single bit of information. We derive a lower bound on the Euclidian norm that the signal needs to have in order to be detectable. Moreover, we exhibit optimal distributed testing strategies that attain the lower bound.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Hadamard Extensions and the Identification of Mixtures of Product
           Distributions

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      Authors: Spencer L. Gordon;Leonard J. Schulman;
      Pages: 4085 - 4089
      Abstract: The Hadamard Extension $mathbb H({mathrm {m}})$ of an $n times k$ matrix m is the collection of all Hadamard products of subsets of its rows. This construction is essential for source identification (parameter estimation) of a mixture of $k$ product distributions over $n$ binary random variables. A necessary requirement for such identification is that $mathbb H({mathrm {m}})$ have full column rank; conversely, identification is possible if apart from each row there exist two disjoint sets of rows of m, each of whose extension has full column rank. It is necessary therefore to understand when $mathbb H({mathrm {m}})$ has full column rank; we provide two results in this direction. The first is that if $mathbb H({mathrm {m}})$ has full column rank then there exists a set of at most $k-1$ rows of m, whose extension already has full column rank. The second is a Hall-type condition on the values in the rows of m, that suffices to ensure full column rank of $mathbb H({mathrm {m}})$ .
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Mechanisms for Hiding Sensitive Genotypes With Information-Theoretic
           Privacy

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      Authors: Fangwei Ye;Hyunghoon Cho;Salim El Rouayheb;
      Pages: 4090 - 4105
      Abstract: Motivated by the growing availability of personal genomics services, we study an information-theoretic privacy problem that arises when sharing genomic data: a user wants to share his or her genome sequence while keeping the genotypes at certain positions hidden, which could otherwise reveal critical health-related information. A straightforward solution of erasing (masking) the chosen genotypes does not ensure privacy, because the correlation between nearby positions can leak the masked genotypes. We introduce an erasure-based privacy mechanism with perfect information-theoretic privacy, whereby the released sequence is statistically independent of the sensitive genotypes. Our mechanism can be interpreted as a locally-optimal greedy algorithm for a given processing order of sequence positions, where utility is measured by the number of positions released without erasure. We show that finding an optimal order is NP-hard in general and provide an upper bound on the optimal utility. For sequences from hidden Markov models, a standard modeling approach in genetics, we propose an efficient algorithmic implementation of our mechanism with complexity polynomial in sequence length. Moreover, we illustrate the robustness of the mechanism by bounding the privacy leakage from erroneous prior distributions. Our work is a step towards more rigorous control of privacy in genomic data sharing.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Fundamental Limits of Demand-Private Coded Caching

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      Authors: Chinmay Gurjarpadhye;Jithin Ravi;Sneha Kamath;Bikash Kumar Dey;Nikhil Karamchandani;
      Pages: 4106 - 4134
      Abstract: We consider the coded caching problem with an additional privacy constraint that a user should not get any information about the demands of the other users. We first show that a demand-private scheme for $N$ files and $K$ users can be obtained from a non-private scheme that serves only a subset of the demands for the $N$ files and $NK$ users problem. We further use this fact to construct a demand-private scheme for $N$ files and $K$ users from a particular known non-private scheme for $N$ files and $NK-K+1$ users. It is then demonstrated that, the memory-rate pair $(M,min {N,K}(1-M/N))$ , which is achievable for non-private schemes with uncoded transmissions, is also achievable under demand privacy. We further propose a scheme that improves on these ideas by removing some redundant transmissions. The memory-rate trade-off achieved using our schemes is shown to be within a multiplicative factor of 3 from the optimal when $K < N$ and of 8 when $N leq K$ . Finally, we give the exact memory-rate trade-off for demand-private coded caching problems with $Ngeq K=2$ .
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Latency Optimal Storage and Scheduling of Replicated Fragments for Memory
           Constrained Servers

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      Authors: Rooji Jinan;Ajay Badita;Pradeep Kiran Sarvepalli;Parimal Parag;
      Pages: 4135 - 4155
      Abstract: We consider the setting of a distributed storage system where a single file is subdivided into smaller fragments of same size which are then replicated with a common replication factor across servers of identical cache size. An incoming file download request is sent to all the servers, and the download is completed whenever the request gathers all the fragments. At each server, we are interested in determining the set of fragments to be stored, and the sequence in which fragments should be accessed, such that the mean file download time for a request is minimized. We model the fragment download time as an exponential random variable independent and identically distributed for all fragments across all servers, and show that the mean file download time can be lower bounded in terms of the expected number of useful servers summed over all distinct fragment downloads. We present deterministic storage schemes that attempt to maximize the number of useful servers. We show that finding the optimal sequence of accessing the fragments is a Markov decision problem, whose complexity grows exponentially with the number of fragments. We propose heuristic algorithms that determine the sequence of access to the fragments which are empirically shown to perform well.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Coded Sparse Matrix Computation Schemes That Leverage Partial Stragglers

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      Authors: Anindya Bijoy Das;Aditya Ramamoorthy;
      Pages: 4156 - 4181
      Abstract: Distributed matrix computations over large clusters can suffer from the problem of slow or failed worker nodes (called stragglers) which can dominate the overall job execution time. Coded computation utilizes concepts from erasure coding to mitigate the effect of stragglers by running “coded” copies of tasks comprising a job; stragglers are typically treated as erasures. While this is useful, there are issues with applying, e.g., MDS codes in a straightforward manner. Several practical matrix computation scenarios involve sparse matrices. MDS codes typically require dense linear combinations of submatrices of the original matrices which destroy their inherent sparsity. This is problematic as it results in significantly higher worker computation times. Moreover, treating slow nodes as erasures ignores the potentially useful partial computations performed by them. Furthermore, some MDS techniques also suffer from significant numerical stability issues. In this work we present schemes that allow us to leverage partial computation by stragglers while imposing constraints on the level of coding that is required in generating the encoded submatrices. This significantly reduces the worker computation time as compared to previous approaches and results in improved numerical stability in the decoding process. Exhaustive numerical experiments on Amazon Web Services (AWS) clusters support our findings.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
  • Statistically Optimal Estimation of Signals in Modulation Spaces Using
           Gabor Frames

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      Authors: Stephan Dahlke;Sven Heuer;Hajo Holzmann;Pavel Tafo;
      Pages: 4182 - 4200
      Abstract: Time-frequency analysis deals with signals for which the underlying spectral characteristics change over time. The essential tool is the short-time Fourier transform, which localizes the Fourier transform in time by means of a window function. In a white noise model, we derive rate-optimal and adaptive estimators of signals in modulation spaces, which measure smoothness in terms of decay properties of the short-time Fourier transform. The estimators are based on series expansions by means of Gabor frames and on thresholding the coefficients. The minimax rates have interesting new features, and the derivation of the lower bounds requires the use of test functions which approximately localize both in time and in frequency. Simulations and applications to audio recordings illustrate the practical relevance of our methods. We also discuss the best $N$ -term approximation and the approximation of variational problems in modulation spaces by Gabor frame expansions.
      PubDate: June 2022
      Issue No: Vol. 68, No. 6 (2022)
       
 
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