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# IEEE Transactions on Information Theory

## Volume 63 Issue 11 • Nov. 2017

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## Filter Results

Displaying Results 1 - 25 of 50

Publication Year: 2017, Page(s):C1 - C4
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• ### IEEE Transactions on Information Theory publication information

Publication Year: 2017, Page(s): C2
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• ### Sampling and Distortion Tradeoffs for Indirect Source Retrieval

Publication Year: 2017, Page(s):6833 - 6848
Cited by:  Papers (1)
| | PDF (871 KB) | HTML

Consider a continuous signal that cannot be observed directly. Instead, one has access to multiple corrupted versions of the signal. The available corrupted signals are correlated because they carry information about the common remote signal. The goal is to reconstruct the original signal from the data collected from its corrupted versions. Known as the indirect or remote reconstruction problem, i... View full abstract»

• ### A Sharpening of the Welch Bounds and the Existence of Real and Complex Spherical $t$ –Designs

Publication Year: 2017, Page(s):6849 - 6857
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The Welch bounds for a finite set of unit vectors are a family of inequalities indexed by t = 1, 2, ..., which describe how “evenly spread” the vectors are. They have important applications in signal analysis, where sequences giving equality in the first Welch bound are known as Welch bound equality sequences or as unit norm tight frames. Here, we consider sequences of vectors giving equality in t... View full abstract»

• ### Polarization of the Rényi Information Dimension With Applications to Compressed Sensing

Publication Year: 2017, Page(s):6858 - 6868
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In this paper, we show that the Hadamard matrix acts as an extractor over the reals of the Rényi Information Dimension (RID), in an analogous way to how it acts as an extractor of the discrete entropy over finite fields. More precisely, we prove that the RID of an i.i.d. sequence of mixture random variables polarizes to the extremal values of 0 and 1 (corresponding to discrete and continuous distr... View full abstract»

• ### Linear Convergence of Stochastic Iterative Greedy Algorithms With Sparse Constraints

Publication Year: 2017, Page(s):6869 - 6895
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Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence<sup>1</sup> in expectation to the solution within a specified tolerance. This generalized framework is specialized to the problems of sparse signal recovery in compre... View full abstract»

• ### Does $\ell _{p}$ -Minimization Outperform $\ell _{1}$ -Minimization?

Publication Year: 2017, Page(s):6896 - 6935
Cited by:  Papers (5)
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In many application areas ranging from bioinformatics to imaging, we are faced with the following question: can we recover a sparse vector xo∈ ℝNfrom its undersampled set of noisy observations y ∈ ℝn, y = Axo+w. The last decade has witnessed a surge of algorithms and theoretical results to address this question. One of the most popular schemes is the ℓ View full abstract»

• ### Bounds on Variance for Unimodal Distributions

Publication Year: 2017, Page(s):6936 - 6949
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We show a direct relationship between the variance and the differential entropy for subclasses of symmetric and asymmetric unimodal distributions by providing an upper bound on variance in terms of entropy power. Combining this bound with the well-known entropy power lower bound on variance, we prove that the variance of the appropriate subclasses of unimodal distributions can be bounded below and... View full abstract»

• ### Information Theoretic Cutting of a Cake

Publication Year: 2017, Page(s):6950 - 6978
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Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e., one agent may like chocolate, while the other may like cream). A fair division of the cake is one that takes into account the individual valuations of agents and partitions of the cake based... View full abstract»

• ### Information Complexity Density and Simulation of Protocols

Publication Year: 2017, Page(s):6979 - 7002
Cited by:  Papers (2)
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Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical distance of the joint distribution of the input and the transcript of the original protocol? We present an information spectrum approach for this problem whereby ... View full abstract»

• ### On Distributed Computing for Functions With Certain Structures

Publication Year: 2017, Page(s):7003 - 7017
Cited by:  Papers (1)
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The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be computed, information that is inevitably conveyed to the decoder is identified, and the bound is derived in terms of the optimal rate needed to send that inform... View full abstract»

• ### Information-Theoretic Caching: The Multi-User Case

Publication Year: 2017, Page(s):7018 - 7037
Cited by:  Papers (3)
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In this paper, we consider a cache aided network in which each user is assumed to have individual caches, while upon users' requests, an update message is sent through a common link to all users. First, we formulate a general information theoretic setting that represents the database as a discrete memoryless source, and the users' requests as side information that is available everywhere except at... View full abstract»

• ### The Rate Region for Secure Distributed Storage Systems

Publication Year: 2017, Page(s):7038 - 7051
Cited by:  Papers (2)
| | PDF (351 KB) | HTML

The problem of characterizing the fundamental tradeoff between storage and repair bandwidth of exact-repair regenerating codes against a passive eavesdropper is studied. The eavesdropper is assumed to be capable of observing the data stored in a fixed number of nodes and the data involved in the repair of these nodes. In this paper, the tradeoff for regenerating codes with small parameters is char... View full abstract»

• ### Dual Capacity Upper Bounds for Noisy Runlength Constrained Channels

Publication Year: 2017, Page(s):7052 - 7065
Cited by:  Papers (1)
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Binary-input memoryless channels with a run length constrained input are considered. Upper bounds to the capacity of such noisy run length constrained channels are derived using the dual capacity method with Markov test distributions satisfying the Karush-Kuhn-Tucker conditions for the capacity-achieving output distribution. Simplified algebraic characterizations of the bounds are presented for th... View full abstract»

• ### Linear Programming-Based Converses for Finite Blocklength Lossy Joint Source-Channel Coding

Publication Year: 2017, Page(s):7066 - 7094
Cited by:  Papers (2)
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A linear programming (LP)-based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses, and also extends to multi-terminal settings. The finite blocklength problem is posed equivalently as a nonconvex optimization problem and using a lift-and-proje... View full abstract»

• ### Sequential Necessary and Sufficient Conditions for Capacity Achieving Distributions of Channels With Memory and Feedback

Publication Year: 2017, Page(s):7095 - 7115
Cited by:  Papers (4)
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We derive sequential necessary and sufficient conditions for any channel input conditional distribution P0,n=Δ{PXt|Xt-1,Yt-1: t = 0, ..., n} to maximize the finite-time horizon directed information defined by CXn→YnFB =ΔsupP0,nI(Xn→ Yn), where I(Xn→ Yn) = Σt=0nI(X View full abstract»

• ### Optimal Finite-Length and Asymptotic Index Codes for Five or Fewer Receivers

Publication Year: 2017, Page(s):7116 - 7130
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Index coding models broadcast networks in which a sender sends different messages to different receivers simultaneously, where each receiver may know some of the messages a priori. The aim is to find the minimum (normalized) index codelength that the sender sends. This paper considers unicast index coding, where each receiver requests exactly one message, and each message is requested by exactly o... View full abstract»

• ### Group Testing Schemes From Codes and Designs

Publication Year: 2017, Page(s):7131 - 7141
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In group testing, simple binary-output tests are designed to identify a small number t of defective items that are present in a large population of N items. Each test takes as input a group of items and produces a binary output indicating whether the group is free of the defective items or contains one or more of them. In this paper, we study a relaxation of the combinatorial group testing problem... View full abstract»

• ### The Capacity of Bernoulli Nonadaptive Group Testing

Publication Year: 2017, Page(s):7142 - 7148
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We consider nonadaptive group testing with Bernoulli tests, where each item is placed in each test independently with some fixed probability. We give a tight threshold on the maximum number of tests required to find the defective set under optimal Bernoulli testing. Achievability is given by a result of Scarlett and Cevher; here we give a converse bound showing that this result is best possible. O... View full abstract»

• ### Computationally Tractable Algorithms for Finding a Subset of Non-Defective Items From a Large Population

Publication Year: 2017, Page(s):7149 - 7165
Cited by:  Papers (2)
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In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the complete defective set given the outcomes of different group tests. In contrast, the main goal of a non-defective subset recovery algorithm is to identify a subset of non-defective items given the test outcomes. In this paper, we present a suite of com... View full abstract»

• ### Rates of DNA Sequence Profiles for Practical Values of Read Lengths

Publication Year: 2017, Page(s):7166 - 7177
Cited by:  Papers (2)
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A recent study by one of the authors has demonstrated the importance of profile vectors in DNA-based data storage. We provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size q, read length 1, and word length n. Consequently, we demonstrate that for q ≥ 2 and n ≤ q1/2-1, the number of profile vectors is at least qκnwith κ very ... View full abstract»

• ### The “Art of Trellis Decoding” Is Fixed-Parameter Tractable

Publication Year: 2017, Page(s):7178 - 7205
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Given n subspaces of a finite-dimensional vector space over a fixed finite field F, we wish to find a linear layout V1, V2,..., Vnof the subspaces such that dim((V1+ V2+ ··· + Vi) ∩ (Vi+1+ ··· + Vn)) ≤ k for all i; such a linear layout is said to have width at most k. When restricted to 1-dimensional subspaces,... View full abstract»

• ### On the Correlation Distribution for a Niho Decimation

Publication Year: 2017, Page(s):7206 - 7218
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Let p be a prime, n = 2m and d = 3pm- 2 with m ≥ 2, and gcd(d, pn- 1) = 1. In this paper, the correlation distribution between a p-ary m-sequence of period pn- 1 and its d-decimation sequence is investigated in a unified approach. Some results for the binary case are extended to the general case. It is shown that the problem of determining the correlation distribut... View full abstract»

• ### Narrow-Sense BCH Codes Over ${\mathrm {GF}}(q)$ With Length $n=\frac {q^{m}-1}{q-1}$

Publication Year: 2017, Page(s):7219 - 7236
| | PDF (943 KB) | HTML

Cyclic codes are widely employed in communication systems, storage devices, and consumer electronics, as they have efficient encoding and decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in most cases among the best cyclic codes. A subclass of good BCH codes are the narrow-sense BCH codes over GF(q) with length n = (q<sup>m</sup> -1)/(q -1). Little is known ab... View full abstract»

• ### Explicit Construction of AG Codes From a Curve in the Tower of Bassa-Beelen-Garcia-Stichtenoth

Publication Year: 2017, Page(s):7237 - 7246
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We present multi-point algebraic geometric codes overstepping the Gilbert-Varshamov bound. The construction is based on a curve in the tower introduced by Bassa et al. These codes are described in detail by constructing generator matrices. It turns out that these codes have nice properties similar to those of Hermitian codes. The duals are also such codes and can be expressed as an explicit formul... View full abstract»

## Aims & Scope

IEEE Transactions on Information Theory publishes papers concerned with the transmission, processing, and utilization of information.

Full Aims & Scope

## Meet Our Editors

Editor-in-Chief
Alexander Barg

Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland

email: abarg-ittrans@ece.umd.edu