# IEEE Transactions on Information Theory

## Issue 9 • Sept. 2017

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## Filter Results

Displaying Results 1 - 25 of 47
• ### Table of contents

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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• ### Almost Lossless Analog Signal Separation and Probabilistic Uncertainty Relations

Publication Year: 2017, Page(s):5445 - 5460
Cited by:  Papers (1)
| |PDF (688 KB) | HTML

We propose an information-theoretic framework for analog signal separation. Specifically, we consider the problem of recovering two analog signals, modeled as general random vectors, from the noiseless sum of linear measurements of the signals. Our framework is inspired by the groundbreaking work of Wu and Verdú (2010) on analog compression and encompasses, inter alia, inpainting, declippi... View full abstract»

• ### Non-Asymptotic Analysis of $ell _{1}$ -Norm Support Vector Machines

Publication Year: 2017, Page(s):5461 - 5476
| |PDF (962 KB) | HTML

Support vector machines (SVMs) with the ℓ1-penalty became a standard tool in the analysis of highdimensional classification problems with sparsity constraints in many applications, including bioinformatics and signal processing. We give non-asymptotic results on the performance of ℓ1-SVM in identification of sparse classifiers. We show that an N-dimensional s-sp... View full abstract»

• ### Small Width, Low Distortions: Quantized Random Embeddings of Low-Complexity Sets

Publication Year: 2017, Page(s):5477 - 5495
Cited by:  Papers (1)
| |PDF (736 KB) | HTML

Under which conditions and with which distortions can we preserve the pairwise distances of low-complexity vectors, e.g., for structured sets, such as the set of sparse vectors or the one of low-rank matrices, when these are mapped (or embedded) in a finite set of vectors? This work addresses this general question through the specific use of a quantized and dithered random linear mapping, which co... View full abstract»

• ### A Two Channel System Approximation for Bandlimited Functions

Publication Year: 2017, Page(s):5496 - 5505
| |PDF (344 KB) | HTML

The approximation of stable linear time-invariant (LTI) systems is studied for the Paley-Wiener space PWπ1 of bandlimited functions with absolutely integrable Fourier transform. For pointwise sampling, it is known that there exist stable LTI systems and functions such that the approximation process diverges, regardless of the oversampling factor. Recently, it was shown... View full abstract»

• ### Identifiability for Blind Source Separation of Multiple Finite Alphabet Linear Mixtures

Publication Year: 2017, Page(s):5506 - 5517
| |PDF (683 KB) | HTML

We give under weak assumptions a complete combinatorial characterization of identifiability for linear mixtures of finite alphabet sources, with unknown mixing weights and unknown source signals, but known alphabet. This is based on a detailed treatment of the case of a single linear mixture. Notably, our identifiability analysis applies also to the case of unknown number of sources. We provide su... View full abstract»

• ### Universal Spatiotemporal Sampling Sets for Discrete Spatially Invariant Evolution Processes

Publication Year: 2017, Page(s):5518 - 5528
| |PDF (257 KB) | HTML

Let (I, +) be a finite abelian group and A be a circular convolution operator on ℓ2(I). The problem under consideration is how to construct minimal Ω ⊂ I and li such that Y = {ei, Aei, · · · , Ali ei : i ∈ Ω} is a frame for ℓ2(I), where {ei View full abstract»

• ### Optimized Wavelet Denoising for Self-Similar $alpha$ -Stable Processes

Publication Year: 2017, Page(s):5529 - 5543
| |PDF (541 KB) | HTML

We investigate the performance of wavelet shrinkage methods for the denoising of symmetric-α-stable (SαS) self-similar stochastic processes corrupted by additive white Gaussian noise (AWGN), where α is tied to the sparsity of the process. The wavelet transform is assumed to be orthonormal and the shrinkage function minimizes the mean-square approximation error (MMSE estimator)... View full abstract»

• ### Low Rank Approximation and Decomposition of Large Matrices Using Error Correcting Codes

Publication Year: 2017, Page(s):5544 - 5558
| |PDF (633 KB) | HTML

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate singular value decompositions of large matrices. Similar ideas were used to solve least squares regression problems. In this paper, we show how matrices from e... View full abstract»

• ### An Information-Theoretic Study for Joint Sparsity Pattern Recovery With Different Sensing Matrices

Publication Year: 2017, Page(s):5559 - 5571
| |PDF (361 KB) | HTML

In this paper, we study a support set reconstruction problem for multiple measurement vectors (MMV) with different sensing matrices, where the signals of interest are assumed to be jointly sparse and each signal is sampled by its own sensing matrix in the presence of noise. Using mathematical tools, we develop upper and lower bounds of the failure probability of the support set reconstruction in t... View full abstract»

• ### Minimax Robust Hypothesis Testing

Publication Year: 2017, Page(s):5572 - 5587
Cited by:  Papers (1)
| |PDF (2069 KB) | HTML

Minimax robust hypothesis testing is studied for the cases where the collected data samples are corrupted by outliers and are mismodeled due to modeling errors. For the former case, Huber's clipped likelihood ratio test is introduced and analyzed. For the latter case, first, a robust hypothesis testing scheme based on the Kullback-Leibler divergence is designed. This approach generalizes a previou... View full abstract»

• ### Quickest Detection of Parameter Changes in Stochastic Regression: Nonparametric CUSUM

Publication Year: 2017, Page(s):5588 - 5602
| |PDF (776 KB) | HTML

We consider the problem of detecting abrupt parameter changes in a stochastic regression with unknown noise distribution. The process changes at some unknown point of time. Under general conditions on the regression function and unknown distributions of observations before and after the disruption, the paper develops a nonparametric cumulative sum procedure (CUSUM). Unlike likelihood-based CUSUM a... View full abstract»

• ### Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels

Publication Year: 2017, Page(s):5603 - 5617
| |PDF (301 KB) | HTML

The sphere packing bound, in the form given by Shannon, Gallager, and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the Lovász theta function. In this paper, we extend the study to the case of constant-composition codes. We first extend the sphe... View full abstract»

• ### Multipartite Entangled States, Symmetric Matrices, and Error-Correcting Codes

Publication Year: 2017, Page(s):5618 - 5627
| |PDF (630 KB) | HTML

A pure quantum state is called k-uniform if all its reductions to k-qudit are maximally mixed. We investigate the general constructions of k-uniform pure quantum states of n subsystems with d levels. We provide one construction via symmetric matrices and the second one through the classical error-correcting codes. There are three main results arising from our constructions. First, we show that for... View full abstract»

• ### Sample-Optimal Tomography of Quantum States

Publication Year: 2017, Page(s):5628 - 5641
| |PDF (847 KB) | HTML

It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error ε in trace distance required O(dr2/ε2) copies for a d-dimensional density matrix of rank r. Here, we give a theoretical measurement scheme (POVM) that requires O... View full abstract»

• ### Factor Graphs for Quantum Probabilities

Publication Year: 2017, Page(s):5642 - 5665
| |PDF (3623 KB) | HTML

A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables. All joint probability distributions are marginals of some complex-valued function q, and it is demonstrated how the basic concepts of quantum me... View full abstract»

• ### On Distinguishing of Non-Signaling Boxes via Completely Locality Preserving Operations

Publication Year: 2017, Page(s):5666 - 5683
| |PDF (662 KB) | HTML

We introduce a scenario of discrimination between bipartite boxes and apply it to boxes with two binary inputs and two binary outputs (2 × 2). We develop the analogy between the theory of Bell non-locality and the theory of entanglement by considering the class of completely locality preserving (CLP) operations. A CLP operation satisfies two conditions: 1) transforms boxes with local hidden... View full abstract»

• ### Repairing Reed-Solomon Codes

Publication Year: 2017, Page(s):5684 - 5698
| |PDF (1014 KB) | HTML

We study the performance of Reed-Solomon (RS) codes for the exact repair problem in distributed storage. Our main result is that, in some parameter regimes, Reed-Solomon codes are optimal regenerating codes, among maximum distance separable (MDS) codes with linear repair schemes. Moreover, we give a characterization of MDS codes with linear repair schemes, which holds in any parameter regime, and ... View full abstract»

• ### Two Families of LCD BCH Codes

Publication Year: 2017, Page(s):5699 - 5717
| |PDF (381 KB) | HTML

Historically, LCD cyclic codes were referred to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD codes. In this paper, we explore two special families of LCD cyclic codes, which are both BCH codes. The dimensions and the minimum distances of these LCD BCH codes are investigated. View full abstract»

• ### Construction $pi _{A}$ and $pi _{D}$ Lattices: Construction, Goodness, and Decoding Algorithms

Publication Year: 2017, Page(s):5718 - 5733
| |PDF (1035 KB) | HTML

A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of L linear codes over Fp1,..., FpL, respectively, and hence is referred to as Construction πA. The existence of a sequence of such lattices that is good for chann... View full abstract»

• ### Analysis of Saturated Belief Propagation Decoding of Low-Density Parity-Check Codes

Publication Year: 2017, Page(s):5734 - 5751
| |PDF (357 KB) | HTML

We consider the effect of log-likelihood ratio saturation on the belief-propagation decoding of low-density parity-check codes. Saturation is commonly done in practice and is known to have a significant effect on the error-floor performance. Our focus is on threshold analysis and the stability of density evolution. We analyze the decoder for standard low-density parity-check code ensembles and sho... View full abstract»

• ### Approaching Capacity at High Rates With Iterative Hard-Decision Decoding

Publication Year: 2017, Page(s):5752 - 5773
| |PDF (827 KB) | HTML

A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Speci... View full abstract»

• ### Limited-Magnitude Error-Correcting Gray Codes for Rank Modulation

Publication Year: 2017, Page(s):5774 - 5792
| |PDF (810 KB) | HTML

We construct error-correcting codes over permutations under the infinity-metric, which are also Gray codes in the context of rank modulation, i.e., are generated as simple circuits in the rotator graph. These errors model limited-magnitude or spike errors, for which only single-error-detecting Gray codes are currently known. Surprisingly, the error-correcting codes we construct achieve a better as... View full abstract»

• ### On Quadratic Permutation Polynomials, Turbo Codes, and Butterfly Networks

Publication Year: 2017, Page(s):5793 - 5801
| |PDF (996 KB) | HTML

The use of quadratic permutation polynomials as interleavers for turbo codes is justified, among other things, by the fact that the quadratic permutation polynomials provide turbo codes of very good performance and simultaneously they support a specific conflict-free parallel access to extrinsic values in two different access orders. It is rather easy to write and read in parallel to and from mult... 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
Prakash Narayan

Department of Electrical and Computer Engineering