# IEEE Transactions on Information Theory

## Issue 12 • Dec. 2017

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## Filter Results

Displaying Results 1 - 25 of 28

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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• ### A Simple Proof of Fast Polarization

Publication Year: 2017, Page(s):7617 - 7619
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Fast polarization is a key property of polar codes. It was proved for the binary polarizing 2 × 2 kernel by Arikan and Telatar. The proof was later adapted to the general case by Sasoglu. We give a simplified proof. View full abstract»

• ### Capacity-Achieving Rate-Compatible Polar Codes

Publication Year: 2017, Page(s):7620 - 7632
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A method of constructing rate-compatible polar codes that are capacity achieving at multiple code rates with low-complexity sequential decoders is presented. The underlying idea of the construction exploits certain common characteristics of polar codes that are optimized for a sequence of successively degraded channels. The proposed code consists of parallel concatenation of multiple polar codes w... View full abstract»

• ### Splitter Sets and $k$ -Radius Sequences

Publication Year: 2017, Page(s):7633 - 7645
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Splitter sets are closely related to lattice tilings, and have applications in flash memories and conflict-avoiding codes. The study of k-radius sequences was motivated by some problems occurring in large data transfer. It is observed that the existence of splitter sets yields k-radius sequences of short length. In this paper, we obtain several new results contributing to splitter sets and k-radiu... View full abstract»

• ### Construction of Sequences With High Nonlinear Complexity From Function Fields

Publication Year: 2017, Page(s):7646 - 7650
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Complexity of sequences plays an important role in pseudorandom sequences and cryptography. In this paper, we present a construction of sequences with high nonlinear complexity from function fields. The main idea is to make use of function fields with many rational places as well as an automorphism of large order. We illustrate our construction through rational function fields and cyclotomic funct... View full abstract»

• ### Coset Construction for Subspace Codes

Publication Year: 2017, Page(s):7651 - 7660
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One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so-called subspace codes in Pq(n), i.e., the set of subspaces of Fqn, for a given minimal distance. Here we generalize a construction of Etzion and Silberstein to a wide range of parameters. This construction, named coset constr... View full abstract»

• ### Constacyclic Symbol-Pair Codes: Lower Bounds and Optimal Constructions

Publication Year: 2017, Page(s):7661 - 7666
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Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that pair distance cannot be improved for given length and code size. The contribution of this paper is twofold.... View full abstract»

• ### Constructions of Formally Self-Dual Codes Over ${mathbb Z}_{4}$ and Their Weight Enumerators

Publication Year: 2017, Page(s):7667 - 7675
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We present three explicit methods for construction of formally self-dual codes over ℤ4. We characterize relations between Lee weight enumerators of formally self-dual codes of length n over ℤ4 and those of length n t 2; the first two construction methods are based on these relations. The last construction produces free formally self-dual codes over ℤ... View full abstract»

• ### Coding for the $boldsymbol ell _infty$ -Limited Permutation Channel

Publication Year: 2017, Page(s):7676 - 7686
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We consider the communication of information in the presence of synchronization errors. Specifically, we consider permutation channels in which a transmitted codeword x = (x1, ... , xn) is corrupted by a permutation π ∈ Sn to yield the received wordy = (y1, . . . , yn), where yi = xπ(i). We initiate t... View full abstract»

• ### Index Coding With Erroneous Side Information

Publication Year: 2017, Page(s):7687 - 7697
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In this paper, new index coding problems are studied, where each receiver has erroneous side information. Although side information is a crucial part of index coding, the existence of erroneous side information has not been considered yet. We study an index code with receivers that have erroneous side information symbols in the error-free broadcast channel, which is called an index code with side ... View full abstract»

• ### Zero-Error Capacity of $P$ -ary Shift Channels and FIFO Queues

Publication Year: 2017, Page(s):7698 - 7707
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The objects of study of this paper are communication channels in which the dominant type of noise are symbol shifts, the main motivating examples being timing and bit-shift channels. Two channel models are introduced and their zeroerror capacities and zero-error-detection capacities determined by explicit constructions of optimal codes. Model A can be informally described as follows: 1) The inform... View full abstract»

• ### Zero-Error Relaying for Primitive Relay Channels

Publication Year: 2017, Page(s):7708 - 7715
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In a primitive relay channel, a new one-shot relaying scheme termed color-and-forward is proposed that guarantees a probability of error equal to zero. This relaying scheme constructs a relaying compression graph of relay outputs based on the joint conditional distribution of the relay and destination outputs, and forwards a minimum coloring of this graph. The n-letter extension of the proposed co... View full abstract»

• ### Polynomial Singular Value Decompositions of a Family of Source-Channel Models

Publication Year: 2017, Page(s):7716 - 7728
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In this paper, we show that the conditional expectation operators corresponding to a family of source-channel models, defined by natural exponential families with quadratic variance functions and their conjugate priors, have orthonormal polynomials as singular vectors. These models include the Gaussian channel with Gaussian source, the Poisson channel with gamma source, and the binomial channel wi... View full abstract»

• ### On Empirical Cumulant Generating Functions of Code Lengths for Individual Sequences

Publication Year: 2017, Page(s):7729 - 7736
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We consider the problem of lossless compression of individual sequences using finite-state (FS) machines, from the perspective of the best achievable empirical cumulant generating function (CGF) of the code length, i.e., the normalized logarithm of the empirical average of the exponentiated code length. Since the probabilistic CGF is minimized in terms of the Rényi entropy of the source, o... View full abstract»

• ### A Proof of the Strong Converse Theorem for Gaussian Broadcast Channels via the Gaussian Poincaré Inequality

Publication Year: 2017, Page(s):7737 - 7746
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We prove that the Gaussian broadcast channel with two destinations admits the strong converse property. This implies that for every sequence of block codes operated at a common rate pair with an asymptotic average error probability <; 1, the rate pair must lie within the capacity region derived by Cover and Bergmans. The main mathematical tool required for our analysis is a logarithmic Sobolev ... View full abstract»

• ### Variants of the Entropy Power Inequality

Publication Year: 2017, Page(s):7747 - 7752
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An extension of the entropy power inequality to the form Nrα (X + Y) ≥ Nrα (X) + Nrα (Y) with arbitrary independent summands X and Y in Rn is obtained for the Rényi entropy and powers α ≥ (r + 1)/2. View full abstract»

• ### Secure Transmission on the Two-Hop Relay Channel With Scaled Compute-and-Forward

Publication Year: 2017, Page(s):7753 - 7769
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In this paper, we consider communication on a two-hop channel in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper, and there is a cooperative node, which sends a jamming signal to confuse the relay when it is r... View full abstract»

• ### MSE Estimates for Multitaper Spectral Estimation and Off-Grid Compressive Sensing

Publication Year: 2017, Page(s):7770 - 7776
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We obtain estimates for the mean squared error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals. We confirm a fact discovered by Thomson [Spectrum estimation and harmonic analysis, Proc. IEEE, 1982]: assuming bandwidth W and N time domain observations, the average of the square of the first K = ⌊2NW⌋ Slepian functions appr... View full abstract»

• ### Distributions of Multivariate Correlated Rayleigh and Rician Fading

Publication Year: 2017, Page(s):7777 - 7779
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Single-integral expressions for cumulative distribution functions of multivariate correlated Rayleigh and Rician fading are studied. Mathematical mistakes in the literature are identified and corrected. Corrections are cross-verified against well-known findings in the literature, which can be employed to advance further theoretical developments for correlated fading. View full abstract»

• ### Polynomially Solvable Instances of the Shortest and Closest Vector Problems With Applications to Compute-and-Forward

Publication Year: 2017, Page(s):7780 - 7792
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A particular instance of the shortest vector problem (SVP) appears in the context of compute-and-forward. Despite the NP-hardness of the SVP, we will show that this certain instance can be solved in complexity order O(nψ log(nψ)), where ψ = √P∥h∥2 + 1 depends on the transmission power and the norm of the channel vector. We will then extend our r... View full abstract»

• ### Duplication Distance to the Root for Binary Sequences

Publication Year: 2017, Page(s):7793 - 7803
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We study the tandem duplication distance between binary sequences and their roots. In other words, the quantity of interest is the number of tandem duplication operations of the form x = abc → y = abbc, where x and y are sequences and a, b, and c are their substrings, needed to generate a binary sequence of length n starting from a square-free sequence from the set {0, 1, 01, 10, 010, 101}.... View full abstract»

• ### Decomposing Generalized Bent and Hyperbent Functions

Publication Year: 2017, Page(s):7804 - 7812
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In this paper, we introduce generalized hyperbent functions from F2n to ℤ2k, and investigate decompositions of generalized (hyper)bent functions. We show that generalized (hyper)bent functions f from F2n to ℤ2k consist of components which are generalized (hyper)bent functions from F2 View full abstract»

• ### Further Results on the Optimal Sequence Family $mathcal {IP}_{8}$ Over 8-Ary Q-PAM Constellation

Publication Year: 2017, Page(s):7813 - 7820
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A family IP8 of sequences over the 8-ary quadrature-pulse amplitude modulation (Q-PAM) constellation with asymptotically optimal correlation property was presented by Anand and Kumar in 2008. This is the only known family of sequences over the quadrature amplitude modulation (QAM) constellation whose correlation magnitude asymptotically achieves the Welch bound. In this paper, a larger ... View full abstract»

• ### Quantum Dynamical Entropy, Chaotic Unitaries and Complex Hadamard Matrices

Publication Year: 2017, Page(s):7821 - 7831
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We introduce two information-theoretical invariants for the projective unitary group acting on a finite-dimensional complex Hilbert space: PVM- and POVM-dynamical (quantum) entropies, which are analogues of the classical Kolmogorov-Sinai entropy rate. They quantify the maximal randomness of the successive quantum measurement results in the case where the evolution of the system between each two co... 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