IEEE Transactions on Information Theory

Issue 12 • Dec. 2017

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  • 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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  • A Simple Proof of Fast Polarization

    Publication Year: 2017, Page(s):7617 - 7619
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (168 KB) | HTML iconHTML

    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»

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  • Capacity-Achieving Rate-Compatible Polar Codes

    Publication Year: 2017, Page(s):7620 - 7632
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1193 KB) | HTML iconHTML

    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»

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  • Splitter Sets and $k$ -Radius Sequences

    Publication Year: 2017, Page(s):7633 - 7645
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (856 KB) | HTML iconHTML

    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»

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  • Construction of Sequences With High Nonlinear Complexity From Function Fields

    Publication Year: 2017, Page(s):7646 - 7650
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (169 KB) | HTML iconHTML

    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»

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  • Coset Construction for Subspace Codes

    Publication Year: 2017, Page(s):7651 - 7660
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (398 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7661 - 7666
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (218 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7667 - 7675
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1016 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7676 - 7686
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (442 KB) | HTML iconHTML

    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»

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  • Index Coding With Erroneous Side Information

    Publication Year: 2017, Page(s):7687 - 7697
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (842 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7698 - 7707
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (555 KB) | HTML iconHTML

    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»

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  • Zero-Error Relaying for Primitive Relay Channels

    Publication Year: 2017, Page(s):7708 - 7715
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (703 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7716 - 7728
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (313 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7729 - 7736
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (248 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7737 - 7746
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (223 KB) | HTML iconHTML

    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»

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  • Variants of the Entropy Power Inequality

    Publication Year: 2017, Page(s):7747 - 7752
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (221 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7753 - 7769
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1224 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7770 - 7776
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (277 KB) | HTML iconHTML

    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»

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  • Distributions of Multivariate Correlated Rayleigh and Rician Fading

    Publication Year: 2017, Page(s):7777 - 7779
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (290 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7780 - 7792
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (572 KB) | HTML iconHTML

    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»

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  • Duplication Distance to the Root for Binary Sequences

    Publication Year: 2017, Page(s):7793 - 7803
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (648 KB) | HTML iconHTML

    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»

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  • Decomposing Generalized Bent and Hyperbent Functions

    Publication Year: 2017, Page(s):7804 - 7812
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (268 KB) | HTML iconHTML

    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»

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

    Publication Year: 2017, Page(s):7813 - 7820
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1366 KB) | HTML iconHTML

    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»

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  • Quantum Dynamical Entropy, Chaotic Unitaries and Complex Hadamard Matrices

    Publication Year: 2017, Page(s):7821 - 7831
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (616 KB) | HTML iconHTML

    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»

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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