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TOC Alert for Publication# 18 2014August 21<![CDATA[Table of contents]]>609C1C4169<![CDATA[IEEE Transactions on Information Theory publication information]]>609C2C2142<![CDATA[Encoding Tasks and Rényi Entropy]]>(rho ) th moment of the number of performed tasks are derived. The case where a sequence of tasks is produced by a source and (n) tasks are jointly described using (nR) bits is considered. If (R) is larger than the Rényi entropy rate of the source of order (1/(1+rho )) (provided it exists), then the (rho ) th moment of the ratio of performed tasks to (n) can be driven to one as (n) tends to infinity. If (R) is smaller than the Rényi entropy rate, this moment tends to infinity. The results are generalized to account for the presence of side-information. In this more general setting, the key quantity is a conditional version of Rényi entropy that was introduced by Arimoto. For IID sources, two additional extensions are solved, one of a rate-distortion flavor and the other where different tasks may have different nonnegative costs. Finally, a divergence that was identified by Sundaresan as a mismatch penalty in the Massey-Arikan guessing problem is shown to play a similar role here.]]>60950655076356<![CDATA[Codeword or Noise? Exact Random Coding Exponents for Joint Detection and Decoding]]>60950775094600<![CDATA[Error Exponent for Multiple-Access Channels: Lower Bounds]]>60950955115698<![CDATA[Beyond the Entropy Power Inequality, via Rearrangements]]>60951165137442<![CDATA[Capacity and Coding for the Ising Channel With Feedback]]>(C=({2H_{b}(a)}/{3+a})approx 0.575522) , where (a) is a particular root of a fourth-degree polynomial and (H_{b}(x)) denotes the binary entropy function. Simultaneously, (a=arg max _{0leq x leq 1} ({2H_{b}(x)}/{3+x})) . Finally, an error-free, capacity-achieving coding scheme is provided together with the outlining of a strong connection between the DP results and the coding scheme.]]>609513851491450<![CDATA[To Feed or Not to Feedback]]>609515051721083<![CDATA[Private Broadcasting Over Independent Parallel Channels]]>60951735187783<![CDATA[On Characterization of Elementary Trapping Sets of Variable-Regular LDPC Codes]]>(d_{l}) and girth (g) , we identify all the nonisomorphic structures of an arbitrary class of ((a,b)) ETSs, where (a) is the number of variable nodes and (b) is the number of odd-degree check nodes in the induced subgraph of the ETS. This paper leads to a simple characterization of dominant classes of ETSs (those with relatively small values of (a) and (b) ) based on short cycles in the Tanner graph of the code. For such classes of ETSs, we prove that any set ({cal S}) in the class is a layered superset (LSS) of a short cycle, where the term layered is used to indicate that there is a nested sequence of ETSs that starts from the cycle and grows, one variable node at a time, to generate ({cal S}) . This characterization corresponds to a simple search algorithm that starts from the short cycles of the graph and finds all the ETSs with LSS property in a guaranteed fashion. Specific results on the structure of ETSs are presented for (d_{l} = 3, 4, 5, 6) , (g = 6, 8) , and (a, b leq 10) in this paper. The results of this paper can be used for the error floor analysis and for the design of LDPC codes with low error floors.]]>609518852034169<![CDATA[On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes]]>(q) and (m) , where (q) is an odd prime and (m leq q) . In the literature, the minimum/stopping distance of these codes (denoted by (d(q,m)) and (h(q,m)) , respectively) has been thoroughly studied for (m leq 5) . Both exact results, for small values of (q) and (m) , and general (i.e., independent of (q) ) bounds have been established. For (m=6) , the best known minimum distance upper bound, derived by Mittelholzer, is (d(q,6) leq 32) . In this paper, we derive an improved upper bound of (d(q,6) leq 20) and a new upper bound (d(q,7) leq 24) by using the concept of a template support matrix of a codeword/stopping set. The bounds are tight with high probability in the sense that we have not been able to find codewords of strictly lower weight for several values of (q) using a minimum distance probabilistic algorithm. Finally, we provide new specific minimum/stopping distance results for (m leq 7) and low-to-moderate values of (q leq 79) .]]>60952045214511<![CDATA[Pseudocodewords of Parity-Check Codes Over Fields of Prime Cardinality]]>(p) for use over the (p) -ary symmetric channel. Pseudocodewords are decoding algorithm outputs that may not be legitimate codewords. Here, we consider pseudocodewords arising from graph cover decoding and linear programming decoding. For codes over the binary alphabet, such pseudocodewords correspond to rational points of the fundamental polytope. They can be characterized via the fundamental cone, which is the conic hull of the fundamental polytope; the pseudocodewords are precisely those integer vectors within the fundamental cone that reduce modulo 2 to a codeword. In this paper, we determine a set of conditions that pseudocodewords of codes over ( mathbb F_{p}) , the finite field of prime cardinality (p) , must satisfy. To do so, we introduce a class of critical multisets and a mapping, which associates a real number to each pseudocodeword over ( mathbb F_{p}) . The real numbers associated with pseudocodewords are subject to lower bounds imposed by the critical multisets. The inequalities are given in terms of the parity-check matrix entries and critical multisets. This gives a necessary and sufficient condition for pseudocodewords of codes over ( mathbb F_{2}) and ( mathbb F_{3}) and a necessary condition for those over larger alphabets. In addition, irreducible pseudocodewords of codes over ( mathbb F_{3})-
are found as a Hilbert basis for the lifted fundamental cone.]]>60952155227470<![CDATA[Secure Cooperative Regenerating Codes for Distributed Storage Systems]]>609522852441602<![CDATA[Explicit Maximally Recoverable Codes With Locality]]>60952455256278<![CDATA[New Bounds on Separable Codes for Multimedia Fingerprinting]]>( overline {2}) -separable codes with asymptotically optimal rate are obtained by the deletion method.]]>60952575262394<![CDATA[List Permutation Invariant Linear Codes: Theory and Applications]]>(q) -ary list permutation invariant linear codes is introduced in this paper along with probabilistic arguments that validate their existence when certain conditions are met. The specific class of codes is characterized by an upper bound that is tighter than the generalized Shulman–Feder bound and relies on the distance of the codes’ weight distribution to the binomial (multinomial, respectively) one. The bound applies to cases where a code from the proposed class is transmitted over a (q) -ary output symmetric discrete memoryless channel and list decoding with fixed list size is performed at the output. In the binary case, the new upper bounding technique allows the discovery of list permutation invariant codes whose upper bound coincides with sphere-packing exponent. Furthermore, the proposed technique motivates the introduction of a new class of upper bounds for general (q) -ary linear codes whose members are at least as tight as the DS2 bound as well as all its variations for the discrete channels treated in this paper.]]>60952635282948<![CDATA[Higher-Order CIS Codes]]>(tk) and dimension (k) is called a complementary information set code of order (t) ((t) -CIS code for short) if it has (t) pairwise disjoint information sets. The duals of such codes permit to reduce the cost of masking cryptographic algorithms against side-channel attacks. As in the case of codes for error correction, given the length and the dimension of a (t) -CIS code, we look for the highest possible minimum distance. In this paper, this new class of codes is investigated. The existence of good long CIS codes of order 3 is derived by a counting argument. General constructions based on cyclic and quasi-cyclic codes and on the building up construction are given. A formula similar to a mass formula is given. A classification of 3-CIS codes of length (le 12) is given. Nonlinear codes better than linear codes are derived by taking binary images of ( {mathbb Z}_{4}) -codes. A general algorithm based on Edmonds’ basis packing algorithm from matroid theory is developed with the following property: given a binary linear code of rate (1/t) , it either provides (t) disjoint information sets or proves that the code is not (t) -CIS. Using this algorithm, all optimal or best known ([tk, k]) codes, where (t=3, 4, {dots }, 256) and (1 le k le lfloor 256/t rfloor ) are shown to be (t) -CIS for all such (k) and (t) , except for (t=3) with (k=44) and (t=4) with (k=37) .]]>60952835295403<![CDATA[A Generalized Construction of Extended Goppa Codes]]>(mathbb {F}_{q}) for (q=4,7,8,9) with better minimum distance than the previously known codes with the same length and dimension.]]>609529653031842<![CDATA[Irregular MDS Array Codes]]>60953045314567<![CDATA[Covering Sets for Limited-Magnitude Errors]]>( {mathcal M}={ -mu ,-mu +1,ldots , lambda }setminus {0}) with nonnegative integers (lambda ,mu <q) not both 0, a subset ( {mathcal S}) of the residue class ring ( {mathbb Z}_{q}) modulo an integer (qge 1) is called a ((lambda ,mu ;q)) -covering set if ( {mathcal M} {mathcal S} ={ms bmod q~:~min {mathcal M} ,~sin {mathcal S} }= {mathbb Z}_{q}.) Small covering sets play an important role in codes correcting limited-magnitude errors. We give an explicit construction of a ((lambda ,mu ;q)) -covering set ( {mathcal S}) , which is of the size (q^{1 + o(1)}max {lambda ,mu }^{-1/2}) for almost all integers (qge 1) and optimal order of magnitude (that is up to a multiplicative constant) (pmax {lambda ,mu }^{-1}) if (q=p) is prime. Furthermore, using a bound on the fourth moment of character sums of Cochrane and Shi that there is a ((lambda ,mu ;q)) -covering set of size at most for any integer (qge 1) , however the proof of this bound is not constructive.]]>60953155321197<![CDATA[Batched Sparse Codes]]>609532253461542<![CDATA[Network Coding Capacity Regions via Entropy Functions]]>60953475374958<![CDATA[A Graph Minor Perspective to Multicast Network Coding]]>(K_{4}) , (K_{5}) , (K_{6}) , and (K_{O(q/log {q})}) minors, for networks that require (mathbb {F}_{3}) , (mathbb {F}_{4}) , (mathbb {F}_{5}) , and (mathbb {F}_{q}) to multicast two flows, respectively. We finally pro-
e that, for the general case of multicasting arbitrary number of flows, network coding can make a difference from routing only if the network contains a (K_{4}) minor, and this minor containment result is tight. Practical implications of the above results are discussed.]]>609537553861260<![CDATA[On Network Functional Compression]]>609538754011015<![CDATA[Index Coding—An Interference Alignment Perspective]]>({1}/(L+1)) per message when each destination desires at least (L) messages, are similarly obtained. Finally, capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks. The solutions are based on vector linear coding.]]>609540254322287<![CDATA[An Achievable Rate Region for Joint Compression and Dispersive Information Routing for Networks]]>[1], DIR ensures that each sink receives just the information needed to reconstruct the sources it is required to reproduce. We demonstrate using simple examples that the proposed approach offers better asymptotic performance than conventional routing techniques. We show that, under certain assumptions on the cost function, the problem of finding the minimum cost under DIR essentially reduces to characterizing an achievable rate region for a new multiterminal information theoretic setup. While it is possible to derive an achievable region for this setup using prior results from general multiterminal source coding [3], these techniques do not exploit the underlying problem structure and thereby lead to suboptimal regions. In this paper, we propose a new coding scheme, using principles from multiple descriptions encoding [2], and show that it strictly improves upon a corresponding variant of coding scheme in [3]. We further show that the new coding scheme achieves the complete rate region for certain special cases of the general setup and thereby achieves the minimum communication cost under this routing paradigm.]]>609543354561113<![CDATA[Network Capacity Under Traffic Symmetry: Wireline and Wireless Networks]]>60954575469610<![CDATA[Delay and Redundancy in Lossless Source Coding]]>60954705485331<![CDATA[Optimal Merging Algorithms for Lossless Codes With Generalized Criteria]]>60954865499952<![CDATA[Weakly Symmetric Fix-Free Codes]]>609550055151420<![CDATA[Source Coding Problems With Conditionally Less Noisy Side Information]]>60955165532538<![CDATA[Vector Gaussian Multiterminal Source Coding]]>(L) -terminal CEO problem by establishing a lower bound on each supporting hyperplane of the rate region. To this end, we prove a new extremal inequality by exploiting the connection between differential entropy and Fisher information as well as some fundamental estimation-theoretic inequalities. It is shown that the outer bound matches the Berger–Tung inner bound in the high-resolution regime. We then derive a lower bound on each supporting hyperplane of the rate region of the direct vector Gaussian (L) -terminal source coding problem by coupling it with the CEO problem through a limiting argument. The tightness of this lower bound in the high-resolution regime and the weak-dependence regime is also proved.]]>60955335552371<![CDATA[Second-Order Slepian-Wolf Coding Theorems for Non-Mixed and Mixed Sources]]>second-order achievable rate region in Slepian-Wolf source coding systems is investigated. The concept of second-order achievable rates, which enables us to make a finer evaluation of achievable rates, has already been introduced and analyzed for general sources in the single-user source coding problem. Analogously, in this paper, we first define the second-order achievable rate region for the Slepian–Wolf coding system to establish the source coding theorem in the second-order sense. The Slepian–Wolf coding problem for correlated sources is one of typical problems in the multiterminal information theory. In particular, Miyake and Kanaya, and Han have established the first-order source coding theorems for general correlated sources. On the other hand, in general, the second-order achievable rate problem for the Slepian–Wolf coding system with general sources remains still open up to present. In this paper, we present the analysis concerning the second-order achievable rates for general sources, which are based on the information spectrum methods developed by Han and Verdú. Moreover, we establish the explicit second-order achievable rate region for independently and identically distributed (i.i.d.) correlated sources with countably infinite alphabets and mixtures of i.i.d. correlated sources, respectively, using the relevant asymptotic normality.]]>60955535572911<![CDATA[Feasibility of Interference Alignment for the MIMO Interference Channel]]>(d) dimensions, all transmitters have (M) antennas and all receivers have (N) antennas, as well as feasibility of alignment for the fully symmetric ((M=N) ) channel with an arbitrary number of users. An implication of our results is that the total degrees of freedom available in a (K) -user interference channel, using only spatial diversity from the multiple antennas, is at most 2. This is in sharp contrast to the (K/2) degrees of freedom shown to be possible by Cadambe and Jafar with arbitrarily large time or frequency diversity. Moving beyond the question of feasibility, we additionally discuss computation of the number of solutions using Schubert calculus in cases where there are a finite number of solutions.]]>60955735586927<![CDATA[The Degrees of Freedom of MIMO Networks With Full-Duplex Receiver Cooperation but no CSIT]]>60955875596999<![CDATA[The Capacity Region of Two-Receiver Multiple-Input Broadcast Packet Erasure Channels With Channel Output Feedback]]>609559756261040<![CDATA[Compress-and-Forward Scheme for Relay Networks: Backword Decoding and Connection to Bisubmodular Flows]]>60956275638581<![CDATA[Capacity Bounds for Relay Channels With Intersymbol Interference and Colored Gaussian Noise]]>609563956521536<![CDATA[Fading Channels With Arbitrary Inputs: Asymptotics of the Constrained Capacity and Information and Estimation Measures]]>({mathsf {snr}}) ) for coherent channels subject to Rayleigh, Ricean or Nakagami fading and driven by discrete inputs and continuous inputs. The construction of these expansions leverages the fact that the average MMSE can be seen as an (psi ) -transform with a kernel of monotonic argument: this offers the means to use a powerful asymptotic expansion of integrals technique—the Mellin transform method—that leads immediately to the expansions of the average MMSE and—via the I-MMSE relationship—to expansions of the average mutual information, in terms of the so called canonical MMSE of a standard additive white Gaussian noise (AWGN) channel. We conclude with applications of the results to the optimization of the constrained capacity of a bank of parallel independent coherent fading channels driven by arbitrary discrete inputs.]]>60956535672707<![CDATA[Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels]]>(1-{Q}/{N}) . Here, (N) is the number of symbols transmitted within one fading block, and (Q) is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as (1-1/N) . Since the capacity pre-log corresponding to symbol-rate sampling is (1-Q/N) , our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.]]>60956735681251<![CDATA[Stationary and Transition Probabilities in Slow Mixing, Long Memory Markov Processes]]>(n) sample generated by an unknown, stationary ergodic Markov process (model) over a finite alphabet ( {cal A}) . Given any string ( {mathbf{w}}) of symbols from ( {cal A}) we want estimates of the conditional probability distribution of symbols following ( {mathbf{w}}) , as well as the stationary probability of ( {mathbf{w}}) . Two distinct problems that complicate estimation in this setting are: 1) long memory and 2) slow mixing, which could happen even with only one bit of memory.]]>609568257011681<![CDATA[An Improved RIP-Based Performance Guarantee for Sparse Signal Recovery via Orthogonal Matching Pursuit]]>(K) -sparse vector via orthogonal matching pursuit (OMP) in (K) iterations (when there is no noise) is that the restricted isometry constant (RIC) of the sensing matrix satisfies (delta _{K+1} <({1}/{sqrt {K} +1})) . In the noisy case, this RIC upper bound along with a requirement on the minimal signal entry magnitude is known to guarantee exact support identification. In this paper, we show that, in the presence of noise, a relaxed RIC upper bound (delta _{K+1} <({sqrt {4K+1} -1}/{2K})) together with a relaxed requirement on the minimal signal entry magnitude suffices to achieve perfect support identification using OMP. In the noiseless case, our result asserts that such a relaxed RIC upper bound can ensure exact support recovery in (K) iterations: this narrows the gap between the so far best known bound (delta _{K+1} <({1}/{sqrt {K} +1})) and the ultimate performance guarantee (delta _{K+1} =({1}/{sqrt {K}})) . Our approach relies on a newly established near orthogonality condition, characterized via the achievable angles between two orthogonal sparse vectors upon compression, and, thus, better exploits the knowledge about the geometry of the compressed space. The proposed near orthogonality condition can be also exploited to derive less restricted sufficient conditions for signal reconstruction in two other compressive sensing problems, namely, compressive domain interferen-
e cancellation and support identification via the subspace pursuit algorithm.]]>60957025715969<![CDATA[Online Learning as Stochastic Approximation of Regularization Paths: Optimality and Almost-Sure Convergence]]>60957165735393<![CDATA[Quaternion Reproducing Kernel Hilbert Spaces: Existence and Uniqueness Conditions]]>609573657491528<![CDATA[Efficient Classification for Metric Data]]>60957505759581<![CDATA[New Constructions of Quadratic Bent Functions in Polynomial Form]]>(p) -ary bent functions. Based on (boldsymbol {mathbb {Z}}_{4}) -valued quadratic forms, a simple method provides several new constructions of generalized Boolean bent functions. From these generalized Boolean bent functions a method is presented to transform them into Boolean bent and semi-bent functions. Moreover, many new (p) -ary bent functions can also be obtained by applying similar methods.]]>60957605767214<![CDATA[Optimal Odd-Length Binary Z-Complementary Pairs]]>(2^alpha 10^beta 26^gamma ) (where (alpha ,beta ,gamma ) are nonnegative integers). To fill the gap left by the odd-lengths, we investigate the optimal odd-length binary (OB) pairs, which display the closest correlation property to that of GCPs. Our criteria of closeness is that each pair has the maximum possible zero-correlation zone (ZCZ) width and minimum possible out-of-zone aperiodic autocorrelation sums. Such optimal pairs are called optimal OB Z-complementary pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of ((N+1)/2) , and minimum out-of-zone aperiodic sum magnitude of 2, where (N) denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li–Fan–Tang–Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications, where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families, which are useful in studying partially balanced incomplete block design.]]>60957685781771<![CDATA[A New Construction of Frequency-Hopping Sequences With Optimal Partial Hamming Correlation]]>et al. and Zhou et al. A construction of FHSs and FHS sets having optimal partial Hamming correlation with respect to the improved bounds is also presented based on the theory of generalized cyclotomy. Our construction yields optimal FHSs and FHS sets with new and flexible parameters not covered in this paper.]]>60957825790584<![CDATA[Partial-Period Correlations of Zadoff–Chu Sequences and Their Relatives]]>60957915802529<![CDATA[Comments on “A New Method to Compute the 2-Adic Complexity of Binary Sequences”]]>60958035804115<![CDATA[Correction to “Toward Photon-Efficient Key Distribution over Optical Channels”]]>6095805580570<![CDATA[[Blank page]]]>609B5806B58086<![CDATA[IEEE Transactions on Information Theory information for authors]]>609C3C382