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Information Theory, IEEE Transactions on

Issue 3 • Date March 2014

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Displaying Results 1 - 25 of 47
  • Table of contents

    Publication Year: 2014 , Page(s): C1 - C4
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  • IEEE Transactions on Information Theory publication information

    Publication Year: 2014 , Page(s): C2
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  • A Universal Grammar-Based Code for Lossless Compression of Binary Trees

    Publication Year: 2014 , Page(s): 1373 - 1386
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (425 KB) |  | HTML iconHTML  

    We consider the problem of lossless compression of binary trees, with the aim of reducing the number of code bits needed to store or transmit such trees. A lossless grammar-based code is presented, which encodes each binary tree into a binary codeword in two steps. In the first step, the tree is transformed into a context-free grammar from which the tree can be reconstructed. In the second step, the context-free grammar is encoded into a binary codeword. The decoder of the grammar-based code decodes the original tree from its codeword by reversing the two encoding steps. It is shown that the resulting grammar-based binary tree compression code is a universal code on a family of probabilistic binary tree source models satisfying certain weak restrictions. View full abstract»

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  • Universal Enumerative Coding for Tree Models

    Publication Year: 2014 , Page(s): 1387 - 1411
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1160 KB) |  | HTML iconHTML  

    Efficient enumerative coding for tree sources is, in general, surprisingly intricate-a simple uniform encoding of type classes, which is asymptotically optimal in expectation for many classical models, such as FSMs, turns out not to be so in this case. We describe an efficiently computable enumerative code that is universal in the family of tree models in the sense that, for a string emitted by an unknown source whose model is supported on a known tree, the expected normalized code length of the encoding approaches the entropy rate of the source with a convergence rate (K/2)(log n)/n, where K is the number of free parameters of the model family. Based on recent results characterizing type classes of context trees, the code consists of the index of the sequence in the tree type class, and an efficient description of the class itself using a nonuniform encoding of selected string counts. The results are extended to a twice-universal setting, where the tree underlying the source model is unknown. View full abstract»

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  • Huffman Redundancy for Large Alphabet Sources

    Publication Year: 2014 , Page(s): 1412 - 1427
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (573 KB) |  | HTML iconHTML  

    The performance of optimal prefix-free encoding for memoryless sources with a large alphabet size is studied. It is shown that the redundancy of the Huffman code for almost all sources with a large alphabet size n is very close to that of the average distribution of the monotone sources with n symbols. This value lies between 0.02873 and 0.02877 bit for sufficiently large n. View full abstract»

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  • On the Information Theoretic Performance Comparison of Causal Video Coding and Predictive Video Coding

    Publication Year: 2014 , Page(s): 1428 - 1446
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (557 KB) |  | HTML iconHTML  

    Causal video coding is a coding paradigm where video source frames X1, X2,..., XN are encoded in a frame-by-frame manner, the encoder for each frame can use all previous source frames and all previous encoded frames, and the corresponding decoder can use only all previous encoded frames. In the special case where the encoder for each frame Xk is further restricted to enlist help only from all previous encoded frames, causal video coding is reduced to predictive video coding, which all MPEG-series and H-series video coding standards proposed so far are based upon. In this paper, we compare the rate distortion performance of causal video coding with that of predictive video coding from an information theoretic perspective by modeling each frame Xk itself as a source Xk={Xk(i)}i=1. Let Rc*(D1,...,DN) (Rp*(D1,...,DN), respectively) denote the minimum total rate required to achieve a given distortion level D1,...,DN in causal video coding (predictive video coding, respectively). We first show that like Rc*(D1,..., DN), for jointly stationary and totally ergodic sources X1, X2,..., XN, Rp*(D1,...,DN) is equal to the infimum of the nth order total rate distortion function Rp,n(D1,...,DN) over all n, where Rp,n(D1,...,DN) itself is given by the minimum of an information quantity over a set of auxiliary random variables. We then prove that if the jointly stationary and totally ergodic sources X1,..., XN form a (first-order) Markov chain, we have Rp*(D1,...,DN)=Rc*(D1,...,DN). However, this is not true in general if X1,..., XN do not form a (first-order) Markov chain. Specifica- ly, we demonstrate that for independent and identically distributed vector source (X1,..., XN), if X1,..., XN do not form a (first-order) Markov chain, then under some conditions on source frames and distortion, Rc*(D1,..., DN) is strictly less than Rp*(D1,..., DN) in general. Our techniques allow us to compare Rp*(D1,..., DN) with Rc*(D1,..., DN) even when the single-letter characterization of Rp*(D1,..., DN), if any, is unknown. View full abstract»

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  • Lossless Coding for Distributed Streaming Sources

    Publication Year: 2014 , Page(s): 1447 - 1474
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1032 KB) |  | HTML iconHTML  

    Distributed source coding is traditionally viewed in a block coding context wherein all source symbols are known in advance by the encoders. However, many modern applications to which distributed source coding ideas are applied, are better modeled as having streaming data. In a streaming setting, source symbol pairs are revealed to separate encoders in real time and need to be reconstructed at the decoder with subject to some tolerable end-to-end delay. In this paper, a causal sequential random binning encoder is introduced and paired with maximum likelihood (ML) and universal decoders. The latter uses a novel weighted empirical suffix entropy decoding rule. We derive a lower bounds on the error exponent with delay for each decoder. We also provide upper bounds for the special case of streaming with decoder side information and discuss when upper and lower bounds match. We show that both ML and universal decoders achieve the same (positive) error exponents for all rate pairs inside the Slepian-Wolf achievable rate region. The dominant error events in streaming are different from those in block-coding and result in different exponents. Because the sequential random binning scheme is also universal over delays, the resulting code eventually reconstructs every source symbol correctly with probability one. View full abstract»

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  • Some Bounds on the Size of Codes

    Publication Year: 2014 , Page(s): 1475 - 1480
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (398 KB) |  | HTML iconHTML  

    We present some upper bounds on the size of nonlinear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g., the Griesmer bound, the Johnson bound, the Plotkin bound, and of linear programming bounds. One of the new bound is actually an improvement of a bound by Zinoviev, Litsyn, and Laihonen. Our experiments show that in the linear case our bounds provide the best value in a wide range, compared with all other closed-formula upper bounds. In the nonlinear case, we also compare our bound with the linear programming bound and with some improvements on it, show that there are cases where we beat these bounds. In particular, we obtain a new bound in Brouwer's table for A3(16,3). View full abstract»

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  • Capacity-Achieving Multiwrite WOM Codes

    Publication Year: 2014 , Page(s): 1481 - 1487
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (209 KB) |  | HTML iconHTML  

    In this paper, we give an explicit construction of a family of capacity-achieving binary t-write WOM codes for any number of writes t, which have polynomial time encoding and decoding algorithms. The block length of our construction is N=(t/ε)O(t/(δε)) when ε is the gap to capacity and encoding and decoding run in time N1+δ. This is the first deterministic construction achieving these parameters. Our techniques also apply to larger alphabets. View full abstract»

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  • Stopping Sets of Algebraic Geometry Codes

    Publication Year: 2014 , Page(s): 1488 - 1495
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (218 KB) |  | HTML iconHTML  

    Stopping sets and stopping set distribution of a linear code play an important role in the performance analysis of iterative decoding for this linear code. Let C be an [n, k] linear code over Fq with parity-check matrix H, where the rows of H may be dependent. Let [n] = {1, 2,...,n} denote the set of column indices of H. A stopping set S of C with parity-check matrix H is a subset of [n] such that the restriction of H to S does not contain a row of weight 1. The stopping set distribution {Ti(H)}i=0n enumerates the number of stopping sets with size i of C with parity-check matrix H. Denote H*, the parity-check matrix, consisting of all the nonzero codewords in the dual code C. In this paper, we study stopping sets and stopping set distributions of some residue algebraic geometry (AG) codes with parity-check matrix H*. First, we give two descriptions of stopping sets of residue AG codes. For the simplest AG codes, i.e., the generalized Reed-Solomon codes, it is easy to determine all the stopping sets. Then, we consider the AG codes from elliptic curves. We use the group structure of rational points of elliptic curves to present a complete characterization of stopping sets. Then, the stopping sets, the stopping set distribution, and the stopping distance of the AG code from an elliptic curve are reduced to the search, counting, and decision versions of the subset sum problem in the group of rational points of the elliptic curve, respectively. Finally, for some special cases, we determine the stopping set distributions of the AG codes from elliptic curves. View full abstract»

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  • Hermitian Self-Dual Abelian Codes

    Publication Year: 2014 , Page(s): 1496 - 1507
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (691 KB) |  | HTML iconHTML  

    Hermitian self-dual abelian codes in a group ring Fq2[G], where Fq2 is a finite field of order q2 and G is a finite abelian group, are studied. Using the well-known discrete Fourier transform decomposition for a semisimple group ring, a characterization of Hermitian self-dual abelian codes in Fq2[G] is given, together with an alternative proof of necessary and sufficient conditions for the existence of such a code in Fq2[G], i.e., there exists a Hermitian self-dual abelian code in Fq2[G] if and only if the order of G is even and q = 2l for some positive integer l. Later on, the study is further restricted to the case where F22l [G] is a principal ideal group ring, or equivalently, G ≅ A⊕Z2k with 2 ≠ |A|. Based on the characterization obtained, the number of Hermitian self-dual abelian codes in F22l [A⊕Z2k] can be determined easily. When A is cyclic, this result answers an open problem of Jia et al. concerning Hermitian self-dual cyclic codes. In many cases, F22l [A⊕Z2k] contains a unique Hermitian self-dual abelian code. The criteria for such cases are determined in terms of l and the order of A. Finally, the distribution of finite abelian groups A such that a unique Hermitian self-dual abelian code exists in F22l [A ⊕ Z2] is established, together with the distribution of odd integers m such that a unique Hermitian self-dual cyclic code of length 2 m over F22l exists. View full abstract»

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  • BBZ_{2}BBZ_{4} -Additive Cyclic Codes

    Publication Year: 2014 , Page(s): 1508 - 1514
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (659 KB) |  | HTML iconHTML  

    In this paper, we study Z2Z4-additive cyclic codes. These codes are identified as Z4[x]-submodules of the ring Rr,s=Z2[x]/〈xr-1〉×Z4[x]/〈xs-1〉. The algebraic structure of this family of codes is studied and a set of generator polynomials for this family as a Z4[x]-submodule of the ring Rr,s is determined. We show that the duals of Z2Z4-additive cyclic codes are also cyclic. We also present an infinite family of Maximum Distance separable with respect to the singleton bound codes. Finally, we obtain a number of binary linear codes with optimal parameters from the Z2Z4-additive cyclic codes. View full abstract»

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  • Optimal Index Codes With Near-Extreme Rates

    Publication Year: 2014 , Page(s): 1515 - 1527
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (704 KB) |  | HTML iconHTML  

    The min-rank of a digraph was shown to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this paper, the graphs and digraphs of near-extreme min-ranks are studied. Those graphs and digraphs correspond to the ICSI instances having near-extreme transmission rates when using optimal scalar linear index codes. In particular, it is shown that the decision problem whether a digraph has min-rank two is NP-complete. By contrast, the same question for graphs can be answered in polynomial time. In addition, a circuit-packing bound is revisited, and several families of digraphs, optimal with respect to this bound, whose min-ranks can be found in polynomial time, are presented. View full abstract»

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  • On the Construction of Nonbinary Quantum BCH Codes

    Publication Year: 2014 , Page(s): 1528 - 1535
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (631 KB) |  | HTML iconHTML  

    Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive nonnarrow-sense, Bose-Chaudhuri-Hocquenghem codes, are presented in this paper. The first two are based on Calderbank-Shor-Steane (CSS) construction derived from two nonprimitive Bose-Chaudhuri-Hocquenghem codes. The third one is based on Steane's enlargement of nonbinary CSS codes applied to suitable subfamilies of nonprimitive nonnarrow-sense Bose-Chaudhuri-Hocquenghem codes. The fourth construction is derived from suitable subfamilies of Hermitian dual-containing nonprimitive nonnarrow-sense Bose-Chaudhuri-Hocquenghem codes. These constructions generate new families of quantum codes whose parameters are better than the ones available in the literature. View full abstract»

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  • The Entropy Power Inequality for Quantum Systems

    Publication Year: 2014 , Page(s): 1536 - 1548
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (293 KB) |  | HTML iconHTML  

    When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the entropy power inequality (EPI), which states that e2H(Z) ≥ e2H(X)+e2H(Y), gives a very tight restriction on the entropy of Z. This inequality has found many applications in information theory and statistics. The quantum analogue of adding two random variables is the combination of two independent bosonic modes at a beam splitter. The purpose of this paper is to give a detailed outline of the proof of two separate generalizations of the EPI to the quantum regime. Our proofs are similar in spirit to the standard classical proofs of the EPI, but some new quantities and ideas are needed in the quantum setting. In particular, we find a new quantum de Bruijin identity relating entropy production under diffusion to a divergence-based quantum Fisher information. Furthermore, this Fisher information exhibits certain convexity properties in the context of beam splitters. View full abstract»

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  • When Do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination?

    Publication Year: 2014 , Page(s): 1549 - 1561
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB) |  | HTML iconHTML  

    In this paper, we consider the conditions under which a given ensemble of two-qubit states can be optimally distinguished by local operations and classical communication (LOCC). We begin by completing the perfect distinguishability problem of two-qubit ensembles-both for separable operations and LOCC-by providing necessary and sufficient conditions for the perfect discrimination of one pure and one mixed state. Then, for the well-known task of minimum error discrimination, it is shown that almost all two-qubit ensembles consisting of three pure states cannot be optimally discriminated using LOCC. This is surprising considering that any two pure states can be distinguished optimally by LOCC. Special attention is given to ensembles that lack entanglement, and we prove an easy sufficient condition for when a set of three product states cannot be optimally distinguished by LOCC, thus providing new examples of the phenomenon known as non-locality without entanglement. We next consider an example of N parties who each share the same state but who are ignorant of its identity. The state is drawn from the rotationally invariant trine ensemble, and we establish a tight connection between the N-copy ensemble and Shor's lifted single-copy ensemble. For any finite N, we prove that optimal identification of the states cannot be achieved by LOCC; however, as N→∞, LOCC can indeed discriminate the states optimally. This is the first result of its kind. Finally, we turn to the task of unambiguous discrimination and derive new lower bounds on the LOCC inconclusive probability for symmetric states. When applied to the double trine ensemble, this leads to a rather different distinguishability character than when the minimum error probability is considered. View full abstract»

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  • A Decoupling Approach to Classical Data Transmission Over Quantum Channels

    Publication Year: 2014 , Page(s): 1562 - 1572
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB) |  | HTML iconHTML  

    Most coding theorems in quantum Shannon theory can be proven using the decoupling technique. To send data through a channel, one guarantees that the environment gets no information about it. Uhlmann's theorem then ensures that the receiver must be able to decode. While a wide range of problems can be solved this way, one of the most basic coding problems remains impervious to a direct application of this method, sending classical information through a quantum channel. We will show that this problem can, in fact, be solved using decoupling ideas, specifically by proving a dequantizing theorem, which ensures that the environment is only classically correlated with the sent data. Our techniques naturally yield a generalization of the Holevo-Schumacher-Westmoreland theorem to the one-shot scenario, where a quantum channel can be applied only once. View full abstract»

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  • Smooth Max-Information as One-Shot Generalization for Mutual Information

    Publication Year: 2014 , Page(s): 1573 - 1581
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (230 KB) |  | HTML iconHTML  

    We study formal properties of smooth max-information, a generalization of von Neumann mutual information derived from the max-relative entropy. Recent work suggests that it is a useful quantity in one-shot channel coding, quantum rate distortion theory, and the physics of quantum many-body systems. Max-information can be defined in multiple ways. We demonstrate that different smoothed definitions are essentially equivalent (up to logarithmic terms in the smoothing parameters). These equivalence relations allow us to derive new chain rules for the max-information in terms of min- and max-entropies, thus extending the smooth entropy formalism to mutual information. View full abstract»

    Open Access
  • Extremal Channels of Gallager's E_{0} Under the Basic Polarization Transformations

    Publication Year: 2014 , Page(s): 1582 - 1591
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB) |  | HTML iconHTML  

    We study the extremality of the binary erasure channel and the binary symmetric channel for Gallager's reliability function E0 of binary input discrete memoryless channels evaluated under the uniform input distribution from the aspect of channel polarization. In particular, we show that amongst all binary discrete memoryless channels of a given E0(ρ) value, for a fixed ρ ≥ 0, the binary erasure channel and the binary symmetric channel are extremal in the evolution of E0 under the one-step polarization transformations. View full abstract»

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  • Refinement of the Sphere-Packing Bound: Asymmetric Channels

    Publication Year: 2014 , Page(s): 1592 - 1614
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (619 KB) |  | HTML iconHTML  

    We provide a refinement of the sphere-packing bound for constant composition codes over asymmetric discrete memoryless channels that improves the subexponential factor in front of the exponent. The order of our subexponential factor is Ω(N-0.5(1+ε+ρR*)) for any ϵ > 0, where ρR* is the left derivative of the sphere-packing exponent at rate R and N is the blocklength. View full abstract»

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  • Capacity of Gaussian Channels With Duty Cycle and Power Constraints

    Publication Year: 2014 , Page(s): 1615 - 1629
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (767 KB) |  | HTML iconHTML  

    In many wireless communication systems, radios are subject to a duty cycle constraint, that is, a radio can only actively transmit signals over a fraction of the time. For example, it is desirable to have a small duty cycle in some low power systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen and detect primary users frequently. This paper studies the capacity of point-to-point scalar discrete-time Gaussian channels subject to a duty cycle constraint as well as an average transmit power constraint. An idealized duty cycle constraint is first studied, which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword. Independent input with a unique discrete distribution is shown to achieve the channel capacity. In many situations, numerically optimized on-off signaling can achieve much higher rate than Gaussian signaling over a deterministic transmission schedule. This is in part because the positions of nontransmissions in a codeword can convey information. A more realistic duty cycle constraint is also studied, where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for. The capacity-achieving input is correlated over time and is hard to compute. A lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first-order Markov input process, whose stationary distribution is also discrete and can be computed efficiently. The results in this paper suggest that, under various duty cycle constraints, departing from the usual paradigm of intermittent packet transmissions may yield substantial gain. View full abstract»

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  • On Extracting Common Random Bits From Correlated Sources on Large Alphabets

    Publication Year: 2014 , Page(s): 1630 - 1637
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (239 KB) |  | HTML iconHTML  

    Suppose Alice and Bob receive strings X=(X1,...,Xn) and Y=(Y1,...,Yn) each uniformly random in [s]n, but so that X and Y are correlated. For each symbol i, we have that Yi=Xi with probability 1-ε and otherwise Yi is chosen independently and uniformly from [s]. Alice and Bob wish to use their respective strings to extract a uniformly chosen common sequence from [s]k, but without communicating. How well can they do? The trivial strategy of outputting the first k symbols yields an agreement probability of (1-ε+ε/s)k. In a recent work by Bogdanov and Mossel, it was shown that in the binary case where s=2 and k=k(ε) is large enough then it is possible to extract k bits with a better agreement probability rate. In particular, it is possible to achieve agreement probability (kε)-1/2·2-kε/(2(1-ε/2)) using a random construction based on Hamming balls, and this is optimal up to lower order terms. In this paper, we consider the same problem over larger alphabet sizes s and we show that the agreement probability rate changes dramatically as the alphabet grows. In particular, we show no strategy can achieve agreement probability better than (1-ε)k(1+δ(s))k where δ(s)→ 0 as s→∞. We also show that Hamming ball-based constructions have much lower agreement probability rate than the trivial algorithm as s→∞. Our proofs and results are intimately related to subtle properties of hypercontractive inequalities. View full abstract»

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  • Constructions of Resilient S-Boxes With Strictly Almost Optimal Nonlinearity Through Disjoint Linear Codes

    Publication Year: 2014 , Page(s): 1638 - 1651
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2059 KB) |  | HTML iconHTML  

    In this paper, a novel approach of finding disjoint linear codes is presented. The cardinality of a set of [u, m, t+1] disjoint linear codes largely exceeds all the previous best known methods used for the same purpose. Using such sets of disjoint linear codes, not necessarily of the same length, we have been able to provide a construction technique of t-resilient S-boxes F:F2n→2m ( n even, ) with strictly almost optimal nonlinearity . This is the first time that the bound 2n-1-2n/2 has been exceeded by multiple output resilient functions. Actually, the nonlinearity of our functions is in many cases equal to the best known nonlinearity of balanced Boolean functions. A large class of previously unknown cryptographic resilient S-boxes is obtained, and several improvements of the original approach are proposed. Some other relevant cryptographic properties are also briefly discussed. It is shown that these functions may reach Siegenthaler's bound n-t-1, and can be either of optimal algebraic immunity or of slightly suboptimal algebraic immunity, which was confirmed by simulations. View full abstract»

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  • Natural Generalizations of Threshold Secret Sharing

    Publication Year: 2014 , Page(s): 1652 - 1664
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (331 KB) |  | HTML iconHTML  

    We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure the proofs for the existence of ideal secret sharing schemes for them. View full abstract»

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  • Necessary Conditions for the Existence of Regular p -Ary Bent Functions

    Publication Year: 2014 , Page(s): 1665 - 1672
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (286 KB) |  | HTML iconHTML  

    We find some necessary conditions for the existence of regular p-ary bent functions (from Znp to Zp), where p is a prime. In more detail, we show that there is no regular p-ary bent function f in n variables with w(Mf) larger than n/2, and for a given nonnegative integer k, there is no regular p-ary bent function f in n variables with w(Mf)=n/2-k ( n+3/2-k, respectively) for an even n ≥ Np,k (an odd n ≥ Np,k, respectively), where Np,k is some positive integer, which is explicitly determined and the w(Mf) of a p-ary function f is some value related to the power of each monomial of f. For the proof of our main results, we use some properties of regular p-ary bent functions, such as the MacWilliams duality, which is proved to hold for regular p-ary bent functions in this paper. View full abstract»

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

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Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering