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Information Theory, IEEE Transactions on

Issue 2 • Date Mar 1999

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  • Coded diversity on block-fading channels

    Publication Year: 1999 , Page(s): 771 - 781
    Cited by:  Papers (110)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (460 KB)  

    This paper considers coded diversity schemes over block-fading Rician channels using random coding techniques. Two random coding upper bounds on the error probability of block codes are derived: a new bound and a simpler but looser bound assuming binary input distribution. Also, a new lower bound for any block code is derived using the strong converse to channel coding theorem. The lower bound shows that the new random coding upper bound is quite tight. Furthermore, it is shown that the maximum achievable diversity order in a block-fading channel with finite interleaving depends not only on the number of subchannels L, but also on the code rate R and that the performance can only marginally be improved by increasing the block length of the code. The random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths N, demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes View full abstract»

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  • Spectral efficiency of CDMA with random spreading

    Publication Year: 1999 , Page(s): 622 - 640
    Cited by:  Papers (427)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (704 KB)  

    The CDMA channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods. Furthermore, its analysis provides a comparison baseline for CDMA channels with deterministic signature waveforms spanning one symbol period. We analyze the spectral efficiency (total capacity per chip) as a function of the number of users, spreading gain, and signal-to-noise ratio, and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading. White Gaussian background noise and equal-power synchronous users are assumed. The following receivers are analyzed: (a) optimal joint processing, (b) single-user matched filtering, (c) decorrelation, and (d) MMSE linear processing View full abstract»

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  • An improved upper bound of the rate of Euclidean superimposed codes

    Publication Year: 1999 , Page(s): 799 - 802
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB)  

    A family of n-dimensional unit norm vectors is an Euclidean superimposed code if the sums of any two distinct at most m-tuples of vectors are separated by a certain minimum Euclidean distance d. Ericson and Gyorfi (1988) proved that the rate of such a code is between (log m)/4m and (log m)/m for m large enough. In this paper-improving the above long-standing best upper bound for the rate-it is shown that the rate is always at most (log m)/2m, i.e., the size of a possible superimposed code is at most the root of the size given by Ericson et al. We also generalize these codes to other normed vector spaces View full abstract»

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  • Linear complexity of de Bruijn sequences-old and new results

    Publication Year: 1999 , Page(s): 693 - 698
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (308 KB)  

    The linear complexity of a de Bruijn sequence is the degree of the shortest linear recursion which generates the sequence. It is well known that the complexity of a binary de Bruijn sequence of length 2n is bounded below by 2n-1+n and above by 2n-1 for n⩾3. We briefly survey the known knowledge in this area. Some new results are also presented, in particular, it is shown that for each interval of length 2[log n]+1 in the above range, there exist binary de Bruijn sequences of length 2n with linear complexity in the interval View full abstract»

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  • Generalized cyclotomic codes of length p1e(1)...pte(t)

    Publication Year: 1999 , Page(s): 467 - 474
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (456 KB)  

    We first introduce a generalized cyclotomy of order 2 with respect to p1e(1)...pte(t). We then present two classes of new error-correcting binary cyclic codes of length p1e(1)...pte(t) based on this generalized cyclotomy. We prove either a square-root bound or a similar bound on the minimum odd weight of those codes with length n=p 1e(1) p2e(2) View full abstract»

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  • Arbitrarily varying multiple-access channels. I. Ericson's symmetrizability is adequate, Gubner's conjecture is true

    Publication Year: 1999 , Page(s): 742 - 749
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB)  

    In 1981 Jahn used the elimination technique of the first author to determine the average errors capacity region of an arbitrarily varying multiple-access channel (AVMAC), when this region has a nonempty interior. Here we remove this restriction. In his thesis (1990), Gubner (1990) missed this result because he used the first author's first approach to the MAC, which is based on conditional decoding, and not the first author's second approach, which is based on maximum likelihood decoding. This second approach was originally needed for a kind of compound MAC. For the AVMBC the difference between the approaches is naturally even more essential View full abstract»

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  • Generalized Hamming weights of nonlinear codes and the relation to the Z4-linear representation

    Publication Year: 1999 , Page(s): 713 - 720
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    We give a new definition of generalized Hamming weights of nonlinear codes and a new interpretation connected with it. These generalized weights are determined by the entropy/length profile of the code. We show that this definition characterizes the performance of nonlinear codes on the wire-tap channel of type II. The new definition is invariant under translates of the code, it satisfies the property of strict monotonicity and the generalized Singleton bound. We check the relations between the generalized weight hierarchies of Z4-linear codes and their binary image under the Gray map. We also show that the binary image of a Z4-linear code is a symmetric, not necessarily rectangular code. Moreover, if this binary image is a linear code then it admits a twisted squaring construction View full abstract»

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  • A low-weight trellis-based iterative soft-decision decoding algorithm for binary linear block codes

    Publication Year: 1999 , Page(s): 731 - 741
    Cited by:  Papers (5)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (476 KB)  

    This paper presents a new low-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test. The initial candidate codeword is generated by a simple decoding method. The subsequent candidate codewords, if needed, are generated by a chain of low-weight trellis searches, one at a time. Each search is conducted through a low-weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested. This improvement is then used as the next candidate codeword for a test of optimality. The decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low-weight trellis search results in a repetition of a previously generated candidate codeword. A divide-and-conquer technique is also presented for codes that are not spanned by their minimum-weight codewords. The proposed decoding algorithm has been applied to some well-known codes of lengths 48, 64, and 128. Simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the (128, 29, 32) RM code with a significant reduction in computational decoding complexity View full abstract»

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  • Randomly chosen index assignments are asymptotically bad for uniform sources

    Publication Year: 1999 , Page(s): 788 - 794
    Cited by:  Papers (9)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (308 KB)  

    It is known that among all redundancy-free codes (or index assignments), the natural binary code minimizes the mean-squared error (MSE) of the uniform source and uniform quantizer on a binary symmetric channel. We derive a code which maximizes the MSE and demonstrate that the code is linear and its distortion is asymptotically equivalent, as the block length grows, to the expected distortion of an index assignment chosen uniformly at random View full abstract»

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  • List decoding of algebraic-geometric codes

    Publication Year: 1999 , Page(s): 432 - 437
    Cited by:  Papers (22)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (316 KB)  

    We generalize Sudan's (see J. Compl., vol.13, p.180-93, 1997) results for Reed-Solomon codes to the class of algebraic-geometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-correction bound (d-1)/2, d being the minimum distance of the code. Our main algorithm is based on an interpolation scheme and factorization of polynomials over algebraic function fields. For the latter problem we design a polynomial-time algorithm and show that the resulting overall list-decoding algorithm runs in polynomial time under some mild conditions. Several examples are included View full abstract»

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  • Note on taking square-roots modulo N

    Publication Year: 1999 , Page(s): 807 - 809
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (116 KB)  

    In this article it is shown how Gauss' (1981) famous cyclotomic sum formula can be used for extracting square-roots modulo N View full abstract»

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  • Efficient code constructions for certain two-dimensional constraints

    Publication Year: 1999 , Page(s): 794 - 799
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB)  

    Efficient encoding algorithms are presented for two types of constraints on two-dimensional binary arrays. The first constraint considered is that of t-conservative arrays, where each row and each column has at least t transitions of the form `0'→`1' or `1'→`0.' The second constraint is that of two-dimensional DC-free arrays, where in each row and each column the number of `0's equals the number of `1's View full abstract»

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  • Binomial moments of the distance distribution: bounds and applications

    Publication Year: 1999 , Page(s): 438 - 452
    Cited by:  Papers (20)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (748 KB)  

    We study a combinatorial invariant of codes which counts the number of ordered pairs of codewords in all subcodes of restricted support in a code. This invariant can be expressed as a linear form of the components of the distance distribution of the code with binomial numbers as coefficients. For this reason we call it a binomial moment of the distance distribution. Binomial moments appear in the proof of the MacWilliams (1963) identities and in many other problems of combinatorial coding theory. We introduce a linear programming problem for bounding these linear forms from below. It turns out that some known codes (1-error-correcting perfect codes, Golay codes, Nordstrom-Robinson code, etc.) yield optimal solutions of this problem, i.e., have minimal possible binomial moments of the distance distribution. We derive several general feasible solutions of this problem, which give lower bounds on the binomial moments of codes with given parameters, and derive the corresponding asymptotic bounds. Applications of these bounds include new lower bounds on the probability of undetected error for binary codes used over the binary-symmetric channel with crossover probability p and optimality of many codes for error detection. Asymptotic analysis of the bounds enables us to extend the range of code rates in which the upper bound on the undetected error exponent is tight View full abstract»

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  • Capacity of Markov channels with receiver CSI and delayed feedback

    Publication Year: 1999 , Page(s): 761 - 771
    Cited by:  Papers (55)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (416 KB)  

    While feedback does not increase the capacity of memoryless channels, the capacity of time-varying channels with feedback can be increased by exploiting the structure in the channel variations. Feedback information from the receiver is usually available at the transmitter only after some time delay. The capacity increase due to feedback depends on the feedback delay relative to the channel decorrelation time. We model time-varying channels as finite-state Markov channels and determine their capacity as a function of the feedback delay assuming perfect channel state information at the receiver. We apply the result to derive power control strategies to maximize the capacity for finite-state additive Gaussian noise channels and log-normal shadow fading channels View full abstract»

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  • Trellis-coded quantization for binary erasure channels

    Publication Year: 1999 , Page(s): 781 - 787
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (272 KB)  

    Trellis-coded quantizers (TCQ) are designed for the binary erasure channel (BEC) for memoryless sources. When the bit erasure rate is large, the channel-optimized TCQ can provide up to 1.4 dB improvement over TCQ designed for a lossless channel View full abstract»

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  • Improved rates and asymptotic normality for nonparametric neural network estimators

    Publication Year: 1999 , Page(s): 682 - 691
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (580 KB)  

    We obtain an improved approximation rate (in Sobolev norm) of r -1/2-α(d+1)/ for a large class of single hidden layer feedforward artificial neural networks (ANN) with r hidden units and possibly nonsigmoid activation functions when the target function satisfies certain smoothness conditions. Here, d is the dimension of the domain of the target function, and α∈(0, 1) is related to the smoothness of the activation function. When applying this class of ANNs to nonparametrically estimate (train) a general target function using the method of sieves, we obtain new root-mean-square convergence rates of Op([n/log(n)]-(1+2α/(d+1))/[4(1+α/(d+1))])=op(n -1/4) by letting the number of hidden units τn, increase appropriately with the sample size (number of training examples) n. These rates are valid for i.i.d. data as well as for uniform mixing and absolutely regular (β-mixing) stationary time series data. In addition, the rates are fast enough to deliver root-n asymptotic normality for plug-in estimates of smooth functionals using general ANN sieve estimators. As interesting applications to nonlinear time series, we establish rates for ANN sieve estimators of four different multivariate target functions: a conditional mean, a conditional quantile, a joint density, and a conditional density. We also obtain root-n asymptotic normality results for semiparametric model coefficient and average derivative estimators View full abstract»

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  • New families of almost perfect nonlinear power mappings

    Publication Year: 1999 , Page(s): 475 - 485
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (600 KB)  

    A power mapping f(x)=xd over GF(pn) is said to be differentially k-uniform if k is the maximum number of solutions x∈GF(pn) of f(x+a)-f(x)=b where a, b∈GF(pn ) and a≠0. A 2-uniform mapping is called almost perfect nonlinear (APN). We construct several new infinite families of nonbinary APN power mappings View full abstract»

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  • Variable-rate trellis source encoding

    Publication Year: 1999 , Page(s): 586 - 608
    Cited by:  Papers (19)  |  Patents (19)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1424 KB)  

    The fixed slope lossy algorithm derived from the kth-order adaptive arithmetic codeword length function is extended to finite-state decoders or trellis-structured decoders. When this algorithm is used to encode a stationary, ergodic source with a continuous alphabet, the Lagrangian performance converges with probability one to a quantity computable as the infimum of an information-theoretic functional over a set of auxiliary random variables and reproduction levels, where λ>0 and -λ are designated to be the slope of the rate distortion function R(D) of the source at some D; the quantity is close to R(D)+λD when the order k used in the arithmetic coding or the number of states in the decoders is large enough, An alternating minimization algorithm for computing the quantity is presented; this algorithm is based on a training sequence and in turn gives rise to a design algorithm for variable-rate trellis source codes. The resulting variable-rate trellis source codes are very efficient in low-rate regions. With k=8, the mean-squared error encoding performance at the rate 1/2 bits/sample for memoryless Gaussian sources is comparable to that afforded by trellis-coded quantizers; with k=8 and the number of states in the decoder=32, the mean-squared error encoding performance at the rate 1/2 bits/sample for memoryless Laplacian sources is about 1 dB better than that afforded by the trellis-coded quantizers with 256 states, with k=8 and the number of states in the decoder=256, the mean-squared error encoding performance at the rates of a fraction of 1 bit/sample for highly dependent Gauss-Markov sources with correlation coefficient 0.9 is within about 0.6 dB of the distortion rate function View full abstract»

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  • Codes of lengths 120 and 136 meeting the Grey-Rankin bound and quasi-symmetric designs

    Publication Year: 1999 , Page(s): 703 - 706
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (188 KB)  

    In this correspondence, we give a characterization of certain quasi-cyclic self-complementary codes with parameters [120,9,56] and [136,9,64], some quasi-cyclic self-complementary codes are also constructed with parameters [496,11,240] and [528,11,256]. These codes are optimal in the sense that they meet the Grey-Rankin bound, new quasi-symmetric SDP (symmetric difference property) designs are constructed from these codes View full abstract»

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  • High-resolution source coding for non-difference distortion measures: multidimensional companding

    Publication Year: 1999 , Page(s): 548 - 561
    Cited by:  Papers (30)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (736 KB)  

    Entropy-coded vector quantization is studied using high-resolution multidimensional companding over a class of nondifference distortion measures. For distortion measures which are “locally quadratic” a rigorous derivation of the asymptotic distortion and entropy-coded rate of multidimensional companders is given along with conditions for the optimal choice of the compressor function. This optimum compressor, when it exists, depends on the distortion measure but not on the source distribution. The rate-distortion performance of the companding scheme is studied using an asymptotic expression for the rate-distortion function which parallels the Shannon lower bound for difference distortion measures. It is proved that the high-resolution performance of the scheme is arbitrarily close to the rate-distortion limit for large quantizer dimensions if the compressor function and the lattice quantizer used in the companding scheme are optimal, extending an analogous statement for entropy-coded lattice quantization and MSE distortion. The companding approach is applied to obtain a high-resolution quantizing scheme for noisy sources View full abstract»

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  • On symmetrical multilevel diversity coding

    Publication Year: 1999 , Page(s): 609 - 621
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (924 KB)  

    Symmetrical multilevel diversity coding with independent data streams has been studied by Roche et al. (1992), and the admissible coding rate region was determined for the case of three levels. In particular, it was shown that coding by superposition is optimal, which means that optimality can be achieved by very simple coding. However, it is very difficult to generalize their proof to an arbitrary number of levels. In this paper, we use a new approach to study this problem, and we show that coding by superposition is optimal for symmetrical multilevel diversity coding in general. We also discuss how our result can be applied when the source consists of correlated data streams. The techniques we use are new in multiuser information theory, and our work sheds some light on the standing problem of characterizing those multilevel diversity coding systems for which coding by superposition is optimal View full abstract»

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  • Constructions of generalized concatenated codes and their trellis-based decoding complexity

    Publication Year: 1999 , Page(s): 725 - 731
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB)  

    In this article, constructions of generalized concatenated (GC) codes with good rates and distances are presented. Some of the proposed GC codes have simpler trellis complexity than Euclidean geometry (EG), Reed-Muller (RM), or Bose-Chaudhuri-Hocquenghem (BCH) codes of approximately the same rates and minimum distances, and in addition can be decoded with trellis-based multistage decoding up to their minimum distances. Several codes of the same length, dimension, and minimum distance as the best linear codes known are constructed View full abstract»

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  • Codes on Garcia-Stichtenoth curves with true distance greater than Feng-Rao distance

    Publication Year: 1999 , Page(s): 706 - 709
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (172 KB)  

    We give codes on all members after level 4 of the family of Garcia-Stichtenoth (see Invent. Math., vol.121, p.211-22, 1995) curves with the property dtrue>dFR. These codes also give an improvement on Tsfasman-Vladut-Zink bound View full abstract»

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  • Unconditionally secure key agreement and the intrinsic conditional information

    Publication Year: 1999 , Page(s): 499 - 514
    Cited by:  Papers (76)  |  Patents (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (784 KB)  

    This paper is concerned with secret-key agreement by public discussion. Assume that two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X, Y, and Z, respectively, with joint distribution PXYZ. The secret-key rate S(X;Y||Z) has been defined as the maximal rate at which Alice and Bob can generate a secret key by communication over an insecure, but authenticated channel such that Eve's information about this key is arbitrarily small. We define a new conditional mutual information measure, the intrinsic conditional mutual information between S and Y when given Z, denoted by I(X;Y↓Z), which is an upper bound on S(X;Y||Z). The special scenarios are analyzed where X, Y, and Z are generated by sending a binary random variable R, for example a signal broadcast by a satellite, over independent channels, or two scenarios in which Z is generated by sending X and Y over erasure channels. In the first two scenarios it can be shown that the secret-key rate is strictly positive if and only if I(X;Y↓Z) is strictly positive. For the third scenario, a new protocol is presented which allows secret-key agreement even when all the previously known protocols fail View full abstract»

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  • On the Hamming distance between two i.i.d. random n-tuples over a finite set

    Publication Year: 1999 , Page(s): 803 - 807
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB)  

    We study the Hamming distance dH(X,Y) between two independent identical distributed (i.i.d.) random n-tuples X and Y over some finite set, both lower and upper bounds are derived for the expectation EdH(X,Y) and the variance DdH(X,Y). Also, a generalization of the Grey-Rankin bound is given 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