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Information Theory, IEEE Transactions on

Issue 5 • Date September 1984

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Displaying Results 1 - 22 of 22
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  • Review of 'Digital Communications' (Proakis, J.G.; 1983)

    Page(s): 780 - 781
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    Freely Available from IEEE
  • Nonbinary codes, correcting single deletion or insertion (Corresp.)

    Page(s): 766 - 769
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    In many digital communications systems, bursts of insertions or deletions are typical errors. A new class of nonbinary codes is proposed that correct a single deletion or insertion. Asymptotically, the cardinality of these codes is close to optimal. The codes can be easily implemented. View full abstract»

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  • A product construction for perfect codes over arbitrary alphabets (Corresp.)

    Page(s): 769 - 771
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    A general product construction for perfect single-error-correcting codes over an arbitrary alphabet is presented. Given perfect single-error-correcting codes of lengthsn, m, andq + 1over an alphabet of orderq, one can construct perfect single-error-correcting codes of length(q - 1)nm + n + mover the same alphabet. Moreover, if there exists a perfect single-error-correcting code of lengthq + 1over an alphabet of orderq, then there exist perfect single-error-correcting codes of lengthn,n = (q^{t} _ 1)/(q - 1), and(t > 0, an integer). Finally, connections between projective planes of orderqand perfect codes of lengthq + 1over an alphabet of orderqare discussed. View full abstract»

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  • A polynomial-time algorithm for breaking the basic Merkle - Hellman cryptosystem

    Page(s): 699 - 704
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    The Merkle-Hellman cryptosystem is one of the two major public-key cryptosystems proposed so far. It is shown that the basic variant of this cryptosystem, in which the elements of the public key are modular multiples of a superincreasing sequence, is breakable in polynomial time. View full abstract»

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  • Construction of de Bruijn sequences of minimal complexity

    Page(s): 705 - 709
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    It is well known that the linear complexity of a de Bruijn sequenceSof length2^{n}is bounded below by2^{n- 1} + nforn geq 3. It is shown that this lower bound is attainable for alln. View full abstract»

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  • Poisson multiple-access contention with binary feedback

    Page(s): 745 - 751
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    Communication over a random multiple-access, collision-type, time-slotted, packet-switched channel with binary feedback is considered for a Poisson infinite-user model. Three different types of binary feedback are introduced and confusion resolution algorithms (CRA) are discussed for each. The CRA proposed for the feedback that tells only whether or not there was a collision in the previous slot achieves a throughput of0.442. The CRA proposed for the feedback that tells whether or not the previous slot was empty achieves a throughput of0.279. View full abstract»

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  • Duadic Codes

    Page(s): 709 - 714
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    A new family of binary cyclic(n,(n + 1)/2)and(n,(n - 1)/2)codes are introduced, which include quadratic residue (QR) codes whennis prime. These codes are defined in terms of their idempotent generators, and they exist for all oddn = p_{1}^{a_{1}} p_{2}^{a_{2}} cdots p_{r}^{a_{r}}where eachp_{i}is a primeequiv pm 1 pmod{8}. Dual codes are identified. The minimum odd weight of a duadic(n,(n + 1)/2)code satisfies a square root bound. When equality holds in the sharper form of this bound, vectors of minimum weight hold a projective plane. The unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent(73,37,9)duadic codes. All duadic codes of length less than127are identified, and the minimum weights of their extensions are given. One of the duadic codes of length113has greater minimum weight than the QR code of that length. View full abstract»

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  • On noiseless source coding with specified encoder output symbol frequencies (Corresp.)

    Page(s): 752 - 754
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    A method is presented for generating prefix-condition codes in which the relative frequencies of the encoder output symbols are close to a previously specified probability distribution. A Kraft-like inequality is developed for this purpose. View full abstract»

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  • An approach to an arithmetic analog of Berlekamp's algorithm (Corresp.)

    Page(s): 758 - 762
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    The Berlekamp algorithm used for generating convergents (polynomial fractions) to a polynomial sequence is altered for use with binary numbers. This provides an alternative to continued fraction generation of convergents, and the proposed algorithm uses no division. However optimality has not been proved unlike the case for the Berlekamp algorithm with polynomial sequences. View full abstract»

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  • Coin flipping by telephone (Corresp.)

    Page(s): 775 - 776
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    Two parties, who do not trust each other, wish to agree on the result of a coin toss while they are conversing by telephone. A new protocol which solves this problem is proposed and compared with previous protocols. View full abstract»

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  • A [55,16,19] binary Goppa code (Corresp.)

    Page(s): 773
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    A[55, 16, 19]binary Goppa code and some related codes are described. These codes are found to contain more codewords than any previously known codes of the same length and minimum distance. View full abstract»

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  • Some new bounds for the maximum length of circuit codes (Corresp.)

    Page(s): 754 - 756
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    Ad-dimensional circuit code of spreadsis a simple circuitCin the graph of thed-dimensional unit cube with the property that for any verticesxandyofCthat differ in exactlyrcoordinatesr < s, there exists a path fromxtoyconsisting ofredges ofC. Some new lower bounds will be given for the maximum length of ad-dimensional circuit code of spreadsfor some values ofdand fors = 4, s = 6, ands = 7. View full abstract»

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  • A new upper bound on the first-event error probability for maximum-likelihood decoding of fixed binary convolutional codes (Corresp.)

    Page(s): 762 - 766
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    An upper bound on the first-event error probability for maximum-likelihood decoding of fixed binary convolutional codes on the binary symmetric channel is derived. The bound is evaluated for rate1/2codes, and comparisons are made with simulations and with the bounds of Viterbi, Van de Meeberg, and Post. In particular, the new bound is significantly better than Van de Meeberg's bound for rates aboveR_{comp}. View full abstract»

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  • Characterization and estimation of two-dimensional ARMA models

    Page(s): 736 - 745
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    A class of finite-order two-dimensional autoregressive moving average (ARMA) is introduced that can represent any process with rational spectral density. In this model the driving noise is correlated and need not be Gaussian. Currently known classes of ARMA models or AR models are shown to be subsets of the above class. The three definitions of Markov property are discussed, and the class of ARMA models are precisely stated which have the noncausal and semicausal Markov property without imposing any specific boundary conditions. Next two approaches are considered to estimate the parameters of a model to fit a given image. The first method uses only the empirical correlations and involves the solution of linear equations. The second method is the likelihood approach. Since the exact likelihood function is difficult to compute, we resort to approximations suggested by the toroidal models. Numerical experiments compare the quality of the two estimation schemes. Finally the problem of synthesizing a texture obeying an ARMA model is considered. View full abstract»

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  • Shape and duration of clicks in modulated FM transmission

    Page(s): 728 - 735
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    A Slepian model is derived for the shape of dicks in modulated FM transmission. The modulated signal may be a deterministic periodic function or a stationary stochastic process, not necessarily Gaussian. To describe the clicks one first derives the stochastic properties of noise and signal at the clicks. (For a periodic signal this amounts to giving the relative number of clicks in any given part of the period.) Then the conditional distributions of noise and signal near clicks are derived in explicit form, using the noise and signal values at the click as (random) parameters, and finally these conditional distributions are mixed into a total model for the click shapes. For increasing carrier-to-noise power ratioA^{2}/2, the Slepian model converges after normalization to a rational function with random coefficients. The amplitude of a click is shown to be of the orderA^{2}, in contrast to the unmodulated ease, where click amplitudes are of the orderA. View full abstract»

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  • Correlation-immunity of nonlinear combining functions for cryptographic applications (Corresp.)

    Page(s): 776 - 780
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    Pseudonoise generators for cryptographic applications consisting of several linear feedback shift registers with a nonlinear combining function have been proposed as running key generators in stream ciphers. These running key generators eau sometimes be broken by (ciphertext-only) correlation attacks on individual subsequences. A new class of combining functions is presented, which provides better security against such attacks. The security is quantified by the smallest numberm + 1of subsequences that must be simultaneously considered in a correlation attack. A necessary condition for suchmth-order correlation-immunity is proved. A recursive construction is given that permits the construction of anmth-order immune combining function fornsubsequences for anymandnwith1 leq m < n. Finally, the trade-off between the length of the linear equivalent of the nonlinear generator and the ordermof its immunity against correlation attacks is considered. View full abstract»

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  • A note on binary arrays with a certain window property (Corresp.)

    Page(s): 774 - 775
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    For somers = 2^{mn}, there exist periodicr times sbinary arrays such that allm times nbinary matrices will appear in it. As two-dimensional versions of de Bruijn sequences, these kinds of arrays have possible applications in cryptography and the design of mask configurations for spectrometers. View full abstract»

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  • Generalization of chase algorithms for soft decision decoding of binary linear codes

    Page(s): 714 - 721
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    Soft decision decoding of binary linear block codes transmitted over the additive white Gaussian channel (AWGN) using antipodal signaling is considered. A set of decoding algorithms called generalized Chase algorithms is proposed. In contrast to Chase algorithms, which require alfloor (d- 1)/2 rfloorbinary error-correcting decoder for decoding a binary linear block code of minimum distanced, the generalized Chase algorithms can use a binary decoder that can correct less thanlfloor ( d - 1)/2 rfloorhard errors. The Chase algorithms are particular cases of the generalized Chase algorithms. The performance of all proposed algorithms is asymptotically optimum for high signal-to-noise ratio (SNR). Simulation results for the(47, 23)quadratic residue code indicate that even for low SNR the performance level of a maximum likelihood decoder can be approached by a relatively simple decoding procedure. View full abstract»

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  • Predictive source coding techniques using maximum likelihood prediction for compression of digitized images

    Page(s): 722 - 727
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    A predictive compression technique is examined, using maximum likelihood prediction of the image pixel based on the Markov mesh model, that encodes the differences via Gordon block-bit-plane (GBBP) encoding. The procedure is very efficient in that it requires a bit rate near the entropy of the source. For images with many quantization levels, maximum likelihood prediction can be cumbersome to implement. Thus, a suboptimal procedure called differential bit-plane coding (DBPC) is investigated. This is easily implemented, even for a large number of quantization levels, and is reasonably efficient. View full abstract»

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  • A note on the variance of polarity-coincidence correlation with an arbitrary covariance matrix (Corresp.)

    Page(s): 756 - 758
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    Polarity-coincidence correlation (PCC) is usually analyzed under the assumption of independent noise inputs and small input-signal power. Thus, the difficulty of evaluating the variance of the PCC statistics for inputs with arbitrary cross correlations is avoided. Recently, a series expansion method was considered to obtain a variance expression for a strong Markovian signal that is added to two independent white-noise inputs and for a small Markovian signal added to two dependent Markovian noise inputs. The series expansion method converges slowly and requires six joint summations with infinite limits, so that some alternative approach is desirable. Our objective is to compute the variance of the PCC statistic by an alternative method for the above mentioned examples. View full abstract»

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  • Generalizations of the Korzhik bound (Corresp.)

    Page(s): 771 - 773
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    The probability of undetected error is studied when a code is used both for error correction and error detection. A number of generalizations is given of an upper bound of Korzhik on the minimal probability of undetected error for an(n, k)code. 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.

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Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering