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Information Theory, IEEE Transactions on

Issue 1 • Date Jan 1994

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Displaying Results 1 - 25 of 41
  • Sequential amplitude estimation in multiuser communications

    Page(s): 11 - 20
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (676 KB)  

    Considers the problem of multiuser amplitude estimation, i.e., the problem of estimating the amplitudes of several digital communications signals superimposed in the same channel. This problem is of importance in communications environments such as spread-spectrum radio networks, in which nonorthogonal multiplexing is used. Multiuser amplitude estimation is a critical prerequisite to the optimum demodulation of such signals using, for example, Verdu's algorithm. In the present paper, a sequential detection-estimation approach is applied to this problem, and several estimation paradigms, including the method of moments and likelihood-based estimators, are considered. The consistency, asymptotic variance, and complexity of these estimators are examined. A new method of constructing a recursive consistent and asymptotically efficient estimation algorithm out of a consistent estimator sequence is also suggested and is applied to the current setup. It is seen that detector-estimators that use these estimators in Verdu's algorithm result, asymptotically, in (known-amplitude) optimum error probabilities with little relative increase in complexity per demodulated bit View full abstract»

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  • Some notes on Varn coding

    Page(s): 181 - 186
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    A duality between Varn (1971) coding and Tunstall (1968) coding is demonstrated and new bounds on the expected transmission cost per source symbol for Varn codes are established. For binary channels, the superiority of the new upper bound over Krause's (1962) upper bound is proven View full abstract»

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  • Five new optimal ternary linear codes

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    Optimal ternary linear codes with parameters [29,5,18], [34,5,21], [43,5,27], [61,5,39], and [31,6,18] have been found. Codes with these parameters were not known until now View full abstract»

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  • Minimax robust decentralized detection

    Page(s): 35 - 40
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    Decentralized detection problems are studied where the sensor distributions are not specified completely. The sensor distributions are assumed to belong to known uncertainty classes. It is shown for a broad class of such problems that a set of least favorable distributions exists for minimax robust testing between the hypotheses. It is hence established that the corresponding minimax robust tests are solutions to simple decentralized detection problems for which the sensor distributions are specified to be the least favorable distributions View full abstract»

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  • Codes over Gaussian integers

    Page(s): 207 - 216
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    The author shows how block codes over Gaussian integers can be used for coding over two-dimensional signal space. He introduces a two-dimensional modular distance called the Mannheim distance and proposes using codes designed for this distance. Some simple constructions of such codes are given, among them icyclic codes which belong to the class of constacyclic codes. As a special case icyclic codes include perfect one Mannheim error correcting codes. For most of the codes considered efficient decoders are given and their performance on the Gaussian channel is investigated View full abstract»

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  • Estimation of the autocorrelation function of complex Gaussian stationary processes by amplitude clipped signals

    Page(s): 239 - 245
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (536 KB)  

    The normalized autocorrelation function of a Gaussian process may be recovered from second order moments of their polarity, through the arcsin law. By analogy, it is possible to calculate the normalized autocorrelation function of a circularly complex Gaussian process from the knowledge of moments of its instantaneous phase. In the present paper, two estimators of the normalized autocorrelation function based on the phase only are presented. Their theoretical accuracy is evaluated and compared to the accuracy of the direct estimate View full abstract»

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  • Performance limits for channelized cellular telephone systems

    Page(s): 21 - 34
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    Studies the performance of channel assignment algorithms for “channelized” (e.g., FDMA or TDMA) cellular telephone systems, via mathematical models, each of which is characterized by a pair (H,p), where H is a hypergraph describing the channel reuse restrictions, and p is a probability vector describing the variation of traffic intensity from cell to cell. For a given channel assignment algorithm, the authors define T(r) to be the amount of carried traffic, as a function of the offered traffic, where both r and T(r) are measured in Erlangs per channel. They show that for a given H and p, there exists a function TH,p(r), which can be computed by linear programming, such that for every channel assignment algorithm, T(r)⩽TH,p(r). Moreover, they show that there exist channel assignment algorithms whose performance approaches TH,p (r) arbitrarily closely as the number of channels increases. As a corollary, they show that for a given (H,p) there is a number r0 , which also can be computed by linear programming, such that if the offered traffic exceeds r0, then for any channel assignment algorithm, a positive fraction of all call requests must be blocked, whereas if the offered traffic is less than r0, all call requests can be honored, if the number of channels is sufficiently large. The authors call r0, whose units are Erlangs per channel, the capacity of the cellular system View full abstract»

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  • Arithmetic coding into fixed-length codewords

    Page(s): 219 - 223
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    Arithmetic coding is known to be optimal in compressing strings of independent symbols, the probabilities of which are given. However the method has some disadvantages that the present variant tries to overcome. The idea here is to apply arithmetic coding piecewise, by cutting the process regularly. The result consists of fixed-length sequences of bits, representing variable-length substrings of the source. For implementation reasons, the bit sequences are composed of machine words, allowing one to use basic arithmetic efficiently. The compression gain approaches the optimum when the sequence size is increased View full abstract»

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  • A finite group of complex integers and its application to differentially coherent detection of QAM signals

    Page(s): 216 - 219
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    A finite multiplicative group of complex integers is constructed and its application to differential detection of 16 QAM signals is given. In this group the algebraic properties of regular complex multiplication, such as commutativity, associativity, and conjugation are preserved. The challenge in finding such a group lies in the requirements for the existence of multiplicative inverses for numbers that have magnitudes different from 1, and for maintaining associativity. The group properties are used to demodulate 16 QAM signals in a differentially coherent way View full abstract»

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  • Design of entropy-constrained multiple-description scalar quantizers

    Page(s): 245 - 250
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    The problem of entropy-constrained multiple-description scalar quantizer design is posed as an optimization problem, necessary conditions for optimality are derived, and an iterative design algorithm is presented. Performance results are presented for a Gaussian source, along with comparisons to the multiple-description rate distortion bound and a reference system View full abstract»

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  • A performance comparison of the binary quadratic residue codes with the 1/2-rate convolutional codes

    Page(s): 126 - 136
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    The 1/2-rate binary quadratic residue (QR) codes, using binary phase-shift keyed (BPSK) modulation and hard decoding, are presented as an efficient system for reliable communication. Performance results of error correction are obtained both theoretically and by means of computer calculations for a number of binary QR codes. These results are compared with the commonly used 1/2-rate convolutional codes with constraint lengths from 3 to 7 for the hard-decision case. The binary QR codes of different lengths are shown to be equivalent in error-correction performance to some 1/2-rate convolutional codes, each of which has a constraint length K that corresponds to the error-control rate d/n and the minimum distance d of the QR codes View full abstract»

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  • Fast decoding of codes from algebraic curves

    Page(s): 223 - 229
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    The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error locator polynomial, and also shows that the cost of doing this increases with the dimension of the space. Unfortunately, the error-correcting capability gets worse for codes from curves in higher dimensional spaces. For a specific curve, he determines the error values faster than by solving linear equations. The method is an extension of the transformation method known from cyclic codes View full abstract»

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  • Performance of a general decoding technique over the class of randomly chosen parity check codes

    Page(s): 160 - 166
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    The paper extends a general decoding technique developed by Metzner and Kapturowski (1990) for concatenated code outer codes and for file disagreement location. That work showed the ability to correct most cases of d-2 or fewer erroneous block symbols, where d is the outer code minimum distance. Any parity check code can be used as the basis for the outer codes, and yet decoding complexity increases at most as the third power of the code length. In this correspondence, it is shown that, with a slight modification and no significant increase in complexity, the general decoding technique can be applied to the correction of many other cases beyond the code minimum distance. By considering average performance over all binary randomly chosen codes, it is seen that most error patterns of tM or fewer block errors can be corrected, where: 1) tM in most cases is much greater than the code minimum distance, and 2) asymptotically, the ratio of tM to the theoretical maximum (the number of parity symbol blocks) approaches 1. Moreover, most cases of noncorrectable error block patterns are detected View full abstract»

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  • Successive refinement of information: characterization of the achievable rates

    Page(s): 253 - 259
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (564 KB)  

    Let R(·) be the rate-distortion function. Assume that we want to describe a source with distortion no larger than Δ1 . From the rate-distortion theory we know that we need to do so at a rate R1 no smaller than R(Δ1) [bits/symbol]. If it turns out that a more accurate description at distortion Δ2, Δ21 , is desirable, one can transmit additional information at some rate ΔR. What is the minimal value for ΔR? More generally, which are the achievable (R1, R2) pairs for which, with high probability, one can describe the source at rate R1 and incur distortion not exceeding Δ1 and refine this description at a rate R2-R1 obtaining a final distortion not exceeding Δ2? The achievable region containing those pairs is characterized. An interpretation of Equitz and Cover's Markov condition is given. The Markov condition characterizes those cases for which (R(Δ1), R(Δ2)) is an achievable pair View full abstract»

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  • On maximizing linear system output energy with an input envelope constraint

    Page(s): 251 - 253
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    This correspondence addresses the problem of finding an input signal u that maximizes the output energy of a linear filter subject to the constraint |u|⩽e where e is a specified envelope. The main contribution is to provide a new direct proof of the necessity of a certain fixed point condition. Using the weak* topology on the input signal space, the author also proves certain compactness and continuity properties that further illuminate the nature of the problem View full abstract»

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  • Decomposition constructions for secret-sharing schemes

    Page(s): 118 - 125
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    The paper describes a very powerful decomposition construction for perfect secret-sharing schemes. The author gives several applications of the construction and improves previous results by showing that for any graph G of maximum degree d, there is a perfect secret-sharing scheme for G with information rate 2/(d+1). As a corollary, the maximum information rate of secret-sharing schemes for paths on more than three vertices and for cycles on more than four vertices is shown to be 2/3 View full abstract»

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  • Idempotents and the BCH bound

    Page(s): 204 - 207
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    Using a characterization of the idempotents of a narrow-sense primitive binary BCH code, the authors are able to give classes of such codes whose minimum distance does not exceed the BCH bound. Their results are compiled in a table View full abstract»

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  • Relations between entropy and error probability

    Page(s): 259 - 266
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    The relation between the entropy of a discrete random variable and the minimum attainable probability of error made in guessing its value is examined. While Fano's inequality provides a tight lower bound on the error probability in terms of the entropy, the present authors derive a converse result-a tight upper bound on the minimal error probability in terms of the entropy. Both bounds are sharp, and can draw a relation, as well, between the error probability for the maximum a posteriori (MAP) rule, and the conditional entropy (equivocation), which is a useful uncertainty measure in several applications. Combining this relation and the classical channel coding theorem, the authors present a channel coding theorem for the equivocation which, unlike the channel coding theorem for error probability, is meaningful at all rates. This theorem is proved directly for DMCs, and from this proof it is further concluded that for R⩾C the equivocation achieves its minimal value of R-C at the rate of n1/2 where n is the block length View full abstract»

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  • Locally optimum Bayes detection in ergodic Markov noise

    Page(s): 41 - 55
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    The locally optimum Bayes theory of signal detection in non-Gaussian noise/interference environments is extended to include ergodic Markov noise models under mild regularity assumptions on the conditional probability density functions. The proposed method expresses the log-likelihood ratio under the null hypothesis, via martingale limit theory, as a locally asymptotically normal likelihood ratio, which yields under the implied condition of contiguity the statistics of the detection algorithm under the alternative hypothesis. Thus, optimum detection algorithms in both coherent and incoherent cases are obtained, which are canonical in signal waveform and noise statistics and which have the desired property of asymptotic optimality (acceptably small error probabilities as sample size becomes necessarily large, while the terms in the Taylor expansion of the log-likelihood ratio about the null signal remain fixed). Furthermore, locally optimum detection structures in Gauss-Markov noise are given together with a specific example in the coherent mode of reception in order to demonstrate the significant improvement in performance obtained over independent sampling View full abstract»

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  • Fast and efficient coding of information sources

    Page(s): 96 - 99
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (336 KB)  

    The author considers the problem of source coding and investigates the cases of known and unknown statistics. The efficiency of the compression codes can be estimated by three characteristics: 1) the redundancy (r), defined as the maximal difference between the average codeword length and Shannon entropy in case the letters are generated by a Bernoulli source; 2) the size (in bits) of the encoder and the encoder programs (S) when implemented on a computer; and 3) the average time required for encoding and decoding of a single letter (T). He investigates S and T as a function of r when r→0. All known methods may be divided into two classes. The Ziv-Lempel codes and their variants fall under the first class, and the arithmetic code with the Lynch-Davisson code fall under the second one. The codes from the first class need exponential memory size S=0(exp(1/r)) for redundancy r when r→O. The methods from the second class have a small memory size but a low encoding speed: S=0(1/rconst), T=0(logconst(1/r) log log (1/r)). In this paper, the author presents a code that combines the merits of both classes; the memory size is small and the speed is high: S=0(1/rconst),T=0(log const(1/r) log log (1/r)) View full abstract»

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  • Codes satisfying the chain condition

    Page(s): 175 - 180
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    The authors considered weight hierarchies of codes satisfying the chain condition, they called these chain-good. First, they gave a set of simple necessary conditions for a sequence to be chain-good. They proved that given one chain-good sequence, there is an infinite set of chain-good sequences that can be constructed from this one sequence. Finally, they used this result to completely describe the sets of chain-good sequences of dimensions up to 5 View full abstract»

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  • Geometrically uniform TCM codes over groups based on L×MPSK constellations

    Page(s): 137 - 152
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    The theory of geometrically uniform signal sets and codes over groups is applied to the case of L×MPSK constellations. Conditions for rotational invariance of group codes are discussed. The tables of geometrically uniform partitions found in Benedetto et al. (1993) are used to construct good geometrically uniform trellis codes over nonbinary Abelian groups. The present authors consider L×4PSK and L×8PSK constellations used to transmit information rates of 1 and 2 bit/two dimensions, respectively; and present tables of good codes over generating groups (Z4)L and (Z8)L,for L ranging from 1 to 4. In most cases, they improve the tables of codes known so far. Moreover, the geometrical uniformity of codes allows a very easy performance evaluation, so that the authors also present a complete set of curves of error event probability for the obtained codes View full abstract»

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  • DPCM encoding of regenerative composite processes

    Page(s): 153 - 160
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    Fixed (nonadaptive) and forward adaptive differential pulse code modulation of regenerative composite sources is investigated. In the fixed code, an approximate formula is given for the optimal value of the prediction coefficient. This is then used as an initial guess to optimize the code (predictor and quantizer) through a numerical method. In the forward adaptive scheme, the state of the switch in the composite source is estimated using a MAP sequence estimation algorithm, and the code is then matched to the mode process corresponding to the estimated switch state. The performance of the two systems is evaluated with quantizers of 4, 8, and 16 levels. The results show that the forward adaptive scheme significantly outperforms optimized fixed DPCM in the sense of mean-squared error. Stochastic stability of the code is also established for the fixed DPCM scheme as well as for an adaptive scheme which receives the switch state as side information View full abstract»

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  • The n-dimensional key equation and a decoding application

    Page(s): 200 - 203
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    The author introduce the n-dimensional key equation, which exhibits the error-locator polynomial of an n-dimensional cyclic code as a product of n univariate polynomials and the error-evaluator polynomial as an n-variable polynomial. They then reinterpret these polynomials in the context of linear recurring sequences. In particular, they reduce the decoding problem to successive application of the Berlekamp-Massey algorithm. With this new method, they are able to decode (up to half their minimum distance) many codes in a table of 2-D cyclic codes due to Jensen (1985) View full abstract»

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  • Asymptotic normality of some Hermitian forms with complex noisy data

    Page(s): 236 - 239
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    Hermitian forms with complex random data arise in some areas of physics when one studies the effect of the noise in some frequency interval. In this context, a central-limit theorem is proved for independent Gaussian variables in the complex plane. The non-Gaussian case is also studied and the same result holds provided that the fourth-order moments are bounded 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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Meet Our Editors

Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering