IEEE Transactions on Information Theory

Trellis coding using multidimensional quadrature amplitude modulation (QAM) signal sets is investigated. Finite-size 2D signal sets are presented that have minimum average energy, are 90 degrees rotationally symmetric, and have from 16 to 1024 points. The best trellis codes using the finite 16-QAM signal set with two, four, six, and eight dimensions are found by computer search (the multidimension... View full abstract»

A method is presented for protecting the overall realization of digital filters implemented with very dense high-speed electronic devices against both hard and soft errors at the data sample level using the error-detecting properties of real convolutional codes. The normal filter system is surrounded with parallel parity channels defined by a real systematic rate k/n convolutiona... View full abstract»

A class of discrete-time quasi-reversible nodes called monotone, which includes discrete-time analogs of the ./M/∞ and ./M/1 nodes, is considered. For stationary ergodic nonnegative integer valued arrival processes, the existence and uniqueness of stationary regimes are proven when a natural rate condition is met. Coupling is used to prove the contractiveness of the input-output map relative... View full abstract»

BCH decoders based on the Peterson-Gorenstein-Zierler algorithm can malfunction and produce output vectors that are no codewords. To avoid this malfunction a simple additional check is proposed that can be performed before the computation of the error locations. The additional check consists of the minimum number of algebraic equations in the syndrome components that are necessary over a general f... View full abstract»

A class of random time-series inputs for nonlinear time-invariant systems that permit the analytical specification of a set of operators on the input that are orthonormal over all time to the Volterra operators for all orders and all lag sets is introduced. The time series in this class are cyclostationary and complex valued. The orthonormal operators are used to obtain an input-output type of cro... View full abstract»

The effect of feedback on the performance of a distributed Neyman-Pearson detection system consisting of n sensors, two-stage local quantizers, and a global detector is investigated. Two feedback schemes are discussed, only one of which yields an asymptotic gain in performance, as measured by an appropriate error exponent View full abstract»

There are two approaches to the identification of noncausal autoregressive systems in two dimensions differing in the assumed noise model. For both approaches, the maximum likelihood estimator formulated in the frequency domain is presented. The Fisher information matrix is evaluated and found to be the sum of a block-Toeplitz and a block-Hankel matrix. The variance of the parameters, however, can... View full abstract»

Channel codes where the redundancy is obtained not from parity symbols, but from expanding the channel signal-set, are addressed. They were initially proposed by G. Ungerboeck (1982) using a convolutional code. Here, a block coding approach is given. Rate m/(m+1) coded 2m+1-ary phase-shift keying (PSK) is considered. The expanded signal-set is given the structure of a ... View full abstract»

Hypothesis testing for two Markov chains is considered. Under the constraint that the error probability of the first kind is less than or equal to exp(-rn), the error probability of the second kind is minimized. The geodesic that connects the two Markov chains is defined. By analyzing the geodesic, the power exponents are calculated and then represented in terms of Kullback-Leibler diverg... View full abstract»

The expected redundancy per symbol of an n-block prefix code Cn on a source μ measures how far the code is from being optimal for that source. The existence of sequences of codes with expected redundancy per symbol of O((log n)/n) for `nice' classes of sources, such as Markov sources of a given order, is well known. It is shown that some restrictio... View full abstract»

Difference bases are discussed and their relevance to sensor arrays is described. Several new analytical difference base structures that result in near optimal low-redundancy sensor arrays are introduced. Algorithms are also presented for efficiently obtaining sparse sensor arrays and/or difference bases. New bounds, related to arrays that have both redundancies and holes in their coarray, are pre... View full abstract»

Distributed algorithms for finding two disjoint paths of minimum total length from each node to a destination are presented. The algorithms have both node-disjoint and link-disjoint versions and provide each node with information sufficient to forward data on the disjoint paths. It is shown that this problem can be reduced to the problem of finding a minimal shortest path from each node to the des... View full abstract»

Simple statistical hypothesis testing is investigated by making use of the divergence geometric method. The asymptotic behavior of the minimum value of the error probability of the second kind under the constraint that the error probability of the first kind is bounded above by exp(-rn) is looked for, where r is a given positive number. If r is greater than the divergenc... View full abstract»

A class of iterative methods for solving the blind deconvolution problem, i.e. for recovering the input of an unknown possibly nonminimum-phase linear system by observation of its output, is presented. These methods are universal do not require prior knowledge of the input distribution, are computationally efficient and statistically stable, and converge to the desired solution regardless of initi... View full abstract»

The asymptotic efficiency of importance sampling (IS) techniques for the simulation of rare events in a multidimensional nonlinear setting was studied by J.S. Sadowsky and J.A. Bucklew (see ibid., vol.36, p.579-88, 1990). Fundamental results on the asymptotic efficiency of the mean-value modification (MM) technique were derived. Additionally, a statement was made that other IS techniques cannot be... View full abstract»

A decentralized sequential detection problem is considered in which each one of a set of sensors receives a sequence of observations about the hypothesis. Each sensor sends a sequence of summary messages to the fusion center where a sequential test is carried out to determine the true hypothesis. A Bayesian framework for this problem is introduced, and for the case when the information structure i... View full abstract»

A new approach toward robust parameter estimation is presented. As opposed to schemes based on classical saddlepoint techniques, the methods apply quite naturally to dependent and/or nonstationary data and also have the advantage of providing a quantitative measure of the degree of robustness offered by a particular estimator. It is shown why censoring observations of large magnitude does indeed i... View full abstract»

There are many ways to find lower bounds for the minimum distance of a cyclic code, based on investigation of the defining set. Some new theorems are derived. These and earlier techniques are applied to find lower bounds for the minimum distance of ternary cyclic codes. Furthermore, the exact minimum distance of ternary cyclic codes of length less than 40 is computed numerically. A table is given ... View full abstract»

The restriction to Gaussian inputs in the limiting expression for the capacity regions of memoryless Gaussian interference and multiple-access channels is shown to fall short of achieving capacity even if the inputs are allowed to be dependent and nonstationary. In addition, the equality between the limiting and the single-letter characterizations of memoryless multiple-access channel capacity is ... View full abstract»

A coding scheme for the channel under peak power and average power constraints on the input is presented, and its asymptotic error exponent is shown to coincide, at all rates below capacity, with the sphere packing error exponent, which, for the case at hand, is known to be unachievable without feedback for rates below the critical rate. An upper bound on the error exponent achievable with feedbac... View full abstract»

Numerical computer data in many applications contain numerous leading and trailing zeros, and this data feature has been neglected in common source models and related data compression methods. A new approach to source modeling, consisting of the description of this data feature by probabilities pij of data values with i leading and j trailing zeros, is propose... View full abstract»

The valid parameter spaces of infinite- and finite-lattice (2-D noncausal) Gaussian Markov random fields (GMRFs) are investigated. For the infinite-lattice fields, the valid parameter space is shown to admit an explicit description; a procedure that yields the valid parameter space is presented. This procedure is applied to the second-order (neighborhood) 2-D GMRFs to obtain an explicit descriptio... View full abstract»

The use of direct sum codebooks to minimize the memory requirements of vector quantizers is investigated. Assuming arbitrary fixed partitions, necessary conditions for minimum distortion codebooks are derived, first for scalar codebooks, assuming mean-squared error distortion, and then for vector codebooks and a broader class of distortion measures. An iterative procedure is described for designin... View full abstract»

Procedures for obtaining primitive polynomials and m-sequences over GF(qm) in terms of primitive polynomials and m-sequences over GF(q) are presented. Using a degree mn primitive polynomial g( x) in GF[g, x], an m-sequence over GF(qm) can be expressed as a vector m-sequ... View full abstract»

Communication over the additive white Gaussian channel, subject to a discrete phase ambiguity at the receiver, is considered. When this phase ambiguity is considered as a discretely distributed random variable, the channel is termed the acoherent additive white Gaussian (AAWG) channel. It is shown that the optimum decoder for the AAWG channel is not practically implementable and a suboptimum decod... View full abstract»