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»

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 2/sup m+1/-ary phase-shift keying (PSK) is considered. The expanded signal-set is given the structure of a finite field. The code ... 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»

A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-... View full abstract»

Let R(r,m) be the rth-order Reed-Muller code of length 2/sup m/ and let rho (r,m) be its covering radius. R View full abstract»

A communication channel consisting of several subchannels transmitting simultaneously and asynchronously is considered, an example being a board with several chips, where the subchannels are wires connecting the chips and differences in the lengths of the wires can result in asynchronous reception. A scheme that allows transmission without an acknowledgment of the message, therefore permitting pip... 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 p/sub ij/ of data values with i leading and j trailing zeros, is proposed. The entropy of this source mo... View full abstract»

Deterministic prediction in progressive coding of images is investigated. Progressive coding first creates a sequence of resolution layers by beginning with an original image and reducing its resolution several times by factors of some natural number M. The resultant layers are losslessly encoded, beginning with the lowest-resolution layer and, then encoding each higher resolution image incrementa... 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»

A coded automatic repeat request (ARQ) scheme based on a generalized Viterbi decoding algorithm is proposed. The scheme utilizes the error propagation, which is commonly observed in reduced-complexity decoding, as a means of error detection. It is shown that a small undetectable error probability is obtained with a small retransmission probability for a discrete memoryless channel, contrary to the... 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»

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»

A family of queues is studied for which the service time B/sub n/ of customer n and the interarrival time I/sub n/ between customers n-1 and n exhibit some sort of proportionality. The focus is on dependencies that arise naturally in the context of communication systems, where the finite speed of the communication links constrains the amount of data that can be received in a given time interval. T... View full abstract»

Consider N parallel queues competing for the attention of a single server. At each time slot each queue may be connected to the server or not depending on the value of a binary random variable, the connectivity variable. Allocation at each slot; is based on the connectivity information and on the lengths of the connected queues only. At the end of each slot, service may be completed with a given f... View full abstract»

A new mathematical method in coding theory that is applicable to various practical problems in communication systems is introduced. The uniform switching system based on k-sets is defined, and its cardinalities, an index system, and error correctabilities are studied. The cardinalities of a uniform switching system based on general families of switching sets are discussed. The asymptotic cardinali... 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»

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 expected redundancy per symbol of an n-block prefix code C/sub n/ on a source mu 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 restriction on the class of processes is necessary in... 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»

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»

A class of discrete-time quasi-reversible nodes called monotone, which includes discrete-time analogs of the ./M/ infinity 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 relati... 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 convolutional code. Erroneous ... 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»

The following coin tossing game is analyzed: a store of N fair coins is given and it is desired to achieve M heads in a round of tosses of the coins. To allow for unfavorable sequences of tails, restarts are permitted at any epoch in the game where, in any restart, all coins are returned to store and tosses are begun anew from tabula rasa. A restart strategy is a prescription that specifies when a... View full abstract»

The problem of extracting one out of a finite number of possible signals of known form given observations in an additive noise model is considered. Two approaches are studied: either the signal with shortest distance to the observed data or the signal having maximal correlation with some transformation of the observed data is chosen. With a weak signal approach, the limiting error probability is a... View full abstract»