waashk/dblp huggingface dataset:
new results on multiple descriptions in the wyner-ziv setting. some new results of multiple descriptions in the wyner-ziv setting (mdwz) are presented. mdwz uses two pieces of side information (si) for two different side decoders. both si are available to the central decoder, but none to the encoder. the complete achievable region for a quadratic gaussian mdwz system is derived. this result is an extension of ozarow's result on multiple descriptions of a gaussian source without si and diggavi-vaishampayan's result on common si. it is shown that a refinement layer for the central decoder is indispensable if the central distortion is sufficiently small. the tight rate distortion region is also given if one of the side decoders is required to perfectly reconstruct a deterministic function of the source.
approximation of the two-part mdl code. approximation of the optimal two-part minimum description length (mdl) code for given data, through successive monotonically length-decreasing two-part mdl codes, has the following properties: i) computation of each step may take arbitrarily long; ii) we may not know when we reach the optimum, or whether we will reach the optimum at all; iii) the sequence of models generated may not monotonically improve the goodness of fit; but iv) the model associated with the optimum has (almost) the best goodness of fit. to express the practically interesting goodness of fit of individual models for individual data sets we have to rely on kolmogorov complexity.
an elementary condition for non-norm elements. cyclic division algebra (cda) has recently become a major technique to construct space-time block codes with nonvanishing determinant (nvd). one of the key steps in this technique is the determination of non-norm elements and a sufficient condition for the determination has been given by kiran and rajan lately based on algebraic number theory. in this paper, based on kiran and rajan's condition, we present a more elementary condition for non-norm elements when signals are qam or hex, which is easier to check. with this elementary condition, non-norm elements with smaller absolute values than the existing ones can be found.
representation and compression of multidimensional piecewise functions using surflets. we study the representation, approximation, and compression of functions in m dimensions that consist of constant or smooth regions separated by smooth (m - 1)-dimensional discontinuities. examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. for both function classes, we derive the optimal asymptotic approximation and compression rates based on kolmogorov metric entropy. for piecewise constant functions, we develop a multiresolution predictive coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our coder has near-optimal rate-distortion performance. our coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of m-dimensional piecewise constant atoms containing polynomial discontinuities. our coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. both of these schemes achieve the optimal asymptotic approximation performance. key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. we also extend our results to the corresponding discrete function spaces for sampled data. we provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. for approximation of discrete data, we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. simulation results on synthetic signals provide a comparison between surflet-based coders and previously studied approximation schemes based on wedgelets and wavelets.
analysis of optimal high resolution and fixed rate scalar quantization. in 2001, hui and neuhoff proposed a uniform quantizer with overload for the quantization of scalar signals and derived the asymptotically optimal size of the quantization bins in the high-bitrate limit. the purpose of the present paper is to prove a quantitatively more precise version of this result which, at the same time, is valid for a more general, quite natural class of probability distributions that requires only little regularity and includes, for instance, positive lipschitz-continuous functions of unit integral.
hybrid digital-analog relaying for cooperative transmission over slow fading channels. hybrid digital-analog coding schemes have been proposed in source-channel coding to increase the robustness toward channel mismatch, in the absence of transmitter channel state information (csit). recognizing that the same kind of robustness is needed at the relay in a three-node relay network, we propose several novel relaying protocols based on hybrid digital-analog transmission. we compare the performance of the new schemes with traditional digital-only (decode-and-forward or compress-and-forward) or analog-only (amplify-and-forward) relaying, as well as to performance bounds corresponding to genie-aided compress-and-forward relaying. our new protocols achieve significant gains in terms of achievable expected rates, and they are able to close in on the performance bounds. in particular, we conclude that the best overall performance is obtained by an adaptive combination of decode-and-forward and hybrid digital-analog relaying.
sampling and ergodic theorems for weakly almost periodic signals. the theory of abstract harmonic analysis on commutative groups is used to prove sampling and ergodic theorems concerning a particular class of finite-power signals, which are known as weakly almost periodic. the analysis brings to light some noteworthy differences between finite-energy and finite-power signal sampling. it is shown that the bandwidth of the fourier transform of a weakly almost periodic signal is generally larger than the bandwidth of the power spectrum of the signal. consequently, the signal power spectrum by itself does not generally provide enough information to determine the value of the time-domain nyquist rate, that is, the minimum sampling rate necessary for exact signal reconstruction in the time-domain. on the other hand, it is also shown that the minimum sampling rate needed to obtain alias-free spectral estimates is determined by the bandwidth of the power spectrum and, consequently, may be lower than the time-domain nyquist rate. finally, the sampling and ergodic theorems established in this paper are used in an analysis of averaged periodogram estimates of the power spectrum of a weakly almost periodic signal. it is shown that the value of the time shift between consecutive windows may contribute to the asymptotic bias of the estimates.
testing for image symmetries - with application to confocal microscopy. statistical tests are introduced for checking whether an image function f (x, y) defined on the unit disc d = {(x, y) : x2 + y2 ≤ 1} is invariant under certain symmetry transformations of d, given that discrete and noisy data are observed. invariance under reflections or under rotations by rational angles is considered, as well as rotational invariance. these symmetry relations can be naturally expressed as restrictions for the zernike moments of f (x, y). therefore, the test statistics are based on the l2 distance between zernike series estimates of the image function itself and its version obtained after applying the symmetry transformation. the asymptotic distribution of the test statistics under both the hypothesis of symmetry as well as under fixed alternatives is derived. furthermore, the quality of the asymptotic approximations via simulation studies is investigated. the usefulness of our theory is verified by examining an important problem in confocal microscopy, i.e., possible imprecise alignments in the optical path of the microscope are investigated. for optical systems with rotational symmetry, the theoretical point-spread function (psf) is reflection symmetric with respect to two orthogonal axes, and rotationally invariant if the detector plane matches the optical plane of the microscope. the tests are used to investigate whether the required symmetries can indeed be detected in the empirical psf.
a two-stage capacity-achieving demodulation/decoding method for random matrix channels. iterative processing for linear matrix channels, aka turbo equalization, turbo demodulation, or turbo code-division multiple access (cdma), has traditionally been addressed as the concatenation of conventional error control codes with the linear (matrix) channel. however, in several situations, such as cdma, multiple-input-multiple-output (mimo) channels, orthogonal frequency-division multiplexing (ofdm), and intersymbol-interference (isi) channels, the channel itself either contains inherent signal redundancy or such redundancy can readily be introduced at the transmitter. for such systems, iterative demodulation of the linear channel exploiting this redundancy using simple iterative cancellation demodulators, followed by conventional feedforward error control decoding, provides a low-complexity, but extremely efficient decoding alternative. this two-stage demodulator/decoder outperforms more complex turbo cdma methods for equal power modes (users). furthermore, it is shown that arbitrary numbers of modes can be supported if an unequal power distribution is adopted. these power distributions are nested, which means that additional modes can be added without disturbing an existing mode population. the main result shows that these nested power distributions enable the two-stage receiver to approach the shannon capacity of the channel to within less than one bit for any signal-to-noise ratio (snr).
relations between random coding exponents and the statistical physics of random codes. the partition function pertaining to finite-temperature decoding of a (typical) randomly chosen code is known to have three types of behavior, corresponding to three phases in the plane of rate versus temperature: the ferromagnetic phase, corresponding to correct decoding, the paramagnetic phase, of complete disorder, which is dominated by exponentially many incorrect codewords, and the glassy phase (or the condensed phase), where the system is frozen at minimum energy and dominated by subexponentially many incorrect codewords.we show that the statistical physics associated with the two latter phases are intimately related to random coding exponents. in particular, the exponent associated with the probability of correct decoding at rates above capacity is directly related to the free energy in the glassy phase, and the exponent associated with probability of error (the error exponent) at rates below capacity, is strongly related to the free energy in the paramagnetic phase. in fact, we derive alternative expressions of these exponents in terms of the corresponding free energies, and make an attempt to obtain some insights from these expressions. finally, as a side result, we also compare the phase diagram associated with a simple finite-temperature universal decoder, for discrete memoryless channels, to that of the finite-temperature decoder that is aware of the channel statistics.
space-time codes from structured lattices. we present constructions of space-time (st) codes based on lattice coset coding. first, we focus on st code constructions for the short block-length case, i.e., when the block length is equal to or slightly larger than the number of transmit antennas. we present constructions based on dense lattice packings and nested lattice (voronoi) shaping. our codes achieve the optimal diversity-multiplexing tradeoff (dmt) of quasi-static multiple-input multiple-output (mimo) fading channels for any fading statistics, and perform very well also at practical, moderate values of signal-to-noise ratios (snr). then, we extend the construction to the case of large block lengths, by using trellis coset coding. we provide constructions of trellis coded modulation (tcm) schemes that are endowed with good packing and shaping properties. both short-block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean-squared error generalized decision feedback equalizer (mmse-gdfe) lattice decoding and a combination of this with a viterbi tcm decoder for the tcm case. beyond the interesting algebraic structure, we exhibit codes whose performance is among the state-of-the art considering codes with similar encoding/decoding complexity.
bat chirps with good properties: zak space construction of perfect polyphase sequences. previously, a discretization of the linear fm chirp of length n = kl2, l and kl ∈ z, was given and the conditions for its minimal zak space support were derived. chirps satisfying these conditions are known as finite chirps. in this work, subsets of finite chirps of length n = l2, l a prime, are examined. the investigation leads to a new, zak space construction of general polyphase sequence sets of size l - 1 with optimal auto and cross-correlation properties, known as perfect sequence sets. it is shown that perfect sequence sets are closely related to sets of finite chirps and, in particular, include the sets of zadoff-chu sequences (which are identical with subsets of finite chirps) and the sets of generalized frank sequences (which are identical with sets of modulations of finite chirps), as special cases. the entire collection of perfect sequence sets is then given by a partition of the set of perfect auto correlation sequences, obtained by right coset decomposition of the group of all permutations with respect to a certain cyclic group. the construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group.
large system spectral analysis of covariance matrix estimation. eigendecomposition of estimated covariance matrices is a basic signal processing technique arising in a number of applications, including direction-of-arrival estimation, power allocation in multiple-input/multiple-output (mimo) transmission systems, and adaptive multiuser detection. this paper uses the theory of non-crossing partitions to develop explicit asymptotic expressions for the moments of the eigenvalues of estimated covariance matrices, in the large system asymptote as the vector dimension and the dimension of signal space both increase without bound, while their ratio remains finite and nonzero. the asymptotic eigenvalue distribution is also obtained from these eigenvalue moments and the stieltjes transform, and is extended to first-order approximation in the large sample-size limit. numerical simulations are used to demonstrate that these asymptotic results provide good approximations for finite systems of moderate size.
markov random processes are neither bandlimited nor recoverable from samples or after quantization. this paper considers basic questions regarding markov random processes. it shows that continuous-time, continuous-valued, wide-sense stationary, markov processes that have absolutely continuous second-order distribution and finite second moment are not bandlimited. it also shows that continuous-time, stationary, markov processes that are continuous-valued or discrete-valued and satisfy additional mild conditions cannot be recovered from uniform sampling. further it shows that continuous-time, continuous-valued, stationary, markov processes that have absolutely continuous second-order distributions and are continuous almost surely, cannot be recovered without error after quantization. finally, it provides necessary and sufficient conditions for stationary, discrete-time, markov processes to have zero entropy rate, and relates this to information singularity.
further results on the optimality of the likelihood-ratio test for local sensor decision rules in the presence of nonideal channels. in this paper, we consider the design of local decision rules for distributed detection systems where decisions from peripheral detectors are transmitted over dependent nonideal channels. under the conditional independence assumption among multiple sensor observations, we show that the optimal detection performance can be achieved by employing likelihood-ratio quantizers (lrq) as local decision rules under both the bayesian criterion and neyman-pearson (np) criterion even for the cases where the channels between the fusion center and local sensors are dependent and noisy. this work generalizes the previous work where independence among such channels was assumed. a person-by-person optimization (pbpo) procedure to obtain the solution is presented along with an illustrative example.
capacity of cognitive interference channels with and without secrecy. like the conventional two-user interference channel, the cognitive interference channel consists of two transmitters whose signals interfere at two receivers. it is assumed that there is a common message (message 1) known to both transmitters, and an additional independent message (message 2) known only to the cognitive transmitter (transmitter 2). the cognitive receiver (receiver 2) needs to decode messages 1 and 2, while the noncognitive receiver (receiver 1) should decode only message 1. furthermore, message 2 is assumed to be a confidential message which needs to be kept as secret as possible from receiver 1, which is viewed as an eavesdropper with regard to message 2. the level of secrecy is measured by the equivocation rate. in this paper, a single-letter expression for the capacity-equivocation region of the discrete memoryless cognitive interference channel is obtained. the capacity-equivocation region for the gaussian cognitive interference channel is also obtained explicitly. moreover, particularizing the capacity-equivocation region to the case without a secrecy constraint, the capacity region for the two-user cognitive interference channel is obtained, by providing a converse theorem.
quaternary constant-amplitude codes for multicode cdma. a constant-amplitude code is a code that reduces the peak-to-average power ratio (papr) in multicode code-division multiple access (mc-cdma) systems to the favorable value 1. in this paper, quaternary constant-amplitude codes (codes over z4) of length 2m with error-correction capabilities are studied. these codes exist for every positive integer m, while binary constant-amplitude codes cannot exist if m is odd. every word of such a code corresponds to a function from the binary m-tuples to z4 having the bent property, i.e., its fourier transform has magnitudes 2m/2. several constructions of such functions are presented, which are exploited in connection with algebraic codes over z4 (in particular quaternary reed-muller, kerdock, and delsarte-goethals codes) to construct families of quaternary constant-amplitude codes. mappings from binary to quaternary constant-amplitude codes are presented as well.
multigroup decodable stbcs from clifford algebras. a space-time block code (stbc) in k symbols (variables) is called a g-group decodable stbc if its maximum-likelihood (ml) decoding metric can be written as a sum of g terms, for some positive integer g greater than one, such that each term is a function of a subset of the k variables and each variable appears in only one term. in this paper, we provide a general structure of the weight matrices of multigroup decodable codes using clifford algebras. without assuming that the number of variables in each group is the same, a method of explicitly constructing the weight matrices of full-diversity, delay-optimal multigroup decodable codes is presented for arbitrary number of antennas. for the special case of 2a number of transmit antennas, we construct two subclass of2a codes: 1) a class of 2a-group decodable codes with rate a/2(a-1), which is, equivalently, a class of single-symbol decodable codes, and 2) a class of (2a-2) -group decodable codes with rate (a-1)/2(a-2), i.e., a class of double-symbol decodable codes.
codeword stabilized quantum codes. we present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. we use this framework to generate new codes with superior parameters to any previously known. in particular, we find ((10,18,3)) and ((10,20,3)) codes. we also show how to construct encoding circuits for all codes within our framework.
universal estimation of erasure entropy. erasure entropy rate differs from shannon's entropy rate in that the conditioning occurs with respect to both the past and the future, as opposed to only the past (or the future). in this paper, consistent universal algorithms for estimating erasure entropy rate are proposed based on the basic and extended context-tree weighting (ctw) algorithms. simulation results for those algorithms applied to markov sources, tree sources, and english texts are compared to those obtained by fixed-order plug-in estimators with different orders.
on the existence of (10, 2, 7, 488) resilient functions. using a heuristic search combined with some algebraic techniques, several examples for 10-variable boolean functions with nonlinearity 488, algebraic degree 7, and resiliency degree 2, were constructed. this construction affirmatively answers the open problem about the existence of such functions.
bounds and constructions of optimal (n, 4, 2, 1) optical orthogonal codes. in this paper, a tight upper bound on the maximum possible code size of (n 4, 2, 1,)-oocs and some direct and recursive constructions of optimal (n 4, 2, 1,)-oocs attaining the upper bound are given. as consequences, the following new infinite series of optimal (gn 4, 2, 1,)-oocs are obtained: i) g ∈ {1, 7, 11, 19, 23, 31, 35, 59, 71, 79, 131, 179, 191, 239, 251, 271, 311, 359, 379, 419, 431, 439, 479, 491, 499, 571, 599, 631, 659, 719, 739, 751, 839, 971} or g is a prime > 1000 and ≡ 5 (mod 8), and n = 9h 25i 49j p1 p2...pr where h ∈ {0, 1}, i and j are arbitrary nonnegative integers, and each pi is a prime ≡ 1 (mod 8); ii) g = 2g′ where g′ ∈ {1, 7, 11, 19, 23, 31, 47, 71, 127, 151, 167, 191, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 503, 631, 647, 719, 727, 743, 823, 839, 863, 887, 911, 919, 967, 983, 991} and n = p1 p2...pr where each pi is a prime ≡ 1 (mod 4); iii) g ∈ {4, 20} and n is any positive integer prime to 30; iv) g = 8 and n = p1 p2...pr where each pi is a prime ≡ 1 (mod 4) greater than 5.
the effect of noise correlation in amplify-and-forward relay networks. in wireless relay networks, noise at the relays can be correlated possibly due to common interference or noise propagation from preceding hops. a parallel relay network with noise correlation is considered in this network. for the relay strategy of amplify and forward (af), the optimal rate maximizing relay gains when correlation knowledge is available at the relays are determined. interestingly, it is shown that, on average, noise correlation is beneficial regardless of whether the relays know the noise covariance matrix. however, the knowledge of correlation can greatly improve the performance. typically, the performance improvement from correlation knowledge increases with the relay power and the number of relays. with perfect correlation knowledge the system capable of canceling interference if the number of interferers is less than the number of relays. for a two-hop multiple-access parallel network, closed-form expressions for the maximum sum rate and the optimal relay strategy are determined. relay optimization for networks with three hops is also considered. based on the result of two-hop network with noise correlation, an iterative algorithm proposed for solving the relay optimization problem for three-hop networks.