A signal constellation for wireline or wireless multi-carrier communication systems, such as systems using OFDM or MC-CDMA, has points separated from one another by maximizing a distance between conditional probability distributions, such as a Kullbeck-Leibler (KL) distance. Preferably, the constellation points are arranged in concentric circles, with or without a point at the origin, wherein adjacent circles are rotated to maximize an angular distance between points on adjacent circles. Pilot symbols inserted in the transmitted signal are used by a receiver to estimate the channel of the multi-carrier system. Different constellations show optimum performance for different signal to noise ratios, and for different numbers of taps used to estimate the channel, especially in a fast fading environment where there may be fewer pilots per OFDM or MC-CDMA symbol than channel taps.

Signal constellations for multi-carrier systems

Methods and apparatus, including computer program products, for compression include decomposing an image into wavelet transform coefficients, applying a first quantizer to the wavelet transform coefficients, and applying a second quantizer to a set of wavelet transform coefficients representing a background of the image. The method can include rounding the wavelet transform coefficients and rounding the wavelet transform coefficients can include rounding to a nearest integer value. The method can include multiplying the set rounded quantized background wavelet transform coefficients by the second quantizer and rounding all wavelet transform coefficients. Rounding all wavelet transform coefficients can include rounding to a nearest integer value.

Image region of interest encoding

A multi-level space time signal constellation that is optimized for use with a multi-carrier, multi-path communication scheme includes points on a first level separated from points on a mutually exclusive second level by a minimum distance that is based on a conditional probability distribution, preferably a Kullback-Leibler (KL) distance. Points within one level may be separated by a Euclidean distance, but spherical levels are rotated relative to one another to maximize a minimum inter-level KL distance. A receiver uses pilot symbols to estimate the channels and two-stage symbol detection, determining in one stage the constellation level and in another stage the point in the level. The receiver calculates a likelihood function based on a conditional distribution which does not reduce to the Euclidean-based nearest-neighbor detector. A single stored constellation may be scaled based on received signal to noise ratio. Each constellation defines n=2M real dimensions, wherein M is the number of transmit antennas.

Multiple-antenna partially coherent constellations for multi-carrier systems

We consider the problem of digital communication in a Rayleigh flat fading environment using a multiple antenna system. We assume that the transmitter doesn't know the channel coefficients, and that the receiver has only an estimate of them. We further assume that the transmitter and receiver know the statistics of the estimation error. We will refer to this system as a partially coherent system. In an earlier work, we had derived a design criterion for the partially coherent constellations based on maximizing the minimum KL distance between conditional distributions. We had also designed single transmit antenna constellations using this criterion, which showed substantial improvement in the performance over existing and widely-used constellations. In this work, using the KL-based design criterion, we design partially coherent constellations for multiple antenna systems, and evaluate their performance through simulation. We show that, even with only a few percent channel estimation error, the new constellations achieve significant performance gains over the conventional constellations and existing multiple antenna techniques. The proposed constellations are multi-level, with multi-dimensional spherical constellations at each level. We also propose a recursive construction for the constituent spherical subsets of the multiple-antenna partially coherent constellations.

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Partially coherent constellations for multiple-antenna systems

A method and apparatus is disclosed herein for geometrical image representation and/or compression. In one embodiment, the method comprises creating a representation for image data that includes determining a geometric flow for image data and performing an image processing operation on data in the representation using the geometric flow.

Geometrical image representation and compression

The invention concerns a method for compressing data, in particular images, by transform, in which method this data is projected onto a base of localized orthogonal or biorthogonal functions, such as wavelets To quantize each of the localized functions with a quantization step that enables an overall set rate Rc to be satisfied, the method includes the following steps: a probability density model of coefficients in the form of a generalized Gaussian is associated with each subband, the parameters α and β of this density model are estimated, while minimizing the relative entropy, or Kullback-Leibler distance, between this model and the empirical distribution of coefficients of each subband, and from this model, for each subband, an optimum quantization step is determined such that the rate allocated is distributed in the various subbands and such that the total distortion is minimal As a preference, for each subband, the graphs of rate R and distortion D are deduced, from the parameters α and β, as a function of the quantization step and these graphs are tabulated to determine said optimum quantization step

Method for compressing digital images

The method involves transforming digital image data into coefficients of wavelet distributed in sub-bands. A pair of prediction parameters is estimated for each coefficient of each image sub-band according to the wavelet coefficients values. The predictions are associated to the directions north-west and west-east respectively. The wavelet coefficients are quantized and the quantized coefficients are entropy coded. An independent claim is also included for a digital image data compressor.

Contextual compression of digital images

The invention concerns a device (D) for compressing digital image data by wavelet transform. Said device (D) comprises processing means (PM) provided with i) a module (M1) for transforming digital image data into wavelet coefficients distributed in sub-bands, ii) a module (M2) for estimating for each coefficient of each sub-band of the image, first and second sets of prediction parameters, associated respectively with so-called north-south and west-east directions, based on the values of wavelet coefficients of its north or south neighbours, iii) a module (M3) for quantifying the wavelet coefficients, and iv) an entropy coding module (M4) for determining for each coefficient of each sub-band of the image prediction values of expectation and of the width of a Laplace function representing its probability density, based on said first and/or second sets of prediction parameters and on the wavelet coefficient quantified by its north neighbour or its west neighbour, and for entropy coding of the wavelet coefficients quantified by means of specific associated expectations and widths.

Digital image context compression

Compression contextuelle d'images numeriques

L'invention conceme un procede de compression de donnees par transformee, notamment d'images, dans lequel ces donnees sont projetees sur une base de fonctions localisees orthogonales ou bi-orthogonales, telles que des ondelettes. Pour quantifier chacune des fonctions localisees avec un pas de quantification permettant de respecter un debit Rc de consigne globale, le procede comprend les etapes suivantes : on associe a chaque sous-bande un modele de densite de probabilite des coefficients sous la forme d'une gaussienne generalisee, on estime les parametres α et β de ce modele de densite en minimisant l'entropie relative, ou distance de Kullback-Leibler, entre ce modele et la distribution empirique des coefficients de chaque sous-bande, et a partir de ce modele, on determine, pour chaque sous-bande, un pas de quantification optimal tel que le debit alloue soit reparti dans les differentes sous-bandes et tel que la distorsion totale soit minimale. De preference, pour chaque sous-bande, a partir des parametres α et β on deduit les courbes de debit R et de distorsion D en fonction du pas de quantification et on tabule ces courbes pour determiner ledit pas de quantification optimal.

Christophe Bernard

Papers

Method for compressing digital images

Contextual compression of digital images

Digital image context compression

Compression contextuelle d'images numeriques

Procede de compression d'images numeriques