Performance of Sigma–Delta Quantizations in Finite Frames

Abdelkefi, Fatma

doi:10.1109/tit.2008.929942

Cited by 14 publications

(20 citation statements)

References 39 publications

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“…The fact that using the CGU frame representation can be virtually seen as a RS code leads to a reduced transmitter complexity (since no explicit coder is requested) and robust transmission. Based on the obtained in [5]- [8], [14] could be re-iterated in the case of system based on CGU frame to correct impulsive noise. Furthermore, the signal reconstruction at the receiver gets improved by using a RS decoding scheme.…”

Section: Discussionmentioning

confidence: 99%

“…In a previous work [5], we showed that harmonic frames in R M or C M belong to the CGU frame class. Note that harmonic frame when is defined in C M , can be seen as a DFT code (i.e., the redundant symbols are consecutive).…”

Section: Introductionmentioning

confidence: 87%

“…In this paper, we show that once we use the relationship between some frames and a channel code such as Reed-Solomon (RS) code, we can easily use the results of [5], [8] in order to correct errors occurring over erasure channels where we insight that the redundancy introduced by the frame representation can be exploited such a side information in terms of an implicit coding scheme rather than considering further coder. Many coding techniques exist in the literatures but in this paper we propose to consider a class of finite-dimensional frames with strong symmetry properties, namely the Geometrically Uniform (GU) frames and we show that this class of frame includes the Reed-Solomon (RS) codes.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we consider a more general framework where these redundant symbols can be not consecutive and the considered frame can be not tight contrary to harmonic frame (i.e., DFT codes). It follows that the techniques used in [5], [8] can be used to correct quantization or roundoff errors. The crucial idea of this work is the following: as the CGU frame can be seen as an RS coder then RS can be exploited to establish some specific errors canceler rather than using any further channel coder.…”

Section: Introductionmentioning

confidence: 99%

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Impulsive Noise Correction in Systems Based on CGU Frames

Abdelkefi¹

2010

2010 Sixth Advanced International Conference on Telecommunications

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In this paper, we highlight that when the overcomplete signal representation is based on a class of frames, called Cyclic Geometrically Uniform (CGU) finite frames, family of frames containing finite harmonic frames (both in R M and C M ), this representation becomes equivalent to a Reed-Solomon (RS) coding scheme. Hence, the main benefit obtained from the relationship between the CGU frame and RS code, consists on canceling the errors introduced by the transmission channel. This obviously leads to a quasiperfect reconstructed signal and a robust and low complexity transmission. Simulation results are presented to confirm our claims.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Impulsive Noise Correction in Systems Based on CGU Frames

Abdelkefi¹

2010

2010 Sixth Advanced International Conference on Telecommunications

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“…In [3], constraints on the quantized coefficients were set to satisfy consistent reconstruction conditions that was shown to achieve O(1/r 2 ) performance, where r denotes the logarithm of the frame oversampling factor. Noise shaping of the quantization noise, that mimics sigma-delta converters [8], is used in [5] and [6]. In [5], the quantization noise at time τ is projected onto the following sample in an approximation to first-order sigma-delta converters.…”

Section: Introductionmentioning

confidence: 99%

Turbo quantization of frames

Mansour

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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We describe an iterative algorithm for quantizing overcomplete frames that achieves more than 18 dB/Octave improvement in the reconstruction error due to quantization. It starts with the trellis quantization path then successively refines the estimation with monotonically improving quantization through turbo iterations. We call the procedure turbo quantization because it resembles turbo coding in the error control coding literature.

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Matrix Factorization and Lifting

Jørgensen

Song

2010

STSIP

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As a result recent interdisciplinary work, the processing of signals (audio, still-images, etc), a number of powerful matrix operations have led to advances both in engineering applications, and in mathematics. Much of it is motivated by ideas from wavelet algorithms. The applications are convincing measured against other processing tools already available, for example better compression (details below). We develop a versatile theory of factorization for matrix functions. By a matrix valued function we mean a function of one or more complex variables taking values in the group GL(n, C) of invertible n by n matrices. Starting with this generality, there is a variety of special cases, also of interest, for example, one variable, or restriction to the case n = 2; or consideration of subgroups of GL(n, C); or SL(n, C), i.e., specializing to the case of determinant equal to one. We will prove a number of factorization theorems and sketch their application to signal (image processing) in the framework of multiple frequency bands.

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Performance of Sigma–Delta Quantizations in Finite Frames

Cited by 14 publications

References 39 publications

Impulsive Noise Correction in Systems Based on CGU Frames

Impulsive Noise Correction in Systems Based on CGU Frames

Turbo quantization of frames

Matrix Factorization and Lifting

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