Channel Coding Inspired Contributions to Compressed Sensing

Zorlein, Henning

doi:10.18725/oparu-3247

Cited by 4 publications

(2 citation statements)

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“…The quadratic dependency on m is due to implementation details and can be circumvented. For a reference on execution times, the reader is referred to Table 6.3 of [88], where the method introduced in [20] with approximate integration requires over an hour to construct a BCASC for n = 64 codewords of dimensionality m = 4. Without implementing the approximation the original method took nearly 18 hours for constructing the same BCASC.…”

Section: Methodsmentioning

confidence: 99%

“…An analysis of the original program for generating BCASCs with approximate summation whose performance is evaluated in [20], [88] reveals that the square dependency of the complexity on m is implementation-dependent rather than specific to the algorithm. We observe that an optimization of the code easily reduces the square dependency to a linear dependency, thus yielding complexity O(mn 2 K) per iteration.…”

Section: Methodsmentioning

confidence: 99%

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Fast Approximate Construction of Best Complex Antipodal Spherical Codes

Conde,

Loffeld

2017

Preprint

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Compressive Sensing (CS) theory states that realworld signals can often be recovered from much fewer measurements than those suggested by the Shannon sampling theorem. Nevertheless, recoverability does not only depend on the signal, but also on the measurement scheme. The measurement matrix should behave as close as possible to an isometry for the signals of interest. Therefore the search for optimal CS measurement matrices of size m × n translates into the search for a set of n m-dimensional vectors with minimal coherence. Best Complex Antipodal Spherical Codes (BCASCs) are known to be optimal in terms of coherence. An iterative algorithm for BCASC generation has been recently proposed that tightly approaches the theoretical lower bound on coherence. Unfortunately, the complexity of each iteration depends quadratically on m and n. In this work we propose a modification of the algorithm that allows reducing the quadratic complexity to linear on both m and n. Numerical evaluation showed that the proposed approach does not worsen the coherence of the resulting BCASCs. On the contrary, an improvement was observed for large n. The reduction of the computational complexity paves the way for using the BCASCs as CS measurement matrices in problems with large n. We evaluate the CS performance of the BCASCs for recovering sparse signals. The BCASCs are shown to outperform both complex random matrices and Fourier ensembles as CS measurement matrices, both in terms of coherence and sparse recovery performance, especially for low m/n, which is the case of interest in CS.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Fast Approximate Construction of Best Complex Antipodal Spherical Codes

Conde,

Loffeld

2017

Preprint

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Recursive enhancement of intrinsic soft information for complex reed-solomon codes

Mohamed

Zorlein

Bossert

2016

2016 4th International Workshop on Compressed Sensing Theory and Its Applications to Radar, Sonar and Remote Sensing (CoSeRa)

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An alternative decoding method for Gabidulin codes in characteristic zero

Müelich

Puchinger

Mödinger³

et al. 2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Abstract-Gabidulin codes, originally defined over finite fields, are an important class of rank metric codes with various applications. Recently, their definition was generalized to certain fields of characteristic zero and a Welch-Berlekamp like algorithm with complexity O(n 3 ) was given. We propose a new application of Gabidulin codes over infinite fields: low-rank matrix recovery. Also, an alternative decoding approach is presented based on a Gao type key equation, reducing the complexity to at least O(n 2 ). This method immediately connects the decoding problem to well-studied problems, which have been investigated in terms of coefficient growth and numerical stability.

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Channel Coding Inspired Contributions to Compressed Sensing

Cited by 4 publications

References 0 publications

Fast Approximate Construction of Best Complex Antipodal Spherical Codes

Fast Approximate Construction of Best Complex Antipodal Spherical Codes

Recursive enhancement of intrinsic soft information for complex reed-solomon codes

An alternative decoding method for Gabidulin codes in characteristic zero

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