Discrete-Valued Sparse Signals — Theory, Algorithms, and Applications


It is very attractive to use ideas and tools developed in compressed sensing in digital communications. Exemplary scenarios are transmitter-side signal optimization (e.g., peak-to-average power ratio reduction), multiple-access schemes with small duty cycles, source coding schemes, and radar applications. However, in these scenarios the vector/the signal to be recovered (from noisy measurements) may not only be sparse, but it is beneficial that its elements are taken from a discrete set. Hence, discrete sparse signals are extremely relevant in digital communication systems and signal processing. Unfortunately, such signals and the respective recovery algorithms are not yet studied adequately---if at all---in the literature.

Hence this project aims to develop a comprehensive theory for compressed sensing methodologies specifically designed for discrete-valued sparse signals. Based on this theory for the recovery of discrete sparse signals potential applications in digital communications that can benefit from the developed mathematical insights and algorithms shall then be addressed and explored. In particular, transmitter-side signal generation and source coding strategies shall be studied, and the application to sensor networks and to the identification of channel operators shall be addressed in detail.


  1. A. Flinth and G. Kutyniok, PROMP: A Sparse Recovery Approach to Lattice-Valued Signals, February 2016.

  2. S. Sparrer, R.F.H. Fischer, Algorithms for the Iterative Estimation of Discrete-Valued Sparse Vectors, August 2016.


  1. S. Sparrer and R.F.H. Fischer, Mixed Generalized Gaussian Noise Channels: Capacity, Decoding, and Performance, International ITG Conference on Systems, Communications and Coding (SCC), Hamburg, Germany, Feb. 2015.

  2. S. Sparrer, R.F.H. Fischer, Soft-Feedback OMP for the Recovery of Discrete-Valued Sparse Signals, Proc. European Signal Processing Conference (EUSIPCO), Nice, France, Aug. 2015.

  3. S. Sparrer, R.F.H. Fischer, MMSE-Based Version of OMP for Recovery of Discrete-Valued Sparse Signals, Electronics Letters, Vol. 52, No. 1, pp. 75--77, Jan. 2016.

  4. Axel Flinth, Optimal Choice of Weights for Sparse Recovery With Prior Information, IEEE Transactions on Information Theory, 62(7):4276 - 4284, July 2016.

  5. S. Sparrer, R.F.H. Fischer, Enhanced Iterative Hard Thresholding for the Estimation of Discrete-Valued Sparse Signals, Proc. European Signal Processing Conference (EUSIPCO), Budapest, Hungary, Aug. 2016.

  6. Axel FLinth, A Geometrical Stability Condition for Compressed Sensing, Linear Algebra and its Applications, 50:406-432, September 2016.

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