Due to its attractive properties, generalized frequency division multiplexing (GFDM) is recently being discussed as a candidate waveform for the fifth generation of wireless communication systems (5G). GFDM is introduced as a generalized form of the widely used orthogonal frequency division multiplexing (OFDM) modulation scheme and since it uses only one cyclic prefix (CP) for a group of symbols rather than a CP per symbol, it is more bandwidth efficient than OFDM. In this paper, we propose novel modem structures for GFDM by taking advantage of the particular structure in the modulation matrix. Our proposed transmitter is based on modulation matrix sparsification through application of fast Fourier transform (FFT) to reduce the implementation complexity. A unified demodulator structure for matched filter (MF), zero forcing (ZF), and minimum mean square error (MMSE) receivers is also derived. The proposed demodulation techniques harness the special block circulant property of the matrices involved in the demodulation stage to reduce the computational cost of the system implementation. We have derived the closed forms for the ZF and MMSE receiver filters. Additionally, our algorithms do not incur any performance loss as they maintain the optimal performance. The computational costs of our proposed techniques are analyzed in detail and are compared with the existing solutions that are known to have the lowest complexity. It is shown that through application of our structures a substantial amount of computational complexity reduction can be achieved.

Low-Complexity Modem Design for GFDM

Competitive sliding window detectors require vast training sets. Since a pool of natural images provides a nearly endless supply of negative samples, in the form of patches at different scales and locations, training with all the available data is considered impractical. A staple of current approaches is hard negative mining, a method of selecting relevant samples, which is nevertheless expensive. Given that samples at slightly different locations have overlapping support, there seems to be an enormous amount of duplicated work. It is natural, then, to ask whether these redundancies can be eliminated. In this paper, we show that the Gram matrix describing such data is block-circulant. We derive a transformation based on the Fourier transform that block-diagonalizes the Gram matrix, at once eliminating redundancies and partitioning the learning problem. This decomposition is valid for any dense features and several learning algorithms, and takes full advantage of modern parallel architectures. Surprisingly, it allows training with all the potential samples in sets of thousands of images. By considering the full set, we generate in a single shot the optimal solution, which is usually obtained only after several rounds of hard negative mining. We report speed gains on Caltech Pedestrians and INRIA Pedestrians of over an order of magnitude, allowing training on a desktop computer in a couple of minutes.

/pdf/beyond-hard-negative-mining-efficient-detector-learning-via-3k4zbddgpt.pdf

Beyond Hard Negative Mining: Efficient Detector Learning via Block-Circulant Decomposition

Algorithms based on total variation (TV) minimization are prevalent in image processing. They play a key role in a variety of applications such as image denoising, compressive sensing, and inverse problems in general. In this work, we extend the TV dual framework that includes Chambolle's and Gilboa and Osher's projection algorithms for TV minimization. We use a flexible graph data representation that allows us to generalize the constraint on the projection variable. We show how this new formulation of the TV problem may be solved by means of fast parallel proximal algorithms. In denoising and deblurring examples, the proposed approach is shown not only to perform better than recent TV-based approaches, but also to perform well on arbitrary graphs instead of regular grids. The proposed method consequently applies to a variety of other inverse problems including image fusion and mesh filtering.

/pdf/dual-constrained-tv-based-regularization-on-graphs-25dzkq1fe2.pdf

Dual constrained TV-based regularization on graphs

In this paper we propose an analytical technique for the steady-state dynamic temperature analysis (SSDTA) of multiprocessor systems with periodic applications. The approach is accurate and, moreover, fast, such that it can be included inside an optimization loop for embedded system design. Using the proposed solution, a temperature-aware reliability optimization, based on the thermal cycling failure mechanism, is presented. The experimental results confirm the quality and speed of our SSDTA technique, compared to the state of the art. They also show that the lifetime of an embedded system can significantly be improved, without sacrificing its energy efficiency, by taking into consideration, during the design stage, the steady-state dynamic temperature profile of the system.

/pdf/steady-state-dynamic-temperature-analysis-and-reliability-4r0rfnj5eh.pdf

Steady-state dynamic temperature analysis and reliability optimization for embedded multiprocessor systems

Closed-form expressions of the inverse of a block-circulant matrix (BCM) are well known. Such expressions are derived here following two alternative procedures, which are based on the discrete Fourier transform (DFT) and appear to be simple and brief when compared to previously published procedures. In the case of circulant matrices of scalars, the formulas of inversion are derived using the theory of circular arrays and this approach suggested an extension of the DFT to the BCM case.

Inversion of block-circulant matrices and circular array approach

The inverse A^{-1} of a block-circulant matrix (BCM) A is given in a closed form, by using the fact that a BCM is a combination of permutation matrices, whose eigenvalues and eigenvectors are found with the help of the complex roots of unity. Special results are also given when A is block symmetric or symmetric.

D. Gerlic

Papers

The inverse of a block-circulant matrix