Related papers: Convolutional Polar Kernels
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…
Suppose $C$ is an isogeny class of abelian varieties over a finite field $k$. In this paper we give a partial answer to the question of which finite group schemes over $k$ occur as kernels of polarizations of varieties in $C$. We show that…
A practical $2^m$-ary polar coded modulation (PCM) scheme with optimal constellation labeling is proposed. To efficiently find the optimal labeling rule, the search space is reduced by exploiting the symmetry properties of the channels.…
In this paper, estimates are proven for convolution kernels associated to multipliers from a reasonably general class of compactly supported two-dimensional functions constructed out of real-analytic functions. These estimates are both for…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…
Polar codes with memory (PCM) are proposed in this paper: a pair of consecutive code blocks containing a controlled number of mutual information bits. The shared mutual information bits of the succeeded block can help the failed block to…
Mapping CMB polarization is an essential ingredient of current cosmological research. Particularly challenging is the measurement of an extremely weak B-mode polarization that can potentially yield unique insight on inflation. Achieving…
The generator matrices of polar codes and Reed-Muller codes are obtained by selecting rows from the Kronecker product of a lower-triangular binary square matrix. For polar codes, the selection is based on the Bhattacharyya parameter of the…
The fragmentation equation is commonly expressed in terms of two functions, the rate of fragmentation and the mean number of fragments. In the case of binary fragmentation an alternative description is possible based on the fragmentation…
Polar coding over a class of binary discrete memoryless channels with channel knowledge at the encoder is studied. It is shown that polar codes achieve the capacity of convex and one-sided classes of symmetric channels.
Polar codes can theoretically achieve very competitive Frame Error Rates. In practice, their performance may depend on the chosen decoding procedure, as well as other parameters of the communication system they are deployed upon. As a…
We measure linearly polarized beam patterns for a multi-moded concentrator and compare the results to a simple model based on geometric optics. We convolve the measured co-polar and cross-polar beams with simulated maps of CMB polarization…
We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…
The inherently complex-valued nature of Polarimetric SAR data necessitates using specialized algorithms capable of directly processing complex-valued representations. However, this aspect remains underexplored in the deep learning…
Scalar quantization and probabilistic shaping are applied to the distributed source coding of Gaussian sources, with mean-square error distortion. A coding scheme with a modulo interval, dithering, and truncated Gaussian shaping is shown to…
The characterisation of small low conducting inclusions in an otherwise uniform background from low-frequency electrical field measurements has important applications in medical imaging using electrical impedance tomography as well as in…
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
SCUPOL, the polarimeter for SCUBA on the James Clerk Maxwell Telescope (JCMT), was used for polarization observations of 104 regions at 850 micron wavelength and 15 arcsec resolution in the mapping mode by Matthews et al. (2009). They…
A heuristic construction of polar codes for successive cancellation list (SCL) decoding with a given list size is proposed to balance the trade-off between performance measured in frame error rate (FER) and decoding complexity. Furthermore,…
In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in $\mathbb{R}^n$. Our approach focuses on high dimensions and relies solely on the concentration properties of the components in the…