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Polar codes with Reed-Solomon (RS) kernel have great potential in next-generation communication systems due to their high polarization rate. In this paper, we study the polarization characteristics of RS polar codes and propose two types of…

Information Theory · Computer Science 2023-08-11 Jianhan Zhao , Wei Zhang , Yanyan Liu

In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. The proposed multi-kernel polar…

Information Theory · Computer Science 2020-01-15 Valerio Bioglio , Frederic Gabry , Ingmar Land , Jean-Claude Belfiore

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

Machine Learning · Computer Science 2024-05-01 Corinna Cortes , Mehryar Mohri , Afshin Rostamizadeh

Gaussian Process (GP) kernels are central to Bayesian optimization (BO), yet designing effective kernels for high-dimensional problems still relies on extensive manual engineering. Existing automated approaches struggle in high dimensions…

Machine Learning · Computer Science 2026-05-21 Taeyoung Yun , Woocheol Shin , Inhyuck Song , Jaewoo Lee , Jinkyoo Park

Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…

Statistics Theory · Mathematics 2017-10-13 Alain Celisse , Guillemette Marot , Morgane Pierre-Jean , Guillem Rigaill

Deep polar codes are pre-transformed polar codes that employ a multi-layered polar kernel transformation strategy to enhance code performance in short blocklength regimes. However, like conventional polar codes, their block length is…

Information Theory · Computer Science 2025-05-13 Geon Choi , Namyoon Lee

We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi kernel polar…

Information Theory · Computer Science 2017-03-13 Frederic Gabry , Valerio Bioglio , Ingmar Land , Jean-Claude Belfiore

Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…

Machine Learning · Computer Science 2020-02-17 Mert Al , Zejiang Hou , Sun-Yuan Kung

Herein, we focus on explicit constructions of $\ell\times\ell$ binary kernels with small scaling exponent for $\ell \le 64$. In particular, we exhibit a sequence of binary linear codes that approaches capacity on the BEC with quasi-linear…

Information Theory · Computer Science 2019-02-27 Hanwen Yao , Arman Fazeli , Alexander Vardy

Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…

Machine Learning · Computer Science 2022-03-24 Benedikt Boecking , Vincent Jeanselme , Artur Dubrawski

A reduced complexity sequential decoding algorithm for polar (sub)codes is described. The proposed approach relies on a decomposition of the polar (sub)code being decoded into a number of outer codes, and on-demand construction of codewords…

Information Theory · Computer Science 2020-07-08 Grigorii Trofimiuk , Nikolay Iakuba , Stanislav Rets , Kirill Ivanov , Peter Trifonov

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

Machine Learning · Computer Science 2011-12-21 Arash Afkanpour , Csaba Szepesvari , Michael Bowling

Polar codes that approach capacity at a near-optimal speed, namely with scaling exponents close to $2$, have been shown possible for $q$-ary erasure channels (Pfister and Urbanke), the BEC (Fazeli, Hassani, Mondelli, and Vardy), all BMS…

Information Theory · Computer Science 2024-05-28 Hsin-Po Wang , Venkatesan Guruswami

Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm…

Computer Vision and Pattern Recognition · Computer Science 2017-05-19 Jing Wang , Jie Shen , Ping Li

Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…

Computational Complexity · Computer Science 2018-07-11 Max Bannach , Till Tantau

A decoding algorithm for polar (sub)codes with binary $2^t\times 2^t$ polarization kernels is presented. It is based on the window processing (WP) method, which exploits the linear relationship of the polarization kernels and the Arikan…

Information Theory · Computer Science 2021-04-07 Grigorii Trofimiuk , Peter Trifonov

Kernel methods represent some of the most popular machine learning tools for data analysis. Since exact kernel methods can be prohibitively expensive for large problems, reliable low-rank matrix approximations and high-performance…

Numerical Analysis · Mathematics 2018-04-17 Jianwei Xiao , Ming Gu

In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of…

Data Structures and Algorithms · Computer Science 2016-11-07 Daniel Lokshtanov , Fahad Panolan , M. S. Ramanujan , Saket Saurabh

Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…

Machine Learning · Statistics 2018-06-06 Hiroaki Sasaki , Aapo Hyvärinen

Most design approaches for trellis-coded quantization take advantage of the duality of trellis-coded quantization with trellis-coded modulation, and use the same empirically-found convolutional codes to label the trellis branches. This…

Information Theory · Computer Science 2007-12-20 Lorenzo Cappellari