--- _id: '6665' abstract: - lang: eng text: We prove that, at least for the binary erasure channel, the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but, in fact, do so under the best possible scaling of their block length as a function of the gap to capacity. This result exhibits the first known family of binary codes that attain both optimal scaling and quasi-linear complexity of encoding and decoding. Specifically, for any fixed δ > 0, we exhibit binary linear codes that ensure reliable communication at rates within ε > 0 of capacity with block length n = O(1/ε 2+δ ), construction complexity Θ(n), and encoding/decoding complexity Θ(n log n). author: - first_name: Arman full_name: Fazeli, Arman last_name: Fazeli - first_name: Hamed full_name: Hassani, Hamed last_name: Hassani - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 - first_name: Alexander full_name: Vardy, Alexander last_name: Vardy citation: ama: 'Fazeli A, Hassani H, Mondelli M, Vardy A. Binary linear codes with optimal scaling: Polar codes with large kernels. In: 2018 IEEE Information Theory Workshop. IEEE; 2018:1-5. doi:10.1109/itw.2018.8613428' apa: 'Fazeli, A., Hassani, H., Mondelli, M., & Vardy, A. (2018). Binary linear codes with optimal scaling: Polar codes with large kernels. In 2018 IEEE Information Theory Workshop (pp. 1–5). Guangzhou, China: IEEE. https://doi.org/10.1109/itw.2018.8613428' chicago: 'Fazeli, Arman, Hamed Hassani, Marco Mondelli, and Alexander Vardy. “Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” In 2018 IEEE Information Theory Workshop, 1–5. IEEE, 2018. https://doi.org/10.1109/itw.2018.8613428.' ieee: 'A. Fazeli, H. Hassani, M. Mondelli, and A. Vardy, “Binary linear codes with optimal scaling: Polar codes with large kernels,” in 2018 IEEE Information Theory Workshop, Guangzhou, China, 2018, pp. 1–5.' ista: 'Fazeli A, Hassani H, Mondelli M, Vardy A. 2018. Binary linear codes with optimal scaling: Polar codes with large kernels. 2018 IEEE Information Theory Workshop. ITW: Information Theory Workshop, 1–5.' mla: 'Fazeli, Arman, et al. “Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” 2018 IEEE Information Theory Workshop, IEEE, 2018, pp. 1–5, doi:10.1109/itw.2018.8613428.' short: A. Fazeli, H. Hassani, M. Mondelli, A. Vardy, in:, 2018 IEEE Information Theory Workshop, IEEE, 2018, pp. 1–5. conference: end_date: 2018-11-29 location: Guangzhou, China name: 'ITW: Information Theory Workshop' start_date: 2018-11-25 date_created: 2019-07-23T11:01:42Z date_published: 2018-11-01T00:00:00Z date_updated: 2024-03-07T12:18:50Z day: '01' doi: 10.1109/itw.2018.8613428 extern: '1' external_id: arxiv: - '1711.01339' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1711.01339 month: '11' oa: 1 oa_version: Preprint page: 1-5 publication: 2018 IEEE Information Theory Workshop publication_status: published publisher: IEEE quality_controlled: '1' related_material: record: - id: '9002' relation: later_version status: public status: public title: 'Binary linear codes with optimal scaling: Polar codes with large kernels' type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2018' ...