{"month":"11","date_created":"2019-07-23T11:01:42Z","citation":{"ieee":"A. Fazeli, H. Hassani, M. Mondelli, and A. Vardy, “Binary linear codes with optimal scaling: Polar codes with large kernels,” in <i>2018 IEEE Information Theory Workshop</i>, Guangzhou, China, 2018, pp. 1–5.","ama":"Fazeli A, Hassani H, Mondelli M, Vardy A. Binary linear codes with optimal scaling: Polar codes with large kernels. In: <i>2018 IEEE Information Theory Workshop</i>. IEEE; 2018:1-5. doi:<a href=\"https://doi.org/10.1109/itw.2018.8613428\">10.1109/itw.2018.8613428</a>","mla":"Fazeli, Arman, et al. “Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” <i>2018 IEEE Information Theory Workshop</i>, IEEE, 2018, pp. 1–5, doi:<a href=\"https://doi.org/10.1109/itw.2018.8613428\">10.1109/itw.2018.8613428</a>.","short":"A. Fazeli, H. Hassani, M. Mondelli, A. Vardy, in:, 2018 IEEE Information Theory Workshop, IEEE, 2018, pp. 1–5.","apa":"Fazeli, A., Hassani, H., Mondelli, M., &#38; Vardy, A. (2018). Binary linear codes with optimal scaling: Polar codes with large kernels. In <i>2018 IEEE Information Theory Workshop</i> (pp. 1–5). Guangzhou, China: IEEE. <a href=\"https://doi.org/10.1109/itw.2018.8613428\">https://doi.org/10.1109/itw.2018.8613428</a>","chicago":"Fazeli, Arman, Hamed Hassani, Marco Mondelli, and Alexander Vardy. “Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” In <i>2018 IEEE Information Theory Workshop</i>, 1–5. IEEE, 2018. <a href=\"https://doi.org/10.1109/itw.2018.8613428\">https://doi.org/10.1109/itw.2018.8613428</a>.","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."},"external_id":{"arxiv":["1711.01339"]},"day":"01","status":"public","publisher":"IEEE","year":"2018","page":"1-5","oa":1,"date_published":"2018-11-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","type":"conference","date_updated":"2024-03-07T12:18:50Z","language":[{"iso":"eng"}],"quality_controlled":"1","title":"Binary linear codes with optimal scaling: Polar codes with large kernels","related_material":{"record":[{"status":"public","id":"9002","relation":"later_version"}]},"main_file_link":[{"url":"https://arxiv.org/abs/1711.01339","open_access":"1"}],"_id":"6665","author":[{"last_name":"Fazeli","full_name":"Fazeli, Arman","first_name":"Arman"},{"last_name":"Hassani","first_name":"Hamed","full_name":"Hassani, Hamed"},{"orcid":"0000-0002-3242-7020","first_name":"Marco","full_name":"Mondelli, Marco","id":"27EB676C-8706-11E9-9510-7717E6697425","last_name":"Mondelli"},{"full_name":"Vardy, Alexander","first_name":"Alexander","last_name":"Vardy"}],"doi":"10.1109/itw.2018.8613428","conference":{"name":"ITW: Information Theory Workshop","location":"Guangzhou, China","start_date":"2018-11-25","end_date":"2018-11-29"},"abstract":[{"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).","lang":"eng"}],"oa_version":"Preprint","publication_status":"published","publication":"2018 IEEE Information Theory Workshop"}