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