{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/12060050","title":"List Decoding of Polar Codes","arxiv_id":"1206.0050","date":"2012-05-31","proceeding":null,"authors":["Ido Tal","Alexander Vardy"],"abstract":"We describe a successive-cancellation \\emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\\i}kan. In the proposed list decoder, up to $L$ decoding paths are considered concurrently at each decoding stage. Then, a single codeword is selected from the list as output. If the most likely codeword is selected, simulation results show that the resulting performance is very close to that of a maximum-likelihood decoder, even for moderate values of $L$. Alternatively, if a \"genie\" is allowed to pick the codeword from the list, the results are comparable to the current state of the art LDPC codes. Luckily, implementing such a helpful genie is easy. Our list decoder doubles the number of decoding paths at each decoding step, and then uses a pruning procedure to discard all but the $L$ \"best\" paths. %In order to implement this algorithm, we introduce a natural pruning criterion that can be easily evaluated. Nevertheless, a straightforward implementation still requires $\\Omega(L \\cdot n^2)$ time, which is in stark contrast with the $O(n \\log n)$ complexity of the original successive-cancellation decoder. We utilize the structure of polar codes to overcome this problem. Specifically, we devise an efficient, numerically stable, implementation taking only $O(L \\cdot n \\log n)$ time and $O(L \\cdot n)$ space.","url_abs":"http://arxiv.org/abs/1206.0050v1","url_pdf":"http://arxiv.org/pdf/1206.0050v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"12060050","repo_url":"https://github.com/oobazuaye/WES_207_polar_codes","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"12060050","repo_url":"https://github.com/tavildar/Polar","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1206.0050","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}