{"publisher":"Institute of Electrical and Electronics Engineers","external_id":{"arxiv":["2105.01427"],"isi":["001069680100011"]},"date_created":"2023-07-23T22:01:14Z","month":"07","publication_status":"published","issue":"10","publication":"IEEE Transactions on Information Theory","oa_version":"Preprint","department":[{"_id":"MaMo"}],"doi":"10.1109/TIT.2023.3292219","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-01-29T11:10:54Z","type":"journal_article","acknowledgement":"Nikita Polyanskii’s research was conducted in part during October 2020 - December 2021 with the Technical University of Munich and the Skolkovo Institute of Science and Technology. His work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) under Grant No. WA3907/1-1 and the Russian Foundation for Basic Research (RFBR)\r\nunder Grant No. 20-01-00559.\r\nYihan Zhang is supported by funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 682203-ERC-[Inf-Speed-Tradeoff].","_id":"13269","status":"public","article_type":"original","abstract":[{"text":"This paper is a collection of results on combinatorial properties of codes for the Z-channel . A Z-channel with error fraction τ takes as input a length- n binary codeword and injects in an adversarial manner up to n τ asymmetric errors, i.e., errors that only zero out bits but do not flip 0’s to 1’s. It is known that the largest ( L - 1)-list-decodable code for the Z-channel with error fraction τ has exponential size (in n ) if τ is less than a critical value that we call the ( L - 1)- list-decoding Plotkin point and has constant size if τ is larger than the threshold. The ( L -1)-list-decoding Plotkin point is known to be L -1/L-1 – L -L/ L-1 , which equals 1/4 for unique-decoding with L -1 = 1. In this paper, we derive various results for the size of the largest codes above and below the list-decoding Plotkin point. In particular, we show that the largest ( L -1)-list-decodable code ε-above the Plotkin point, for any given sufficiently small positive constant ε > 0, has size Θ L (ε -3/2 ) for any L - 1 ≥ 1. We also devise upper and lower bounds on the exponential size of codes below the list-decoding Plotkin point.","lang":"eng"}],"oa":1,"year":"2023","isi":1,"page":"6340-6357","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.01427","open_access":"1"}],"day":"04","language":[{"iso":"eng"}],"author":[{"full_name":"Polyanskii, Nikita","last_name":"Polyanskii","first_name":"Nikita"},{"last_name":"Zhang","orcid":"0000-0002-6465-6258","first_name":"Yihan","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","full_name":"Zhang, Yihan"}],"article_processing_charge":"No","citation":{"chicago":"Polyanskii, Nikita, and Yihan Zhang. “Codes for the Z-Channel.” <i>IEEE Transactions on Information Theory</i>. Institute of Electrical and Electronics Engineers, 2023. <a href=\"https://doi.org/10.1109/TIT.2023.3292219\">https://doi.org/10.1109/TIT.2023.3292219</a>.","apa":"Polyanskii, N., &#38; Zhang, Y. (2023). Codes for the Z-channel. <i>IEEE Transactions on Information Theory</i>. Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/TIT.2023.3292219\">https://doi.org/10.1109/TIT.2023.3292219</a>","ama":"Polyanskii N, Zhang Y. Codes for the Z-channel. <i>IEEE Transactions on Information Theory</i>. 2023;69(10):6340-6357. doi:<a href=\"https://doi.org/10.1109/TIT.2023.3292219\">10.1109/TIT.2023.3292219</a>","short":"N. Polyanskii, Y. Zhang, IEEE Transactions on Information Theory 69 (2023) 6340–6357.","ieee":"N. Polyanskii and Y. Zhang, “Codes for the Z-channel,” <i>IEEE Transactions on Information Theory</i>, vol. 69, no. 10. Institute of Electrical and Electronics Engineers, pp. 6340–6357, 2023.","ista":"Polyanskii N, Zhang Y. 2023. Codes for the Z-channel. IEEE Transactions on Information Theory. 69(10), 6340–6357.","mla":"Polyanskii, Nikita, and Yihan Zhang. “Codes for the Z-Channel.” <i>IEEE Transactions on Information Theory</i>, vol. 69, no. 10, Institute of Electrical and Electronics Engineers, 2023, pp. 6340–57, doi:<a href=\"https://doi.org/10.1109/TIT.2023.3292219\">10.1109/TIT.2023.3292219</a>."},"title":"Codes for the Z-channel","intvolume":"        69","publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]},"scopus_import":"1","quality_controlled":"1","volume":69,"date_published":"2023-07-04T00:00:00Z"}