{"language":[{"iso":"eng"}],"acknowledgement":"Part of this work was done while Nicolas Resch was affiliated with the Centrum Wiskunde & Informatica and supported in part by ERC H2020 grant No.74079 (ALGSTRONGCRYPTO). Chen Yuan is supported in part by the National Key Research and Development Projects under Grant 2022YFA1004900 and Grant 2021YFE0109900, the National Natural Science Foundation of China under Grant 12101403 and Grant 12031011.","month":"07","citation":{"ama":"Resch N, Yuan C, Zhang Y. Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery. <i>IEEE Transactions on Information Theory</i>. 2024. doi:<a href=\"https://doi.org/10.1109/TIT.2024.3430842\">10.1109/TIT.2024.3430842</a>","apa":"Resch, N., Yuan, C., &#38; Zhang, Y. (2024). Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2024.3430842\">https://doi.org/10.1109/TIT.2024.3430842</a>","ieee":"N. Resch, C. Yuan, and Y. Zhang, “Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery,” <i>IEEE Transactions on Information Theory</i>. IEEE, 2024.","chicago":"Resch, Nicolas, Chen Yuan, and Yihan Zhang. “Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2024. <a href=\"https://doi.org/10.1109/TIT.2024.3430842\">https://doi.org/10.1109/TIT.2024.3430842</a>.","mla":"Resch, Nicolas, et al. “Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery.” <i>IEEE Transactions on Information Theory</i>, IEEE, 2024, doi:<a href=\"https://doi.org/10.1109/TIT.2024.3430842\">10.1109/TIT.2024.3430842</a>.","short":"N. Resch, C. Yuan, Y. Zhang, IEEE Transactions on Information Theory (2024).","ista":"Resch N, Yuan C, Zhang Y. 2024. Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery. IEEE Transactions on Information Theory."},"date_published":"2024-07-19T00:00:00Z","corr_author":"1","_id":"17330","external_id":{"arxiv":["2210.07754"]},"doi":"10.1109/TIT.2024.3430842","author":[{"full_name":"Resch, Nicolas","first_name":"Nicolas","last_name":"Resch"},{"last_name":"Yuan","first_name":"Chen","full_name":"Yuan, Chen"},{"first_name":"Yihan","full_name":"Zhang, Yihan","orcid":"0000-0002-6465-6258","last_name":"Zhang","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c"}],"day":"19","publication":"IEEE Transactions on Information Theory","oa_version":"Preprint","abstract":[{"lang":"eng","text":"In this work we consider the list-decodability and list-recoverability of arbitrary q -ary codes, for all integer values of q ⩾ 2. A code is called ( p , L ) q -list-decodable if every radius pn Hamming ball contains less than L codewords; ( p , ℓ, L ) q -recoverability is a generalization where we place radius pn Hamming balls on every point of a combinatorial rectangle with side length ℓ and again stipulate that there be less than L codewords. Our main contribution is to precisely calculate the maximum value of p for which there exist infinite families of positive rate ( p , ℓ, L ) q -list-recoverable codes, the quantity we call the zero-rate threshold . Denoting this value by p *, we in fact show that codes correcting a p * + ε fraction of errors must have size O ε (1), i.e., independent of n . Such a result is typically referred to as a “Plotkin bound.” To complement this, a standard random code with expurgation construction shows that there exist positive rate codes correcting a p * − ε fraction of errors. We also follow a classical proof template (typically attributed to Elias and Bassalygo) to derive from the zero-rate threshold other tradeoffs between rate and decoding radius for list-decoding and list-recovery. Technically, proving the Plotkin bound boils down to demon-strating the Schur convexity of a certain function defined on the q -simplex as well as the convexity of a univariate function derived from it. We remark that an earlier argument claimed similar results for q -ary list-decoding; however, we point out that this earlier proof is flawed."}],"year":"2024","date_created":"2024-07-28T22:01:10Z","publication_status":"epub_ahead","publication_identifier":{"eissn":["1557-9654"],"issn":["0018-9448"]},"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","department":[{"_id":"MaMo"}],"related_material":{"record":[{"id":"14083","relation":"earlier_version","status":"public"}]},"publisher":"IEEE","date_updated":"2024-07-29T07:59:41Z","article_type":"original","title":"Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery","quality_controlled":"1","article_processing_charge":"No","scopus_import":"1"}