[{"citation":{"ieee":"Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via error exponents,” <i>IEEE Transactions on Information Theory</i>. IEEE, 2023.","chicago":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Error Exponents.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/TIT.2023.3334032\">https://doi.org/10.1109/TIT.2023.3334032</a>.","short":"Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory (2023).","ama":"Zhang Y, Vatedka S. Multiple packing: Lower bounds via error exponents. <i>IEEE Transactions on Information Theory</i>. 2023. doi:<a href=\"https://doi.org/10.1109/TIT.2023.3334032\">10.1109/TIT.2023.3334032</a>","mla":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Error Exponents.” <i>IEEE Transactions on Information Theory</i>, IEEE, 2023, doi:<a href=\"https://doi.org/10.1109/TIT.2023.3334032\">10.1109/TIT.2023.3334032</a>.","ista":"Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via error exponents. IEEE Transactions on Information Theory.","apa":"Zhang, Y., &#38; Vatedka, S. (2023). Multiple packing: Lower bounds via error exponents. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2023.3334032\">https://doi.org/10.1109/TIT.2023.3334032</a>"},"language":[{"iso":"eng"}],"status":"public","external_id":{"arxiv":["2211.04408"]},"doi":"10.1109/TIT.2023.3334032","date_published":"2023-11-16T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2211.04408"}],"quality_controlled":"1","publication_status":"epub_ahead","oa":1,"publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]},"publication":"IEEE Transactions on Information Theory","_id":"14665","scopus_import":"1","article_processing_charge":"No","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"IEEE","department":[{"_id":"MaMo"}],"year":"2023","arxiv":1,"title":"Multiple packing: Lower bounds via error exponents","date_created":"2023-12-10T23:01:00Z","author":[{"first_name":"Yihan","last_name":"Zhang","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","orcid":"0000-0002-6465-6258","full_name":"Zhang, Yihan"},{"full_name":"Vatedka, Shashank","last_name":"Vatedka","first_name":"Shashank"}],"date_updated":"2023-12-18T07:46:45Z","abstract":[{"lang":"eng","text":"We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. For any N > 0 and L ∈ Z ≥2 , a multiple packing is a set C of points in R n such that any point in R n lies in the intersection of at most L - 1 balls of radius √ nN around points in C . This is a natural generalization of the sphere packing problem. We study the multiple packing problem for both bounded point sets whose points have norm at most √ nP for some constant P > 0, and unbounded point sets whose points are allowed to be anywhere in R n . Given a well-known connection with coding theory, multiple packings can be viewed as the Euclidean analog of list-decodable codes, which are well-studied over finite fields. We derive the best known lower bounds on the optimal multiple packing density. This is accomplished by establishing an inequality which relates the list-decoding error exponent for additive white Gaussian noise channels, a quantity of average-case nature, to the list-decoding radius, a quantity of worst-case nature. We also derive novel bounds on the list-decoding error exponent for infinite constellations and closed-form expressions for the list-decoding error exponents for the power-constrained AWGN channel, which may be of independent interest beyond multiple packing."}],"day":"16","oa_version":"Preprint","type":"journal_article","month":"11"},{"date_updated":"2024-01-09T08:45:24Z","abstract":[{"lang":"eng","text":"We consider zero-error communication over a two-transmitter deterministic adversarial multiple access channel (MAC) governed by an adversary who has access to the transmissions of both senders (hence called omniscient ) and aims to maliciously corrupt the communication. None of the encoders, jammer and decoder is allowed to randomize using private or public randomness. This enforces a combinatorial nature of the problem. Our model covers a large family of channels studied in the literature, including all deterministic discrete memoryless noisy or noiseless MACs. In this work, given an arbitrary two-transmitter deterministic omniscient adversarial MAC, we characterize when the capacity region: 1) has nonempty interior (in particular, is two-dimensional); 2) consists of two line segments (in particular, has empty interior); 3) consists of one line segment (in particular, is one-dimensional); 4) or only contains (0,0) (in particular, is zero-dimensional). This extends a recent result by Wang et al. (201 9) from the point-to-point setting to the multiple access setting. Indeed, our converse arguments build upon their generalized Plotkin bound and involve delicate case analysis. One of the technical challenges is to take care of both “joint confusability” and “marginal confusability”. In particular, the treatment of marginal confusability does not follow from the point-to-point results by Wang et al. Our achievability results follow from random coding with expurgation."}],"type":"journal_article","month":"07","oa_version":"Preprint","page":"4093-4127","date_created":"2024-01-08T13:04:54Z","volume":69,"year":"2023","acknowledgement":"The author would like to thank Amitalok J. Budkuley and Sidharth Jaggi for many helpful discussions at the early stage of this work. He would also like to thank Nir Ailon, Qi Cao, and Chandra Nair for discussions on a related problem regarding zero-error binary adder MACs.\r\nThe work of Yihan Zhang was supported by the European Union’s Horizon 2020 Research and Innovation Programme under Grant 682203-ERC-[Inf-Speed-Tradeoff]","_id":"14751","publication_status":"published","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2101.12426"}],"date_published":"2023-07-01T00:00:00Z","status":"public","external_id":{"arxiv":["2101.12426"]},"citation":{"chicago":"Zhang, Yihan. “Zero-Error Communication over Adversarial MACs.” <i>IEEE Transactions on Information Theory</i>. Institute of Electrical and Electronics Engineers, 2023. <a href=\"https://doi.org/10.1109/tit.2023.3257239\">https://doi.org/10.1109/tit.2023.3257239</a>.","ieee":"Y. Zhang, “Zero-error communication over adversarial MACs,” <i>IEEE Transactions on Information Theory</i>, vol. 69, no. 7. Institute of Electrical and Electronics Engineers, pp. 4093–4127, 2023.","short":"Y. Zhang, IEEE Transactions on Information Theory 69 (2023) 4093–4127.","ama":"Zhang Y. Zero-error communication over adversarial MACs. <i>IEEE Transactions on Information Theory</i>. 2023;69(7):4093-4127. doi:<a href=\"https://doi.org/10.1109/tit.2023.3257239\">10.1109/tit.2023.3257239</a>","apa":"Zhang, Y. (2023). Zero-error communication over adversarial MACs. <i>IEEE Transactions on Information Theory</i>. Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/tit.2023.3257239\">https://doi.org/10.1109/tit.2023.3257239</a>","ista":"Zhang Y. 2023. Zero-error communication over adversarial MACs. IEEE Transactions on Information Theory. 69(7), 4093–4127.","mla":"Zhang, Yihan. “Zero-Error Communication over Adversarial MACs.” <i>IEEE Transactions on Information Theory</i>, vol. 69, no. 7, Institute of Electrical and Electronics Engineers, 2023, pp. 4093–127, doi:<a href=\"https://doi.org/10.1109/tit.2023.3257239\">10.1109/tit.2023.3257239</a>."},"intvolume":"        69","day":"01","author":[{"last_name":"Zhang","first_name":"Yihan","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","orcid":"0000-0002-6465-6258","full_name":"Zhang, Yihan"}],"arxiv":1,"title":"Zero-error communication over adversarial MACs","department":[{"_id":"MaMo"}],"publisher":"Institute of Electrical and Electronics Engineers","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","scopus_import":"1","article_type":"original","publication":"IEEE Transactions on Information Theory","publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]},"quality_controlled":"1","doi":"10.1109/tit.2023.3257239","language":[{"iso":"eng"}],"issue":"7","keyword":["Computer Science Applications","Information Systems"]},{"_id":"13269","year":"2023","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].","date_created":"2023-07-23T22:01:14Z","volume":69,"type":"journal_article","month":"07","oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"date_updated":"2024-01-29T11:10:54Z","page":"6340-6357","citation":{"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>","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>.","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>","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.","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>.","short":"N. Polyanskii, Y. Zhang, IEEE Transactions on Information Theory 69 (2023) 6340–6357."},"intvolume":"        69","status":"public","external_id":{"isi":["001069680100011"],"arxiv":["2105.01427"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.01427","open_access":"1"}],"date_published":"2023-07-04T00:00:00Z","publication_status":"published","oa":1,"article_type":"original","scopus_import":"1","article_processing_charge":"No","publication":"IEEE Transactions on Information Theory","department":[{"_id":"MaMo"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Electrical and Electronics Engineers","arxiv":1,"title":"Codes for the Z-channel","day":"04","author":[{"full_name":"Polyanskii, Nikita","last_name":"Polyanskii","first_name":"Nikita"},{"id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","orcid":"0000-0002-6465-6258","full_name":"Zhang, Yihan","last_name":"Zhang","first_name":"Yihan"}],"issue":"10","language":[{"iso":"eng"}],"isi":1,"quality_controlled":"1","doi":"10.1109/TIT.2023.3292219","publication_identifier":{"eissn":["1557-9654"],"issn":["0018-9448"]}},{"issue":"7","language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"eissn":["1557-9654"],"issn":["0018-9448"]},"quality_controlled":"1","doi":"10.1109/TIT.2023.3260950","department":[{"_id":"MaMo"}],"publisher":"IEEE","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","scopus_import":"1","article_processing_charge":"No","publication":"IEEE Transactions on Information Theory","day":"01","author":[{"full_name":"Zhang, Yihan","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","orcid":"0000-0002-6465-6258","first_name":"Yihan","last_name":"Zhang"},{"full_name":"Vatedka, Shashank","last_name":"Vatedka","first_name":"Shashank"}],"arxiv":1,"title":"Multiple packing: Lower bounds via infinite constellations","external_id":{"arxiv":["2211.04407"],"isi":["001017307000023"]},"status":"public","citation":{"apa":"Zhang, Y., &#38; Vatedka, S. (2023). Multiple packing: Lower bounds via infinite constellations. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2023.3260950\">https://doi.org/10.1109/TIT.2023.3260950</a>","mla":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Infinite Constellations.” <i>IEEE Transactions on Information Theory</i>, vol. 69, no. 7, IEEE, 2023, pp. 4513–27, doi:<a href=\"https://doi.org/10.1109/TIT.2023.3260950\">10.1109/TIT.2023.3260950</a>.","ista":"Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via infinite constellations. IEEE Transactions on Information Theory. 69(7), 4513–4527.","ama":"Zhang Y, Vatedka S. Multiple packing: Lower bounds via infinite constellations. <i>IEEE Transactions on Information Theory</i>. 2023;69(7):4513-4527. doi:<a href=\"https://doi.org/10.1109/TIT.2023.3260950\">10.1109/TIT.2023.3260950</a>","short":"Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory 69 (2023) 4513–4527.","chicago":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Infinite Constellations.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/TIT.2023.3260950\">https://doi.org/10.1109/TIT.2023.3260950</a>.","ieee":"Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via infinite constellations,” <i>IEEE Transactions on Information Theory</i>, vol. 69, no. 7. IEEE, pp. 4513–4527, 2023."},"intvolume":"        69","publication_status":"published","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2211.04407","open_access":"1"}],"date_published":"2023-07-01T00:00:00Z","year":"2023","acknowledgement":"YZ thanks Jiajin Li for making the observation given by Equation (23). He also would like to thank Nir Ailon and Ely Porat for several helpful conversations throughout this project, and Alexander Barg for insightful comments on the manuscript.\r\nYZ has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]. The work of SV was supported by a seed grant from IIT Hyderabad and the start-up research grant from the Science and Engineering Research Board, India (SRG/2020/000910).","_id":"12838","month":"07","type":"journal_article","oa_version":"Preprint","date_updated":"2023-12-13T11:16:46Z","abstract":[{"text":"We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let N > 0 and L ∈ Z ≽2 . A multiple packing is a set C of points in R n such that any point in R n lies in the intersection of at most L – 1 balls of radius √ nN around points in C . Given a well-known connection with coding theory, multiple packings can be viewed as the Euclidean analog of list-decodable codes, which are well-studied for finite fields. In this paper, we derive the best known lower bounds on the optimal density of list-decodable infinite constellations for constant L under a stronger notion called average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory.","lang":"eng"}],"page":"4513-4527","date_created":"2023-04-16T22:01:09Z","volume":69},{"quality_controlled":"1","doi":"10.1109/TIT.2022.3148779","publication_identifier":{"eissn":["1557-9654"],"issn":["0018-9448"]},"language":[{"iso":"eng"}],"issue":"6","isi":1,"arxiv":1,"title":"List-decodability with large radius for Reed-Solomon codes","day":"01","author":[{"first_name":"Asaf","last_name":"Ferber","full_name":"Ferber, Asaf"},{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan","last_name":"Kwan","first_name":"Matthew Alan"},{"first_name":"Lisa","last_name":"Sauermann","full_name":"Sauermann, Lisa"}],"article_processing_charge":"No","scopus_import":"1","article_type":"original","publication":"IEEE Transactions on Information Theory","department":[{"_id":"MaKw"}],"publisher":"IEEE","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://arxiv.org/abs/2012.10584","open_access":"1"}],"date_published":"2022-06-01T00:00:00Z","oa":1,"publication_status":"published","citation":{"ama":"Ferber A, Kwan MA, Sauermann L. List-decodability with large radius for Reed-Solomon codes. <i>IEEE Transactions on Information Theory</i>. 2022;68(6):3823-3828. doi:<a href=\"https://doi.org/10.1109/TIT.2022.3148779\">10.1109/TIT.2022.3148779</a>","apa":"Ferber, A., Kwan, M. A., &#38; Sauermann, L. (2022). List-decodability with large radius for Reed-Solomon codes. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2022.3148779\">https://doi.org/10.1109/TIT.2022.3148779</a>","mla":"Ferber, Asaf, et al. “List-Decodability with Large Radius for Reed-Solomon Codes.” <i>IEEE Transactions on Information Theory</i>, vol. 68, no. 6, IEEE, 2022, pp. 3823–28, doi:<a href=\"https://doi.org/10.1109/TIT.2022.3148779\">10.1109/TIT.2022.3148779</a>.","ista":"Ferber A, Kwan MA, Sauermann L. 2022. List-decodability with large radius for Reed-Solomon codes. IEEE Transactions on Information Theory. 68(6), 3823–3828.","chicago":"Ferber, Asaf, Matthew Alan Kwan, and Lisa Sauermann. “List-Decodability with Large Radius for Reed-Solomon Codes.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2022. <a href=\"https://doi.org/10.1109/TIT.2022.3148779\">https://doi.org/10.1109/TIT.2022.3148779</a>.","ieee":"A. Ferber, M. A. Kwan, and L. Sauermann, “List-decodability with large radius for Reed-Solomon codes,” <i>IEEE Transactions on Information Theory</i>, vol. 68, no. 6. IEEE, pp. 3823–3828, 2022.","short":"A. Ferber, M.A. Kwan, L. Sauermann, IEEE Transactions on Information Theory 68 (2022) 3823–3828."},"intvolume":"        68","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"11145"}]},"status":"public","external_id":{"arxiv":["2012.10584"],"isi":["000799622500022"]},"date_created":"2022-02-20T23:01:34Z","volume":68,"abstract":[{"text":"List-decodability of Reed–Solomon codes has received a lot of attention, but the best-possible dependence between the parameters is still not well-understood. In this work, we focus on the case where the list-decoding radius is of the form r = 1-ε for ε tending to zero. Our main result states that there exist Reed–Solomon codes with rate Ω(ε) which are (1 - ε, O(1/ε))-list-decodable, meaning that any Hamming ball of radius 1-ε contains at most O(1/ε) codewords. This trade-off between rate and list-decoding radius is best-possible for any code with list size less than exponential in the block length. By achieving this trade-off between rate and list-decoding radius we improve a recent result of Guo, Li, Shangguan, Tamo, and Wootters, and resolve the main motivating question of their work. Moreover, while their result requires the field to be exponentially large in the block length, we only need the field size to be polynomially large (and in fact, almost-linear suffices). We deduce our main result from a more general theorem, in which we prove good list-decodability properties of random puncturings of any given code with very large distance.","lang":"eng"}],"date_updated":"2023-08-03T06:57:01Z","oa_version":"Preprint","type":"journal_article","month":"06","page":"3823-3828","_id":"10775","year":"2022","acknowledgement":"Research supported by NSF Award DMS-1953990."},{"acknowledgement":"This work was done when Shashank Vatedka was at the Chinese University of Hong Kong, where he was supported in part by CUHK Direct Grants 4055039 and 4055077. He would like to acknowledge funding from a seed grant offered by IIT Hyderabad and the Start-up Research Grant (SRG/2020/000910) from the Science and Engineering Board, India. Yihan Zhang has received funding from the European Union’s Horizon 2020 research and innovation programme\r\nunder grant agreement No 682203-ERC-[Inf-Speed-Tradeoff].","year":"2022","_id":"11639","page":"7753-7786","abstract":[{"text":"We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints P and N respectively, the list decoding capacity is equal to 1/2logP/N. Random spherical codes achieve constant list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain conjecture that originates in analytic number theory is true, then the list size grows as a polynomial function of the gap-to-capacity.","lang":"eng"}],"date_updated":"2023-08-03T12:12:19Z","month":"12","oa_version":"Preprint","type":"journal_article","volume":68,"date_created":"2022-07-24T22:01:42Z","status":"public","external_id":{"arxiv":["1901.03790"],"isi":["000891796100007"]},"intvolume":"        68","citation":{"ama":"Zhang Y, Vatedka S. List decoding random Euclidean codes and Infinite constellations. <i>IEEE Transactions on Information Theory</i>. 2022;68(12):7753-7786. doi:<a href=\"https://doi.org/10.1109/TIT.2022.3189542\">10.1109/TIT.2022.3189542</a>","apa":"Zhang, Y., &#38; Vatedka, S. (2022). List decoding random Euclidean codes and Infinite constellations. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2022.3189542\">https://doi.org/10.1109/TIT.2022.3189542</a>","ista":"Zhang Y, Vatedka S. 2022. List decoding random Euclidean codes and Infinite constellations. IEEE Transactions on Information Theory. 68(12), 7753–7786.","mla":"Zhang, Yihan, and Shashank Vatedka. “List Decoding Random Euclidean Codes and Infinite Constellations.” <i>IEEE Transactions on Information Theory</i>, vol. 68, no. 12, IEEE, 2022, pp. 7753–86, doi:<a href=\"https://doi.org/10.1109/TIT.2022.3189542\">10.1109/TIT.2022.3189542</a>.","chicago":"Zhang, Yihan, and Shashank Vatedka. “List Decoding Random Euclidean Codes and Infinite Constellations.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2022. <a href=\"https://doi.org/10.1109/TIT.2022.3189542\">https://doi.org/10.1109/TIT.2022.3189542</a>.","ieee":"Y. Zhang and S. Vatedka, “List decoding random Euclidean codes and Infinite constellations,” <i>IEEE Transactions on Information Theory</i>, vol. 68, no. 12. IEEE, pp. 7753–7786, 2022.","short":"Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory 68 (2022) 7753–7786."},"publication_status":"published","oa":1,"date_published":"2022-12-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1901.03790"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"IEEE","department":[{"_id":"MaMo"}],"publication":"IEEE Transactions on Information Theory","scopus_import":"1","article_processing_charge":"No","article_type":"original","author":[{"full_name":"Zhang, Yihan","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","last_name":"Zhang","first_name":"Yihan"},{"full_name":"Vatedka, Shashank","first_name":"Shashank","last_name":"Vatedka"}],"day":"01","arxiv":1,"title":"List decoding random Euclidean codes and Infinite constellations","isi":1,"language":[{"iso":"eng"}],"issue":"12","publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]},"doi":"10.1109/TIT.2022.3189542","quality_controlled":"1"},{"year":"2022","_id":"12273","page":"4901-4948","oa_version":"Preprint","type":"journal_article","month":"08","date_updated":"2023-08-04T10:08:49Z","abstract":[{"lang":"eng","text":"We study communication in the presence of a jamming adversary where quadratic power constraints are imposed on the transmitter and the jammer. The jamming signal is allowed to be a function of the codebook, and a noncausal but noisy observation of the transmitted codeword. For a certain range of the noise-to-signal ratios (NSRs) of the transmitter and the jammer, we are able to characterize the capacity of this channel under deterministic encoding or stochastic encoding, i.e., with no common randomness between the encoder/decoder pair. For the remaining NSR regimes, we determine the capacity under the assumption of a small amount of common randomness (at most 2log(n) bits in one sub-regime, and at most Ω(n) bits in the other sub-regime) available to the encoder-decoder pair. Our proof techniques involve a novel myopic list-decoding result for achievability, and a Plotkin-type push attack for the converse in a subregion of the NSRs, both of which may be of independent interest. We also give bounds on the strong secrecy capacity of this channel assuming that the jammer is simultaneously eavesdropping."}],"volume":68,"date_created":"2023-01-16T10:01:19Z","status":"public","external_id":{"arxiv":["1801.05951"],"isi":["000838527100004"]},"intvolume":"        68","citation":{"ieee":"Y. Zhang, S. Vatedka, S. Jaggi, and A. D. Sarwate, “Quadratically constrained myopic adversarial channels,” <i>IEEE Transactions on Information Theory</i>, vol. 68, no. 8. Institute of Electrical and Electronics Engineers, pp. 4901–4948, 2022.","chicago":"Zhang, Yihan, Shashank Vatedka, Sidharth Jaggi, and Anand D. Sarwate. “Quadratically Constrained Myopic Adversarial Channels.” <i>IEEE Transactions on Information Theory</i>. Institute of Electrical and Electronics Engineers, 2022. <a href=\"https://doi.org/10.1109/tit.2022.3167554\">https://doi.org/10.1109/tit.2022.3167554</a>.","short":"Y. Zhang, S. Vatedka, S. Jaggi, A.D. Sarwate, IEEE Transactions on Information Theory 68 (2022) 4901–4948.","ama":"Zhang Y, Vatedka S, Jaggi S, Sarwate AD. Quadratically constrained myopic adversarial channels. <i>IEEE Transactions on Information Theory</i>. 2022;68(8):4901-4948. doi:<a href=\"https://doi.org/10.1109/tit.2022.3167554\">10.1109/tit.2022.3167554</a>","ista":"Zhang Y, Vatedka S, Jaggi S, Sarwate AD. 2022. Quadratically constrained myopic adversarial channels. IEEE Transactions on Information Theory. 68(8), 4901–4948.","mla":"Zhang, Yihan, et al. “Quadratically Constrained Myopic Adversarial Channels.” <i>IEEE Transactions on Information Theory</i>, vol. 68, no. 8, Institute of Electrical and Electronics Engineers, 2022, pp. 4901–48, doi:<a href=\"https://doi.org/10.1109/tit.2022.3167554\">10.1109/tit.2022.3167554</a>.","apa":"Zhang, Y., Vatedka, S., Jaggi, S., &#38; Sarwate, A. D. (2022). Quadratically constrained myopic adversarial channels. <i>IEEE Transactions on Information Theory</i>. Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/tit.2022.3167554\">https://doi.org/10.1109/tit.2022.3167554</a>"},"oa":1,"publication_status":"published","date_published":"2022-08-01T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1801.05951","open_access":"1"}],"publisher":"Institute of Electrical and Electronics Engineers","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"MaMo"}],"publication":"IEEE Transactions on Information Theory","article_type":"original","scopus_import":"1","article_processing_charge":"No","author":[{"full_name":"Zhang, Yihan","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","last_name":"Zhang","first_name":"Yihan"},{"full_name":"Vatedka, Shashank","last_name":"Vatedka","first_name":"Shashank"},{"first_name":"Sidharth","last_name":"Jaggi","full_name":"Jaggi, Sidharth"},{"first_name":"Anand D.","last_name":"Sarwate","full_name":"Sarwate, Anand D."}],"day":"01","title":"Quadratically constrained myopic adversarial channels","arxiv":1,"isi":1,"issue":"8","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1557-9654"],"issn":["0018-9448"]},"doi":"10.1109/tit.2022.3167554","quality_controlled":"1"},{"publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]},"quality_controlled":"1","doi":"10.1109/TIT.2020.3038806","issue":"9","language":[{"iso":"eng"}],"day":"01","author":[{"first_name":"Arman","last_name":"Fazeli","full_name":"Fazeli, Arman"},{"first_name":"Hamed","last_name":"Hassani","full_name":"Hassani, Hamed"},{"last_name":"Mondelli","first_name":"Marco","id":"27EB676C-8706-11E9-9510-7717E6697425","orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco"},{"full_name":"Vardy, Alexander","first_name":"Alexander","last_name":"Vardy"}],"title":"Binary linear codes with optimal scaling: Polar codes with large kernels","arxiv":1,"department":[{"_id":"MaMo"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"IEEE","article_type":"original","article_processing_charge":"No","scopus_import":"1","publication":"IEEE Transactions on Information Theory","publication_status":"published","date_published":"2021-09-01T00:00:00Z","status":"public","external_id":{"arxiv":["1711.01339"]},"citation":{"chicago":"Fazeli, Arman, Hamed Hassani, Marco Mondelli, and Alexander Vardy. “Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2021. <a href=\"https://doi.org/10.1109/TIT.2020.3038806\">https://doi.org/10.1109/TIT.2020.3038806</a>.","ieee":"A. Fazeli, H. Hassani, M. Mondelli, and A. Vardy, “Binary linear codes with optimal scaling: Polar codes with large kernels,” <i>IEEE Transactions on Information Theory</i>, vol. 67, no. 9. IEEE, pp. 5693–5710, 2021.","short":"A. Fazeli, H. Hassani, M. Mondelli, A. Vardy, IEEE Transactions on Information Theory 67 (2021) 5693–5710.","ama":"Fazeli A, Hassani H, Mondelli M, Vardy A. Binary linear codes with optimal scaling: Polar codes with large kernels. <i>IEEE Transactions on Information Theory</i>. 2021;67(9):5693-5710. doi:<a href=\"https://doi.org/10.1109/TIT.2020.3038806\">10.1109/TIT.2020.3038806</a>","apa":"Fazeli, A., Hassani, H., Mondelli, M., &#38; Vardy, A. (2021). Binary linear codes with optimal scaling: Polar codes with large kernels. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2020.3038806\">https://doi.org/10.1109/TIT.2020.3038806</a>","ista":"Fazeli A, Hassani H, Mondelli M, Vardy A. 2021. Binary linear codes with optimal scaling: Polar codes with large kernels. IEEE Transactions on Information Theory. 67(9), 5693–5710.","mla":"Fazeli, Arman, et al. “Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” <i>IEEE Transactions on Information Theory</i>, vol. 67, no. 9, IEEE, 2021, pp. 5693–710, doi:<a href=\"https://doi.org/10.1109/TIT.2020.3038806\">10.1109/TIT.2020.3038806</a>."},"intvolume":"        67","related_material":{"record":[{"status":"public","id":"6665","relation":"earlier_version"}]},"oa_version":"Preprint","type":"journal_article","month":"09","date_updated":"2024-03-07T12:18:50Z","abstract":[{"text":" We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but 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. Our proof is based on the construction and analysis of binary polar codes with large kernels. When communicating reliably at rates within ε>0 of capacity, the code length n often scales as O(1/εμ), where the constant μ is called the scaling exponent. It is known that the optimal scaling exponent is μ=2, and it is achieved by random linear codes. The scaling exponent of conventional polar codes (based on the 2×2 kernel) on the BEC is μ=3.63. This falls far short of the optimal scaling guaranteed by random codes. Our main contribution is a rigorous proof of the following result: for the BEC, there exist ℓ×ℓ binary kernels, such that polar codes constructed from these kernels achieve scaling exponent μ(ℓ) that tends to the optimal value of 2 as ℓ grows. We furthermore characterize precisely how large ℓ needs to be as a function of the gap between μ(ℓ) and 2. The resulting binary codes maintain the recursive structure of conventional polar codes, and thereby achieve construction complexity O(n) and encoding/decoding complexity O(nlogn).","lang":"eng"}],"page":"5693-5710","date_created":"2021-01-10T23:01:18Z","volume":67,"year":"2021","_id":"9002"},{"main_file_link":[{"url":"https://arxiv.org/abs/1406.7373","open_access":"1"}],"date_published":"2018-05-01T00:00:00Z","oa":1,"publication_status":"published","citation":{"short":"M. Mondelli, H. Hassani, R. Urbanke, IEEE Transactions on Information Theory 64 (2018) 3371–3393.","chicago":"Mondelli, Marco, Hamed Hassani, and Rudiger  Urbanke. “How to Achieve the Capacity of Asymmetric Channels.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2018. <a href=\"https://doi.org/10.1109/tit.2018.2789885\">https://doi.org/10.1109/tit.2018.2789885</a>.","ieee":"M. Mondelli, H. Hassani, and R. Urbanke, “How to achieve the capacity of asymmetric channels,” <i>IEEE Transactions on Information Theory</i>, vol. 64, no. 5. IEEE, pp. 3371–3393, 2018.","apa":"Mondelli, M., Hassani, H., &#38; Urbanke, R. (2018). How to achieve the capacity of asymmetric channels. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/tit.2018.2789885\">https://doi.org/10.1109/tit.2018.2789885</a>","ista":"Mondelli M, Hassani H, Urbanke R. 2018. How to achieve the capacity of asymmetric channels. IEEE Transactions on Information Theory. 64(5), 3371–3393.","mla":"Mondelli, Marco, et al. “How to Achieve the Capacity of Asymmetric Channels.” <i>IEEE Transactions on Information Theory</i>, vol. 64, no. 5, IEEE, 2018, pp. 3371–93, doi:<a href=\"https://doi.org/10.1109/tit.2018.2789885\">10.1109/tit.2018.2789885</a>.","ama":"Mondelli M, Hassani H, Urbanke R. How to achieve the capacity of asymmetric channels. <i>IEEE Transactions on Information Theory</i>. 2018;64(5):3371-3393. doi:<a href=\"https://doi.org/10.1109/tit.2018.2789885\">10.1109/tit.2018.2789885</a>"},"related_material":{"record":[{"relation":"earlier_version","id":"6740","status":"public"}]},"extern":"1","intvolume":"        64","status":"public","external_id":{"arxiv":["1406.7373"]},"date_created":"2019-07-24T12:38:49Z","volume":64,"oa_version":"Preprint","type":"journal_article","month":"05","date_updated":"2023-02-23T12:50:46Z","abstract":[{"text":"We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances in coding for symmetric channels help provide more efficient solutions for the asymmetric case. We consider, in more detail, three basic coding paradigms. The first one is Gallager's scheme that consists of concatenating a linear code with a non-linear mapping so that the input distribution can be appropriately shaped. We explicitly show that both polar codes and spatially coupled codes can be employed in this scenario. Furthermore, we derive a scaling law between the gap to capacity, the cardinality of the input and output alphabets, and the required size of the mapper. The second one is an integrated scheme in which the code is used both for source coding, in order to create codewords distributed according to the capacity-achieving input distribution, and for channel coding, in order to provide error protection. Such a technique has been recently introduced by Honda and Yamamoto in the context of polar codes, and we show how to apply it also to the design of sparse graph codes. The third paradigm is based on an idea of Böcherer and Mathar, and separates the two tasks of source coding and channel coding by a chaining construction that binds together several codewords. We present conditions for the source code and the channel code, and we describe how to combine any source code with any channel code that fulfill those conditions, in order to provide capacity-achieving schemes for asymmetric channels. In particular, we show that polar codes, spatially coupled codes, and homophonic codes are suitable as basic building blocks of the proposed coding strategy. Rather than focusing on the exact details of the schemes, the purpose of this tutorial is to present different coding techniques that can then be implemented with many variants. There is no absolute winner and, in order to understand the most suitable technique for a specific application scenario, we provide a detailed comparison that takes into account several performance metrics.","lang":"eng"}],"page":"3371-3393","_id":"6678","year":"2018","quality_controlled":"1","doi":"10.1109/tit.2018.2789885","publication_identifier":{"issn":["0018-9448","1557-9654"]},"issue":"5","language":[{"iso":"eng"}],"title":"How to achieve the capacity of asymmetric channels","arxiv":1,"day":"01","author":[{"full_name":"Mondelli, Marco","orcid":"0000-0002-3242-7020","id":"27EB676C-8706-11E9-9510-7717E6697425","first_name":"Marco","last_name":"Mondelli"},{"full_name":"Hassani, Hamed","first_name":"Hamed","last_name":"Hassani"},{"full_name":"Urbanke, Rudiger ","first_name":"Rudiger ","last_name":"Urbanke"}],"article_type":"original","publication":"IEEE Transactions on Information Theory","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"IEEE"},{"_id":"6730","year":"2017","volume":63,"date_created":"2019-07-30T07:18:11Z","page":"4298-4316","date_updated":"2021-01-12T08:08:43Z","abstract":[{"lang":"eng","text":"We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, our method exploits code symmetry. In particular, the technique applies to any sequence of linear codes where the blocklengths are strictly increasing, the code rates converge, and the permutation group of each code is doubly transitive. In other words, we show that symmetry alone implies near-optimal performance. An important consequence of this result is that a sequence of Reed-Muller codes with increasing block length and converging rate achieves capacity. This possibility has been suggested previously in the literature but it has only been proven for cases where the limiting code rate is 0 or 1. Moreover, these results extend naturally to all affine-invariant codes and, thus, to extended primitive narrow-sense BCH codes. This also resolves, in the affirmative, the existence question for capacity-achieving sequences of binary cyclic codes. The primary tools used in the proof are the sharp threshold property for symmetric monotone Boolean functions and the area theorem for extrinsic information transfer functions."}],"oa_version":"Preprint","month":"07","type":"journal_article","intvolume":"        63","extern":"1","citation":{"short":"S. Kudekar, S. Kumar, M. Mondelli, H.D. Pfister, E. Sasoglu, R.L. Urbanke, IEEE Transactions on Information Theory 63 (2017) 4298–4316.","ieee":"S. Kudekar, S. Kumar, M. Mondelli, H. D. Pfister, E. Sasoglu, and R. L. Urbanke, “Reed–Muller codes achieve capacity on erasure channels,” <i>IEEE Transactions on Information Theory</i>, vol. 63, no. 7. IEEE, pp. 4298–4316, 2017.","chicago":"Kudekar, Shrinivas, Santhosh Kumar, Marco Mondelli, Henry D. Pfister, Eren Sasoglu, and Ridiger L. Urbanke. “Reed–Muller Codes Achieve Capacity on Erasure Channels.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2017. <a href=\"https://doi.org/10.1109/tit.2017.2673829\">https://doi.org/10.1109/tit.2017.2673829</a>.","ista":"Kudekar S, Kumar S, Mondelli M, Pfister HD, Sasoglu E, Urbanke RL. 2017. Reed–Muller codes achieve capacity on erasure channels. IEEE Transactions on Information Theory. 63(7), 4298–4316.","mla":"Kudekar, Shrinivas, et al. “Reed–Muller Codes Achieve Capacity on Erasure Channels.” <i>IEEE Transactions on Information Theory</i>, vol. 63, no. 7, IEEE, 2017, pp. 4298–316, doi:<a href=\"https://doi.org/10.1109/tit.2017.2673829\">10.1109/tit.2017.2673829</a>.","apa":"Kudekar, S., Kumar, S., Mondelli, M., Pfister, H. D., Sasoglu, E., &#38; Urbanke, R. L. (2017). Reed–Muller codes achieve capacity on erasure channels. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/tit.2017.2673829\">https://doi.org/10.1109/tit.2017.2673829</a>","ama":"Kudekar S, Kumar S, Mondelli M, Pfister HD, Sasoglu E, Urbanke RL. Reed–Muller codes achieve capacity on erasure channels. <i>IEEE Transactions on Information Theory</i>. 2017;63(7):4298-4316. doi:<a href=\"https://doi.org/10.1109/tit.2017.2673829\">10.1109/tit.2017.2673829</a>"},"external_id":{"arxiv":["1601.04689"]},"status":"public","date_published":"2017-07-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1601.04689","open_access":"1"}],"oa":1,"publication_status":"published","publication":"IEEE Transactions on Information Theory","publisher":"IEEE","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Reed–Muller codes achieve capacity on erasure channels","arxiv":1,"author":[{"last_name":"Kudekar","first_name":"Shrinivas","full_name":"Kudekar, Shrinivas"},{"full_name":"Kumar, Santhosh","first_name":"Santhosh","last_name":"Kumar"},{"last_name":"Mondelli","first_name":"Marco","id":"27EB676C-8706-11E9-9510-7717E6697425","orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco"},{"first_name":"Henry D.","last_name":"Pfister","full_name":"Pfister, Henry D."},{"full_name":"Sasoglu, Eren","last_name":"Sasoglu","first_name":"Eren"},{"last_name":"Urbanke","first_name":"Ridiger L.","full_name":"Urbanke, Ridiger L."}],"day":"01","language":[{"iso":"eng"}],"issue":"7","doi":"10.1109/tit.2017.2673829","quality_controlled":"1","publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]}},{"_id":"6732","year":"2016","volume":62,"date_created":"2019-07-31T06:03:49Z","page":"6698-6712","date_updated":"2021-01-12T08:08:44Z","abstract":[{"lang":"eng","text":"Consider the transmission of a polar code of block length N and rate R over a binary memoryless symmetric channel W and let P e be the block error probability under successive cancellation decoding. In this paper, we develop new bounds that characterize the relationship of the parameters R, N, P e , and the quality of the channel W quantified by its capacity I(W) and its Bhattacharyya parameter Z(W). In previous work, two main regimes were studied. In the error exponent regime, the channel W and the rate R <; I(W) are fixed, and it was proved that the error probability Pe scales roughly as 2 -√N . In the scaling exponent approach, the channel W and the error probability Pe are fixed and it was proved that the gap to capacity I(W) - R scales as N -1/μ . Here, μ is called scaling exponent and this scaling exponent depends on the channel W. A heuristic computation for the binary erasure channel (BEC) gives μ = 3.627 and it was shown that, for any channel W, 3.579 ≤ μ ≤ 5.702. Our contributions are as follows. First, we provide the tighter upper bound μ <;≤ 4.714 valid for any W. With the same technique, we obtain the upper bound μ ≤ 3.639 for the case of the BEC; this upper bound approaches very closely the heuristically derived value for the scaling exponent of the erasure channel. Second, we develop a trade-off between the gap to capacity I(W)- R and the error probability Pe as the functions of the block length N. In other words, we neither fix the gap to capacity (error exponent regime) nor the error probability (scaling exponent regime), but we do consider a moderate deviations regime in which we study how fast both quantities, as the functions of the block length N, simultaneously go to 0. Third, we prove that polar codes are not affected by error floors. To do so, we fix a polar code of block length N and rate R. Then, we vary the channel W and study the impact of this variation on the error probability. We show that the error probability Pe scales as the Bhattacharyya parameter Z(W) raised to a power that scales roughly like VN. This agrees with the scaling in the error exponent regime."}],"month":"12","type":"journal_article","oa_version":"Preprint","extern":"1","intvolume":"        62","citation":{"chicago":"Mondelli, Marco, S. Hamed Hassani, and Rudiger L. Urbanke. “Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2016. <a href=\"https://doi.org/10.1109/tit.2016.2616117\">https://doi.org/10.1109/tit.2016.2616117</a>.","ieee":"M. Mondelli, S. H. Hassani, and R. L. Urbanke, “Unified scaling of polar codes: Error exponent, scaling exponent, moderate deviations, and error floors,” <i>IEEE Transactions on Information Theory</i>, vol. 62, no. 12. IEEE, pp. 6698–6712, 2016.","short":"M. Mondelli, S.H. Hassani, R.L. Urbanke, IEEE Transactions on Information Theory 62 (2016) 6698–6712.","ama":"Mondelli M, Hassani SH, Urbanke RL. Unified scaling of polar codes: Error exponent, scaling exponent, moderate deviations, and error floors. <i>IEEE Transactions on Information Theory</i>. 2016;62(12):6698-6712. doi:<a href=\"https://doi.org/10.1109/tit.2016.2616117\">10.1109/tit.2016.2616117</a>","apa":"Mondelli, M., Hassani, S. H., &#38; Urbanke, R. L. (2016). Unified scaling of polar codes: Error exponent, scaling exponent, moderate deviations, and error floors. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/tit.2016.2616117\">https://doi.org/10.1109/tit.2016.2616117</a>","ista":"Mondelli M, Hassani SH, Urbanke RL. 2016. Unified scaling of polar codes: Error exponent, scaling exponent, moderate deviations, and error floors. IEEE Transactions on Information Theory. 62(12), 6698–6712.","mla":"Mondelli, Marco, et al. “Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors.” <i>IEEE Transactions on Information Theory</i>, vol. 62, no. 12, IEEE, 2016, pp. 6698–712, doi:<a href=\"https://doi.org/10.1109/tit.2016.2616117\">10.1109/tit.2016.2616117</a>."},"external_id":{"arxiv":["1501.02444"]},"status":"public","date_published":"2016-12-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1501.02444"}],"publication_status":"published","oa":1,"publication":"IEEE Transactions on Information Theory","article_type":"original","publisher":"IEEE","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"title":"Unified scaling of polar codes: Error exponent, scaling exponent, moderate deviations, and error floors","author":[{"last_name":"Mondelli","first_name":"Marco","id":"27EB676C-8706-11E9-9510-7717E6697425","orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco"},{"first_name":"S. Hamed","last_name":"Hassani","full_name":"Hassani, S. Hamed"},{"last_name":"Urbanke","first_name":"Rudiger L.","full_name":"Urbanke, Rudiger L."}],"day":"01","language":[{"iso":"eng"}],"issue":"12","doi":"10.1109/tit.2016.2616117","quality_controlled":"1","publication_identifier":{"eissn":["1557-9654"],"issn":["0018-9448"]}}]