--- res: bibo_abstract: - Consider the problem of constructing a polar code of block length N for the transmission over a given channel W. Typically this requires to compute the reliability of all the N synthetic channels and then to include those that are sufficiently reliable. However, we know from [1], [2] that there is a partial order among the synthetic channels. Hence, it is natural to ask whether we can exploit it to reduce the computational burden of the construction problem. We show that, if we take advantage of the partial order [1], [2], we can construct a polar code by computing the reliability of roughly N/ log 3/2 N synthetic channels. Such a set of synthetic channels is universal, in the sense that it allows one to construct polar codes for any W, and it can be identified by solving a maximum matching problem on a bipartite graph. Our proof technique consists in reducing the construction problem to the problem of computing the maximum cardinality of an antichain for a suitable partially ordered set. As such, this method is general and it can be used to further improve the complexity of the construction problem in case a new partial order on the synthetic channels of polar codes is discovered.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Marco foaf_name: Mondelli, Marco foaf_surname: Mondelli foaf_workInfoHomepage: http://www.librecat.org/personId=27EB676C-8706-11E9-9510-7717E6697425 orcid: 0000-0002-3242-7020 - foaf_Person: foaf_givenName: S. Hamed foaf_name: Hassani, S. Hamed foaf_surname: Hassani - foaf_Person: foaf_givenName: Rudiger foaf_name: Urbanke, Rudiger foaf_surname: Urbanke bibo_doi: 10.1109/isit.2017.8006850 dct_date: 2017^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/2157-8117 - http://id.crossref.org/issn/9781509040964 dct_language: eng dct_publisher: IEEE@ dct_title: Construction of polar codes with sublinear complexity@ ...