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Codebooks of Complex Lines Based on Binary Subspace Chirps

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Tirkkonen, Olav
dc.contributor.author Calderbank, Robert
dc.date.accessioned 2021-03-31T06:16:54Z
dc.date.available 2021-03-31T06:16:54Z
dc.date.issued 2019-08-01
dc.identifier.citation Tirkkonen , O & Calderbank , R 2019 , Codebooks of Complex Lines Based on Binary Subspace Chirps . in 2019 IEEE Information Theory Workshop, ITW 2019 . , 8989259 , IEEE , pp. 639-643 , IEEE Information Theory Workshop , Visby , Sweden , 25/08/2019 . https://doi.org/10.1109/ITW44776.2019.8989259 en
dc.identifier.isbn 9781538669006
dc.identifier.other PURE UUID: acfbfd41-faf8-4594-802c-ac73a4c704fb
dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/acfbfd41-faf8-4594-802c-ac73a4c704fb
dc.identifier.other PURE LINK: http://www.scopus.com/inward/record.url?scp=85081108266&partnerID=8YFLogxK
dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/61199006/Tirkkonen_CodebooksofComplexLinesBasedonBinarySubspaceChirps.pdf
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/103467
dc.description.abstract Motivated by problems in machine-type wireless communications, we consider codebooks of complex Grassmannian lines in N = 2m dimensions. Binary Chirp (BC) codebooks of prior art are expanded to codebooks of Binary Subspace Chirps (BSSCs), where there is a binary chirp in a subset of the dimensions, while in the remaining dimensions there is a zero. BSSC codebooks have the same minimum distance as BC codebooks, while the cardinality is asymptotically 2.38 times larger. We discuss how BC codebooks can be understood in terms of a subset of the binary symplectic group Sp(2m, 2) in 2m dimensions; Sp(2m, 2) is isomorphic to a quotient group of the Clifford group acting on the codewords in N dimensions. The Bruhat decomposition of Sp(2m, 2) can be described in terms of binary subspaces in m dimensions, with ranks ranging from r=0 to r=m. We provide a unique parameterization of the decomposition. The BCs arise directly from the full-rank part of the decomposition, while BSSCs are a group code arising from the action of the full group with generic r. The rank of the binary subspace is directly related to the number of zeros (sparsity) in the BSSC. We develop a reconstruction algorithm that finds the correct codeword with O(N log2N) complexity, and present performance results in an additive white Gaussian noise scenario. en
dc.format.extent 5
dc.format.extent 639-643
dc.format.mimetype application/pdf
dc.language.iso en en
dc.relation.ispartof IEEE Information Theory Workshop en
dc.relation.ispartofseries 2019 IEEE Information Theory Workshop, ITW 2019 en
dc.rights openAccess en
dc.title Codebooks of Complex Lines Based on Binary Subspace Chirps en
dc.type A4 Artikkeli konferenssijulkaisussa fi
dc.description.version Peer reviewed en
dc.contributor.department Department of Communications and Networking
dc.contributor.department Duke University
dc.identifier.urn URN:NBN:fi:aalto-202103312740
dc.identifier.doi 10.1109/ITW44776.2019.8989259
dc.type.version acceptedVersion


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