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Abstract
Motivated by problems in machinetype wireless communications, we consider codebooks of complex Grassmannian lines in N = 2^{m} 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 fullrank 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 log^{2}N) complexity, and present performance results in an additive white Gaussian noise scenario.
Original language  English 

Title of host publication  2019 IEEE Information Theory Workshop, ITW 2019 
Publisher  IEEE 
Pages  639643 
Number of pages  5 
ISBN (Electronic)  9781538669006 
DOIs  
Publication status  Published  1 Aug 2019 
MoE publication type  A4 Article in a conference publication 
Event  IEEE Information Theory Workshop  Visby, Sweden Duration: 25 Aug 2019 → 28 Aug 2019 
Workshop
Workshop  IEEE Information Theory Workshop 

Abbreviated title  ITW 
Country  Sweden 
City  Visby 
Period  25/08/2019 → 28/08/2019 
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Projects
 1 Finished

Coding for Machinetype Communications
Pääkkönen, J., Deng, J., Tirkkonen, O., Singh, B., Boyd, C., Pllaha, T. & Liao, J.
01/09/2016 → 31/08/2020
Project: Academy of Finland: Other research funding