Codebooks of Complex Lines Based on Binary Subspace Chirps

Olav Tirkkonen, Robert Calderbank

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

64 Downloads (Pure)


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.

Original languageEnglish
Title of host publication2019 IEEE Information Theory Workshop, ITW 2019
Number of pages5
ISBN (Electronic)9781538669006
Publication statusPublished - 1 Aug 2019
MoE publication typeA4 Article in a conference publication
EventIEEE Information Theory Workshop - Visby, Sweden
Duration: 25 Aug 201928 Aug 2019


WorkshopIEEE Information Theory Workshop
Abbreviated titleITW


Dive into the research topics of 'Codebooks of Complex Lines Based on Binary Subspace Chirps'. Together they form a unique fingerprint.
  • Coding for Machine-type Communications

    Tirkkonen, O., Singh, B., Vehkalahti, R., Boyd, C., Deng, J., Pääkkönen, J., Liao, J., Pllaha, T. & Shahbaztabar, D.


    Project: Academy of Finland: Other research funding

Cite this