|Reconstruction of Multi-user Binary Subspace Chirps
|Tefjol Pllaha, Olav Tirkkonen, Aalto University, Finland; Robert Calderbank, Duke University, United States
|C.10: Topics in Coding Theory
|Coding for Communications
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|We consider codebooks of Complex Grassmannian Lines consisting of Binary Subspace Chirps (BSSCs) in $N = 2^m$ dimensions. BSSCs are generalizations of Binary Chirps (BCs), their entries are either fourth-roots of unity, or zero. BSSCs consist of a BC in a non-zero subspace, described by an on-off pattern. Exploring the underlying binary symplectic geometry, we provide a uniﬁed framework for BSSC reconstruction—both on-off pattern and BC identiﬁcation are related to stabilizer states of the underlying Heisenberg-Weyl algebra. In a multi-user random access scenario we show feasibility of reliable reconstruction of multiple simultaneously transmitted BSSCs with low complexity.