A Grassmannian Packing Based on the Nordstrom-Robinson Code

We construct new families of Grassmannian packings associated with the binary Nordstrom-Robinson code. The constituent subspaces are associated with projection operators which which arise in the theory of quantum stabilizer codes. These Grassmannian packings find application as highly structured of dictionaries that admit fast algorithms for identifying sparse representations, and in noncoherent wireless communication with multiple antennas. The capacity of the noncoherent MIMO channel at both low and moderate SNR (under the constraint that only isotropically distributed unitary matrices are used for information transmission) is closely approximated by these packings.