Space-Time Reed-Muller Codes for Noncoherent MIMO Transmission

We present a family of Space-Time codes for the noncoherent MIMO channel. The codes are constructed via functions that can be considered as a generalization of boolean functions to commuting projection operators which arise in the theory of quantum stabilizer codes. These space-time codes are strongly related to standard binary Reed-Muller codes. In particular, they can be decoded by adapting a decoding algorithm for Reed-Muller codes. We show that the first subclass of codes from this family, which we view as the first order space-time Reed-Muller codes, allow transmission with rates close to the MIMO noncoherent channel capacity in the low signal to noise ratio (SNR) regime.