Quantum Codes in Classical Communication: A Space-Time Block Code From Quantum Error Correction

We propose a general framework for noncoherent communication using techniques from the field of quantum error correction (QEC). We first propose an approach for analyzing a classical communication channel as a quantum channel, and develop an extension of the QEC conditions to the classical case. We derive a quantum analogue of the noncoherent multiantenna wireless channel. Restricting to the case in which the number of transmitter and receiver antennas are equal and a power of two, we use the framework to develop a family of space-time block codes for noncoherent multiple-input multiple-output (MIMO) communication. Under a Rayleigh fading assumption, we derive the optimal decoder and bound the probability of symbol detection error. We compare our performance to comparable coherent and noncoherent approaches and achieve competitive performance for various antenna geometries and rates.