Layered Decoding of Quantum LDPC Codes

We address the problem of doing message passing based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling, the usual scheduling on parallel architectures. A generic construction is given to construct layers of hypergraph product codes. In the process, we introduce two new notions, t-covering layers which is a generalization of the usual layer decomposition, and a modified scheduling called random order scheduling. Numerical simulations show that the random ordering is of independent interest as it helps relieve the high error floor typical of message passing decoders on quantum codes for both layered and serial decoding without the need of post-processing.