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In this work, we propose a fully differentiable iterative decoder for quantumlow-density parity-check (LDPC) codes. The proposed algorithm is composed ofclassical belief propagation (BP) decoding stages and intermediate graph neuralnetwork (GNN) layers. Both component decoders are defined over the same sparsedecoding graph enabling a seamless integration and scalability to large codes.The core idea is to use the GNN component between consecutive BP runs, so thatthe knowledge from the previous BP run, if stuck in a local minima caused bytrapping sets or short cycles in the decoding graph, can be leveraged to betterinitialize the next BP run. By doing so, the proposed decoder can learn tocompensate for sub-optimal BP decoding graphs that result from the designconstraints of quantum LDPC codes. Since the entire decoder remainsdifferentiable, gradient descent-based training is possible. We compare theerror rate performance of the proposed decoder against various post-processingmethods such as random perturbation, enhanced feedback, augmentation, andordered-statistics decoding (OSD) and show that a carefully designed trainingprocess lowers the error-floor significantly. As a result, our proposed decoderoutperforms the former three methods using significantly fewer post-processingattempts. The source code of our experiments is available online.

Graph Neural Networks for Enhanced Decoding of Quantum LDPC Codes