Low-Complexity Linear Programming Based Decoding of Quantum LDPC codes

Abstract

This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear programming (SB-LP) decoding algorithm is proposed, and second, the proposed SB-LP is applied as a post-processing step after syndrome-based min-sum (SB-MS) decoding. For the latter case, a new early stopping criterion is introduced to decide when to activate the SB-LP algorithm, avoiding executing a predefined maximum number of iterations for the SB-MS decoder. Simulation results show, for a sample hypergraph code, that the proposed decoder can lower the error floor by two to three orders of magnitude compared to SB-MS for the same total number of decoding iterations.