Effect of redundancy on syndrome-based decoding for QLDPC codes

Adding redundancy to the parity-check matrix representation has been shown to improve iterative decoder performance in the classical setting due to the consequent removal of small stopping sets or other structures that adversely affect the performance. In this paper, we examine the effect of redundancy on iterative syndrome decoder performance, with the goal of improving decoding for quantum LDPC codes. In particular, we provide a sufficient condition for the graph representation of a code to guarantee that the syndrome decoder converges to the input syndrome for any given input error.