Syndrome Decoder Error Characterization For Some Qldpc Codes

Iterative decoder failures of quantum low density parity check (QLDPC) codes are attributed to substructures in the code’s graph, known as trapping sets, as well as degenerate errors that can arise in quantum codes. Failure inducing sets are subsets of codeword coordinates that, when initially in error, lead to decoding failure in a trapping set. In this talk, we examine failure inducing sets of QLDPC codes under syndrome-based iterative decoding. We show how redundancy can affect the presence of these sets for some families of QLPDC codes. In particular, we provide a graph condition that guarantees no syndrome mismatch, thereby giving insight to how to add redundancy to improve the decoder performance.