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Quantum low-density parity-check (QLDPC) codes are among the most promisingcandidates for future quantum error correction schemes. However, a limitednumber of short to moderate-length QLDPC codes have been designed and theirdecoding performance is sub-optimal with a quaternary belief propagation (BP)decoder due to unavoidable short cycles in their Tanner graphs. In this paper,we propose a novel joint code and decoder design for QLDPC codes. Theconstructed codes have a minimum distance of about the square root of the blocklength. In addition, it is, to the best of our knowledge, the first QLDPC codefamily where BP decoding is not impaired by short cycles of length 4. This isachieved by using an ensemble BP decoder mitigating the influence of assembledshort cycles. We outline two code construction methods based on classicalquasi-cyclic codes and finite geometry codes. Numerical results demonstrateoutstanding decoding performance over depolarizing channels.

A Joint Code and Belief Propagation Decoder Design for Quantum LDPC Codes