New Classes of LDPC Stabilizer Codes Using Ideas from Matrix Scrambling

This paper proposes efficient construction of new classes of quantum low-density parity-check (LDPC) codes through quasi-cyclic matrices, symmetric matrices and scrambling matrices. Unlike many of the existing quantum LDPC codes, the proposed construction is based on classic binary codes rather than quaternary codes, targets the general stabilizer formalism rather than the special CSS formalism, employs systematic approaches rather than computer search, and generates a rich class of codes of different rates and lengths rather than a single code. Simulations demonstrate that these new codes outperform the existing non-CSS LDPC stabilizer codes reported in literature.