Optimization of LDGM-based quantum codes using Density Evolution

We introduce the use of Discrete Density Evolution (DDE) to optimize LDGM-based quantum codes. These are Calderbank-Shor-Steane (CSS) codes based on the generator and parity-check matrices of an LDGM code, which is designed with a specific structure inspired in the parallel concatenation of LDGM codes. The proposed codes allow greater flexibility and are easier to design than existing sparse-graph CSS quantum codes, while leading to better performance.