On the Application of Error-Correcting Codes with Low-Density Generator Matrix over Different Quantum Channels

Inhalt:
We propose the use of linear codes with low-density generator matrix in the context of error correction over different quantum channels. The basic idea is to construct a Calderbank-Shor-Steane (CSS) code based on the generator matrix and the parity-check matrix of an LDGM code, applying row operations in both matrices to achieve the desired quantum rate. Decoding is performed in an iterative manner, using message passing over the corresponding graphs. The proposed codes allow greater flexibility and are easier to design than existing sparse-graph quantum codes, while leading to better performance.