Protograph Quantum LDPC Codes from Tensor Product of Parity-Check Matrices

We propose two constructions, namely Construction 1 and Construction 2, for the design of protograph quantum LDPC codes by exploiting conventional quasi cyclic protograph LDPC codes with lift operation, and tensor product operation, respectively. We show that by carefully designing the proto-matrix using quadratic residue sets of parameters p = 4n ± 1, the proposed Construction 1 yields protograph quantum LDPC codes of various rates. Furthermore, by performing tensor product between two non-binary parity-check matrices obtained from idempotent polynomials of a quadratic residue set, the proposed Construction 2 yields a class of protograph quantum LDPC codes with rate at least 0.9. The performance of the proposed codes over quantum depolarizing channel with iterative sum-product decoding algorithm is shown.