System and Method for Determining Quasi-Cyclic Low-Density Parity-Check Codes Having High Girth

A method for determining a quasi-cyclic (QC) low-density parity-check (LDPC) code corresponding to a protograph represented by a connectivity matrix, such that

• duplicating at least several elements of the connectivity matrix along at least one line of duplication to produce an inflated connectivity matrix, wherein values of the at least several elements in the connectivity matrix form a pattern indicated by the predetermined girth;
• determining a hierarchical quasi-cyclic (HQC) LDPC code corresponding to the inflated connectivity matrix, where in the HQC LDPC code is represent by a matrix of circulant sub-matrices;
• and
• removing the at least several elements of the matrix representing the HQC LDPC code, such that the matrix is squashed along the line of duplication to produce the QC LDPC code, wherein the steps of the method are performed by a processor.