Construction of IRA-LDPC codes based on identity column vectors

A random-like framework of the IRA-LDPC codes based on the identity column vectors (ICV) was defined and created. A new family of the IRA-LDPC codes under the constraint of the framework was investigated using algebraic and random methods. Its structural features is that the large-sized sparse parity check matrix H
^d
corresponding to the information bits is extruded into two smaller-sized easy-to-compute matrices, respectively called base matrix and position matrix. The minimum decomposable unit of the parity-check matrix H is the ICV which can provide a wider selection range of code rates than the most extensively studied QC-LDPC codes. Some conditions for the IRA-LDPC code not to have any 4-girth were considered.