Efficient construction of LDPC (Low Density Parity Check) codes with corresponding parity check matrix having CSI (Cyclic Shifted Identity) sub-matrices. These constructed LDPC codes can be implemented in multiple-input-multiple-output (MIMO) communication systems. One LDPC code construction approach uses CSI sub-matrix shift values whose shift values are checked instead of non-zero element positions within the parity check matrix (or its corresponding sub-matrices). When designing an LDPC code, this approach is efficient to find and avoid cycles (or loops) in the LDPC code's corresponding bipartite graph. Another approach involves GRS (Generalized Reed-Solomon) code based LDPC code construction. These LDPC codes can be implemented in a wide variety of communication devices, including those implemented in wireless communication systems that comply with the recommendation practices and standards being developed by the IEEE 802.11n Task Group (i.e., the Task Group that is working to develop a standard for 802.11 TGn (High Throughput)).