Constructing LDPC Codes with Any Desired Girth

In wireless sensor networks, the reliability of communication can be greatly improved by applying low-density parity-check (LDPC) codes. Algorithms based on progressive-edge-growth (PEG) pattern and quasi-cyclic (QC) pattern are the mainstream approaches to constructing LDPC codes with good performance. However, these algorithms are not guaranteed to remove all short cycles to achieve the desired girth, and their excellent inputs are difficult to obtain. Herein, we propose an algorithm, which must be able to construct LDPC codes with the girth desired. In addition, the optimal input to the proposed algorithm is easy to find. Theoretical and experimental evidence of this study shows that the LDPC codes we construct have better decoding performance and less power consumption than the PEG-based and QC-based codes.