Applying QC-LDPC codes with girth 12 Irregular Frame error rate performance, using QR decomposition technique in Water fall region

Abstract

This paper proposes the QR factorization (decomposition) of submatrices, circulant shifting, and random permutation based on formulation of irregular Quasi- Cyclic (QC) and Low-Density Parity-Check (LDPC) codes for higher code lengths.With circulant permutation matrices QC-LDPC is protograph code having every subgraph pattern with inescapable cycles of length is found in this correspondence.It involves decomposing submatrices into upper orthogonal and lower triangular forms to construct the parity-check matrix.Comparative analysis with existing codes demonstrates that the proposed construction methods are more efficient in reducing the density of frame error rate performance in the waterfall region.The decomposition QR method code reduces the sparse behaviour of the constructed QC-LDPC code, helping to improve 30–45% FER when compared to the previously published results. QR decomposition offers numerical stability and is employed in solving linear least squares problems for rapid decoding, particularly for non-binary or specialized structures, contributing to the maintenance of a low error floor.