On LDPC Codes and Their Construction

In this paper, we propose a novel method for constructing low-density parity-check (LDPC) codes that relies on circulant permutation matrices as the main principal elements. A key feature of this construction is the intentional avoidance of short cycles, particularly those of length four, which are known to degrade decoding performance. By eliminating these cycles, the approach contributes to lowering both encoding and decoding complexity, making the codes more efficient to implement. To assess their effectiveness, the proposed LDPC codes are evaluated and compared with uncoded binary phase shift keying (BPSK) transmission over an additive white Gaussian noise (AWGN) channel. The simulation outcomes demonstrate that the structured codes deliver competitive results, achieving error-rate performance similar to, and in some instances exceeding, well-known designs such as progressive edge growth (PEG) and quasi-cyclic (QC) codes.