Quasi-cyclic LDPC codes on Latin squares and the ranks of their parity-check matrices

Quasi-cyclic codes are the most promising class of structured LDPC codes due to their ease of implementation and excellent performance over noisy channels when decoded with message-passing algorithms as extensive simulation studies have shown. An approach for constructing quasi-cyclic LDPC codes based on Latin squares over finite fields is presented. By analyzing the parity-check matrices of these codes, expressions for their ranks are derived. Experimental results show that, with iterative decoding algorithms, the constructed codes perform very well over the AWGN and the binary erasure channels.