On the Stopping Distance of SA-LDPC Codes by Transversal Designs

In this paper, we analyze the size of the smallest stopping set (called the stopping distance) for the parity-check matrix of a superposed array low-density parity-check (SA-LDPC) code for column weights 3 and 4 by using the transversal design (TD) concept. An SA-LDPC code is obtained as the result of an n-fold recursive product operation (a superposition method) on the parity-check matrix of an array low-density parity-check (array LDPC) code, Hn(m, q), where n ≥ 2 and m and q are column and row weights, respectively. We provide the lower and upper bounds for the stopping distance of these codes. Our simulation result shows that the SA-LDPC codes can compete with the TD-LDPC codes, random LDPC codes, and lattice LDPC codes of comparable rates and lengths and can improve the error floor region of the bit error rate curve.