Combinatorial Properties as Predictors for the Performance of the Sum-Product Algorithm

We examine various algebraic/combinatorial properties of Low-Density Parity-Check codes as predictors for the performance of the sum-product algorithm on the AWGN channel in the error floor region. We consider three families of check matrices, two algebraically constructed and one sampled from an ensemble, expurgated to remove short cycles. The three families have similar properties, all are (3; 6)-regular, have girth 8, and have code length roughly 280. The best predictors are small trapping sets, and the predictive value is much higher for the algebraically constructed families than the random ones.