Absorbing sets and cycles

Absorbing sets have been identified as structures in the graph of a low-density parity-check code that cause error floors - in particular in combination with binary message passing decoding algorithms. In this paper it is shown that absorbing sets involving only variable nodes up to degree 3 are equivalent to cycles and a sufficient and necessary condition on the degree distribution to avoid these absorbing sets is derived. The results are extended to irregular graphs and simulation results demonstrate the improvement in the error floor region.