Involve, A Journal of Mathematics

Absorbing sets are graphical structures that cause iterative decoders to fail. The sets depend on the particular iterative decoding algorithm. In this paper, we consider a variant of the wellstudied Gallager B decoding algorithm for binary low-density parity-check codes. Here, a bit node updates its value according to either the number of or fraction of unsatisfied neighboring check nodes. The traditional Gallager B algorithm is the special case in which half (meaning a fraction of ½) of the check nodes being unsatisfied is required for a bit to change its value. We study absorbing sets in these settings along with the received words which give decoder failure. We determine the how changing the update rules pick up new absorbing sets. This allows for fine-tuning the standard algorithm according to the particular channel or error probability. We also connect these notions to Boolean functions.