absorptionset

Absorption set, often referred to as an absorption set, is a concept used in coding theory, particularly in the study of iterative decoding of LDPC codes. It denotes a small subgraph of a code’s Tanner graph consisting of a set S of variable nodes with a characteristic pattern of neighboring check nodes. The exact definition varies by source, but a common framing is that AS(a,b) represents a subgraph with a variable-node set of size a that is adjacent to b neighboring checks that are unsatisfied or have a parity relation that reinforces the erroneous configuration.

The key idea is that, during belief-propagation or min-sum decoding, the messages that circulate within the absorption set tend to reinforce an incorrect state. Because the external checks are predominantly satisfied, the decoder’s updates for the nodes in S remain biased toward the wrong values, causing the decoder to become trapped and fail to converge to the correct codeword. This trapping behavior is central to the concept of the absorption set.

Absorption sets are studied because they contribute to the error floor of LDPC codes—the decline in performance at high signal-to-noise ratios where rare, structured error patterns dominate. Understanding the structure and parameters of absorption sets helps code designers assess vulnerability and explore remedies, such as changing degree distributions, modifying decoding algorithms, or adding post-processing steps to escape traps.

Notes: The terminology can vary in the literature; some sources use “absorbing set” or relate the concept to trapping sets and stopping sets. While AS is most commonly discussed in LDPC decoding contexts, the general idea of a subgraph that traps iterative updates appears in related coding and graph-based analyses.