Message Flow Analysis in Practical LDPC Decoders for the Interpretation of Absorbing Set Thresholds

Absorbing sets (ASs) cause the error floor phenomenon in many low-density parity-check (LDPC) codes by entrapping iterative decoders. A recent simplified system model for practical min-sum (MS) LDPC decoding predicts that if all variable nodes in an AS have channel messages above a certain threshold, the AS cannot entrap the decoder. The threshold is an AS parameter that depends on its Tanner graph, and is the result of a nonlinear optimization. In this paper, we analyze the messages exchanged in the directed graph (digraph) of the AS during MS decoding while evaluating the AS threshold. By doing this, we unveil the meaning of the threshold value, which is the minimum channel message for which positive feedback loops in the digraph involve all the messages exchanged.