A Deviation-Based Conditional Upper Bound on the Error Floor Performance for Min-Sum Decoding of Short LDPC Codes

Conditional upper bounds are given for min-sum decoding of low-density parity-check codes in the error floor region. It is generally thought that absorbing sets, i.e., small collections of variable nodes connected to a relatively small number of unsatisfied check nodes, are the primary source of errors in the error floor region. The conditional upper bounds presented here are based on the assumption that all error floor errors are caused by absorbing sets. In order to bound the probability of error associated with each absorbing set, a directed-edge Tanner graph is used to link absorbing sets to low-weight deviations. These low-weight deviations result when a proportionally large number of nodes within a stopping set belong to an absorbing set contained inside the stopping set. A complete collection of the most problematic absorbing sets, and the minimum deviation weights that result from them, are used to derive a conditional upper bound on the probability of error for min-sum decoding of low-density parity-check codes. Simulation results are given to demonstrate the accuracy of the bound.