Adaptive decoding algorithms for LDPC codes with redundant check nodes

This paper is concerned with decoding of algebraic low-density parity-check (LDPC) codes that are constructed based on finite fields and finite geometries. The parity-check matrices of such codes usually have redundant rows. Equivalently, their Tanner graphs have redundant check nodes. Based on this property, we propose an adaptive decoding algorithm. In the adaptive decoding algorithm, all the check nodes are classified into active nodes and silent nodes according to certain criteria, and only active check nodes are involved in the iterative procession. That is, each variable node collects messages from active check nodes and passes the extrinsic messages to its active neighbors. Two approaches to select the active check nodes are presented. Simulation results show that, the adaptive decoding algorithm can make a trade-off between the complexity and the performance.