Effective identification of dominant fully absorbing sets for Raptor‐like LDPC codes

Abstract

AbstractThe error‐rate floor of low‐density parity‐check (LDPC) codes is attributed to the trapping sets of their Tanner graphs. Among them, fully absorbing sets dominantly affect the error‐rate performance, especially for short blocklengths. Efficient methods to identify the dominant trapping sets of LDPC codes were thoroughly researched as exhaustively searching them is NP‐hard. However, the existing methods are ineffective for Raptor‐like LDPC codes, which have many types of trapping sets. An effective method to identify dominant fully absorbing sets of Raptor‐like LDPC codes is proposed. The search space of the proposed algorithm is optimized into the Tanner subgraphs of the codes to afford time‐efficiency and search‐effectiveness. For 5G New Radio (NR) base graph (BG) 2 LDPC codes for short blocklengths, the proposed algorithm finds more dominant fully absorbing sets within one seventh of the computation time of the existing search algorithm, and its search‐effectiveness is verified using importance sampling. The proposed method is also applied to 5G NR BG1 LDPC code and Advanced Television Systems Committee 3.0 type A LDPC code for large blocklengths.