Edge-Coloring Technique to Analyze Elementary Trapping Sets of Spatially-Coupled LDPC Convolutional Codes

In this letter, for the first time, an edge-coloring technique is proposed to characterize a certain elementary trapping set (ETS) and to obtain sufficient conditions to avoid small ETSs from occurrence in the Tanner graph of SC-LDPC convolutional codes. This technique is applicable to all protograph-based LDPC codes with different girths whose protographs are single-edge, that is, the entries of their base matrices are 0, 1. To further demonstrate the effectiveness of our proposed technique, we apply it to Time-Invariant SC-LDPC-CCs with girths 6 and 8 and column weights up to 5.