Notes: Finite-length Protograph-based Spatially Coupled LDPC Codes

The finite-length performance of multi-edge spatially coupled low-density parity-check (SC-LDPC) codes is analyzed over the binary erasure channel (BEC). Existing scaling laws are extended to arbitrary protograph base matrices including puncturing patterns and multiple edges between nodes. Compared to more involved rate-1/2 structures proposed to improve the threshold to minimum distance trade-off, constructions based on regular (4, 8) protograph LDPC block codes work suprisingly well in the waterfall region. We design codes using scaling laws and estimate the block length an SC-LDPC code to match the performance of another given code. We also estimate the performance degradation if the chain length varies.