Design of Spatially Coupled LDPC Codes based on Symbolic Hyper-Graphs

We consider a special family of spatially coupled low-density parity-check (LDPC) codes known as LDPC convolutional codes and propose a design technique based on symbolic hyper-graphs aimed at achieving good codes with small syndrome former memory order. We define conditions on the minimum syndrome former memory order that must be imposed in order to avoid short local cycles in the codes Tanner graphs and to achieve good minimum distance. Code design examples are provided, accompanied by error rate performance assessments based on Montecarlo simulations.