Increasing the rate of spatially-coupled codes via optimized irregular termination

In this paper, we consider the rate-loss problem for spatially-coupled LDPC (SC-LDPC) codes on the binary erasure channel. Although SC-LDPC codes have good noise thresholds under belief-propagation (BP) decoding, they also suffer a rate-loss due to termination that is significant at moderate blocklengths. Our idea is to attach additional variable nodes at the boundary using an irregular degree distribution. Then, this degree distribution is optimized to improve the code rate without reducing the BP threshold. The optimization is formulated as an linear program and solved numerically. Our results show that the code rate can be increased by a reasonable amount without decreasing the BP threshold.