High-Rate Spatially Coupled LDPC Codes Based on Massey's Convolutional Self-Orthogonal Codes

We propose a new class of high-rate spatially coupled LDPC (SC-LDPC) codes based on the convolutional selforthogonal codes (CSOCs) first introduced by Massey. The SCLDPC codes are constructed by treating the irregular graph corresponding to the parity-check matrix of a systematic rate $R=(n-1) / n$ CSOC as a convolutional protograph. The protograph can then be lifted using permutation matrices to generate a high-rate SC-LDPC code whose strength depends on the lifting factor. The SC-LDPC codes constructed in this fashion can be decoded using iterative belief propagation based sliding window decoding. To improve performance, a non-systematic version of a C SOC parity-check matrix is then proposed by making a slight modification to the systematic construction. Even though the parity-check matrix is in non-systematic form, we show how systematic encoding can still be performed. We also show that the non-systematic convolutional protograph has a guaranteed girth and free distance and that these properties carry over to the lifted versions. Numerical results are included demonstrating that CSOC-based SC-LDPC codes (i) have performance at least as good as that of SC-LDPC codes commonly found in the literature, and (ii) have iterative decoding thresholds comparable to those of existing SC-LDPC code designs.