Recursive encoding of spatially coupled LDPC codes with arbitrary rates

Spatially coupled LDPC codes have attracted much attention due to the promising performance. Recursive encoding with low delay and low complexity has been proposed in the literature for selected node degrees. To realize the recursive encoding of spatially coupled LDPC codes with arbitrary rates, we propose in this paper a modified structure of the parity-check matrix and implement the encoding using a shift-register regardless of the node degrees. By rearranging the edge connections, the parity bits at each coupling position can be jointly determined by the information bits at the current position and the encoded bits at former positions. Performance analysis in terms of design rate and density evolution has been provided. It can be observed that the modified code structure leads to a better belief-propagation threshold. Finite-length simulation results are provided, which verify the theoretical analysis.