Rate-Compatible Puncturing for Finite-Length Low-Density Parity-Check Codes with Zigzag Parity Structure

In this paper we investigate the puncturing scheme of low-density parity-check code with zigzag parity structure (Z-LDPC code) using the fact that two check nodes can be merged if they are connected to the same parity node. By applying this result to Tanner graph of punctured Z-LDPC code, we can obtain simple Tanner graph, called effective Tanner graph (eTanner graph), which does not include the punctured parity nodes. Based on degree distributions of eTanner graph of punctured Z-LDPC code, we propose a simple algorithm to design good rate-compatible puncturing for finite-length Z-LDPC code. It is shown that the proposed algorithm is the optimal for Z-LDPC code and the designed rate-compatible Z-LDPC code outperforms the rate-compatible Turbo code adopted in 3GPP.