A Novel Concatenation Scheme of Protograph-Based LDPC Codes and Markers for Recovering Synchronous Errors

For insertion and deletion channels, there are many coding schemes based on low-density parity-check (LDPC) codes, such as spatially coupled (SC) LDPC codes and concatenated codes of irregular LDPC codes and markers. However, most of the previous works have problems, such as poor finite-length performance and unrealistic settings for codeword lengths and decoding iterations. Moreover, when using markers, the decoder receives log-likelihood (LLR) messages with different statistics depending on code bit position. In this paper, we propose a novel concatenation scheme using protograph-based LDPC code and markers that offers excellent asymptotic/finite-length performance and a structure that controls the irregularity of LLR messages. We also present a density evolution analysis and a simple optimization procedure for the proposed concatenated coding scheme. For two decoding scenarios involving decoding complexity, both asymptotic decoding thresholds and finite-length performance demonstrate that the newly designed concatenated coding scheme outperforms the existing counterparts: the irregular LDPC code with markers, the SC-LDPC code, and the protograph LDPC code, which is optimized for an additive white Gaussian noise channel, with markers.