Hierarchical Interleaving and Chained Recovery Schemes of LDPC Codes for Noisy Insertion and Deletion Channels

Abstract

Error-correcting codes for insertion and deletion (ID) errors have attracted considerable attention because of their potential in future communication and storage systems. Existing schemes based on modern coding approaches approach the information-theoretical limits of an ID channel. However, a scheme that universally performs well across various channel impairments, such as Gaussian noise and bit-flipping noise, is yet to be established. In this study, we proposed a novel coding scheme for cascaded ID-noisy channels. The scheme manages the transmission of multiple codewords using a low-density parity-check code. In the transmitter, a two-stage hierarchical interleaving with the codewords is used, whereas in the receiver, an efficient decoding strategy is used to sequentially estimate the original codewords with a decoding delay. We evaluated the performance of the proposed scheme through achievable information rates, asymptotic analysis, and numerical simulations. The results demonstrated that the proposed scheme achieved universal performance over ID-noisy channels with reduced complexity. Furthermore, to improve performance within the constraints of limited complexity and latency, we proposed an optimization method specifically for the proposed scheme.

Keywords

• Achievable information rates (AIRs)
• low-density parity-check (LDPC) code
• noisy insertion and deletion channels
• spatially coupled code
• synchronization marker