VN-Based Tail-Biting Globally-Coupled LDPC Codes

In this paper, we propose a new class of globally coupled low-density parity-check (GC-LDPC) codes, referred to as variable node (VN) based tail-biting (TB) GC-LDPC codes. Unlike conventional check node (CN) based GC-LDPC codes, which rely on the global CNs for coupling, the proposed codes employ global VNs for the coupling with a TB structure. The innovative coupling structure not only eliminates the rate loss problem inherent in CN-based GC-LDPC codes but also provides greater flexibility in adjusting the degree distribution. Moreover, the TB structure can significantly reduce the hardware complexity of the encoder and decoder of the VN-based TB-GC-LDPC code, making them more practical for implementation. To construct the VN-based TB-GC-LDPC codes, we present two methods based on optimizing girth and degree distributions, respectively. In addition, we introduce the low-complexity encoding scheme and decoding scheme tailored to the special structure of the VN-based TB-GC-LDPC codes. Specifically, the proposed merry-go-round (MGR) component-code-based (CCB) decoding scheme can achieve the global coding gain of the time-invariant VN-based TB-GC-LDPC codes. Simulation results demonstrate that the proposed codes not only outperform existing CN-based GC-LDPC codes but also achieve comparable performance to advanced LDPC codes, such as 5G-LDPC codes, while requiring lower hardware implementation complexity.