Efficient Generation of Puncturing-Assisted Rate-Matched 5G New Radio LDPC Codes for Faster-Than-Nyquist Signaling

Abstract

—This paper presents a comprehensive analysis of the utilization of rate-matched 5G New Radio (NR) Low-Density Parity Check (LDPC) codes for decoding faster-than-Nyquist signaled data symbols in an Additive White Gaussian Noise (AWGN) channel. The rate-matching techniques employing message-bit and parity-bit puncturing are thoroughly explained, showcasing the applications of various rates during the coding process. Moreover, in conjunction with the aforementioned rate-matching and puncturing methods, a puncturing scheme is employed on the first two columns of the parity-check matrix derived from the 5G NR LDPC base graphs. The performance of the 5G NR LDPC code, integrated as the outer decoder in turbo equalization for faster-than-Nyquist signaled data symbols, is thoroughly investigated. The achieved results are compared with the performance of convolutional codes implemented in the same system setup and operating at identical code rates. By analyzing the employment of rate-matched 5G NR LDPC codes, this paper provides valuable insights into their efficacy for decoding faster-than-Nyquist signaled data symbols in the AWGN channel. The comparison with convolutional codes offers a benchmark for performance evaluation, facilitating a deeper understanding of the benefits and trade-offs associated with each coding scheme.