An Introduction to LDPC Codes

Irene Márquez-Corbella, Edgar Martı́nez-Moro

Bane Vasic, Erozan M. Kurtas

Low-density parity-check (LDPC) codes are a class of linear block codes which provide near-capacity performance on a large collection of data transmission and storage channels while simultaneously admitting implementable decoders. LDPC codes were first proposed by Gallager in his 1960 doctoral dissertation [1] and were scarcely considered in the 35 years that followed. One notable exception is the important work of Tanner in 1981 [2] in which Tanner generalized LDPC codes and introduced a graphical representation of LDPC codes, now called Tanner graphs. The study of LDPC codes was resurrected in the mid1990s with the work of MacKay, Luby, and others [3-5] who noticed, apparently independently of the work of Gallager, the advantages of linear block codes which possess sparse (low-density) parity-check matrices.

Henry D. Pfister, Paul H. Siegel

Introduction Sequences of irregular low-density parity-check (LDPC) codes that achieve the capacity of the binary erasure channel (BEC) under iterative decoding were first constructed by Luby, et al. in [11]. This was followed by the work of Chung, et al., which provided evidence suggesting that sequences of iteratively decoded LDPC codes can also achieve the channel capacity of the binary-input additive white Gaussian noise (AWGN) channel [3]. Since then, density evolution (DE) [13] has been used to optimize irregular LDPC codes for a variety of memoryless channels (e.g., [6]), and the results suggest, for each channel, that sequences of iteratively decoded LDPC codes can indeed achieve the channel capacity. In fact, the discovery of a channel whose capacity cannot be approached by LDPC codes would be more surprising than a proof that iteratively decoded LDPC codes can achieve the capacity of any binary-input symmetric channel (BISC). The idea of decoding a code transmitted over a c

Vikram Arkalgud Chandrasetty, Syed Mahfuzul Aziz

Alexios Balatsoukas‐Stimming

Zhewei Tong, Kewu Peng, Zhitong He

Approximately nearest codeword (ANC) is a classic approach for detecting minimum distance of low-density parity-check (LDPC) codes. With the principle of local search, ANC method is capable of detecting minimum distance of LDPC codes within acceptable time. However, the message passing (MP) decoding algorithm and scheduling scheme, as well as the local search strategy, still have much space to improve. To fill the gap, this paper proposes an improved-ANC method which employs novel noise introduction method, decoding algorithm, scheduling scheme and searching strategy, to accelerate the computation of the minimum distance of LDPC codes significantly. Finally, we run simulations on LDPC codes in Wi-Fi5 and 5G-NR standards. The simulation results are presented and demonstrate the effectiveness of our proposal.