“…In 1962, R. Gallager introduced the first classical LDPC codes [ 41 ], and it was rediscovered again by MacKay in the late 1990s [ 42 ]. In 2018, the 3rd Generation Partnership Project (3GPP) chose QC-LDPC codes as the standard codes for 5G networks and applications based on the properties and characteristics of classical LDPC codes, especially for a short-length frame with lower processing throughput for uRLLC and the mMTC or massive Machine-to-Machine (mM2M) communications [ 32 , 34 , 43 , 44 , 45 ]. Moreover, the authors in [ 46 , 47 , 48 ] showed that 5G QC-LDPC codes are also an optimised design for short-packet transmission because of the low error floor and high-speed transmission.…”