“…Both turbo codes [1] and low-density parity-check (LDPC) codes [2] have been demonstrated to be capacity-approaching channel codes [3], [4]. They have been used in a wide variety of communication and data storage systems [5], including 3G/4G/5G cellular communications, optical communications, and magnetic recording systems, [6], [7], [8]; and various encoder/decoder designs have been proposed [9], [10], [11], [12]. In particular, turbo codes can employ the serial Bahl-Cocke-Jelinek-Raviv (BCJR) computational method in the iterative decoding algorithm to P.W.…”