A Low-Complexity Ordered Statistic Decoding of Short Block Codes

Local Constraint-Based Ordered Statistics Decoding for Short Block Codes

“…In this section, we present simulation results to demonstrate the performance of the PC-GRAND algorithm. The SGRAND algorithm [14] and LC-OSD algorithm [10] are also implemented for comparison.…”

“…The FER LC-OSD and SGRAND. We denote by δ the number of partial constraints for PC-GRAND and local constraints for LC-OSD [10].…”

“…Generally, the FER can be improved as δ grows. Also notice that, the performance of FER can hardly be improved as δ grows when δ > 6. for PC-GRAND (δ = 6, ℓmax = 10 6 ), LC-OSD [10] (δ = 8, ℓmax = 16384) and SGRAND [14] (ℓmax = 10 6 ). The ML simulation results [10] are also plotted.…”

“…Example 2. We compare the performance of PC-GRAND (δ = 6, ℓ max = 10 6 ), LC-OSD [10] (δ = 8, ℓ max = 16384) and SGRAND [14] (ℓ max = 10 6 ) for CA-polar code C [128, 105] and Bose-Chaudhuri-Hocquenghem (BCH) code C [127,113]. The simulation results are shown in Fig.…”

“…So the OSD is more promising for short block codes, and many efforts have been paid to reduce the complexity [3]- [8]. Recently, a new variant of the OSD algorithm called locally constrained OSD (LC-OSD) with much lower time complexity is investigated in [9], [10]. Instead of order-t reprocessing on the most reliable independent bits, the LC-OSD searches for test error patterns using the serial list Viterbi algorithm (SLVA) [11] over a trellis specified by a locally constrained parity-check matrix.…”