Shifted Pruning for Path Recovery in List Decoding of Polar Codes

SC List-Flip Decoding of Polar Codes by Shifted Pruning: A General Approach

“…A different metric based on a probability ratio was suggested in [ 15 ]. The approximation of this metric in the log domain is similar to the path metric range (PMR) suggested in [ 12 , 16 , 17 ]. Nevertheless, this metric also suffers from poor performance for relatively long codes.…”

“…Instead of the accurate identification of the bit index, where the correct path is pruned, it was shown in [ 12 ] that when , e.g., , depending on the position of the correct path in the sorted list, it can still avoid the elimination of the correct path, even when the exact elimination index is not among the top T candidate positions for shifting. Figure 2 illustrates an example of elimination due to three penalties at bit , , and , recovered by (right) and (left).…”

“…The metrics proposed in [ 12 , 14 , 15 ] do not provide a good FER performance with medium and long codes. The metric in [ 14 ] computes the probability of finding the correct path among paths at each non-frozen bit position i by summing the probability of each of these paths to be the correct path, i.e., where …”

“…This metric may perform well on short codes, such as P (256,128), but as the numerical results show in [ 14 ], the gain becomes small at longer codes, such as codes with length 1 k bits. The metrics suggested in [ 12 ] also underperform when it comes to longer codes.…”

“…This work was submitted to ITW2019 on 10 April 2019, presented on August 26 in Visby, Sweden, and published on IEEE Xplore on 10 February 2020. Later, this scheme was improved in [ 12 ] by employing a computationally simple LLR-based metric and a variable (e.g., ). The variable shift could correct the error by finding an approximate location of the elimination of the correct path.…”