A Tree Pruning Technique for Decoding Complexity Reduction of Polar Codes and PAC Codes

TL;DR

This paper proposes a pruning technique for SCL decoding of polar and PAC codes that reduces sorting operations and computational complexity without sacrificing error-correction performance, based on bit-metric analysis.

Contribution

It introduces a novel pruning method leveraging bit-metric properties to decrease sorting in SCL decoding of polar and PAC codes, improving efficiency.

Findings

Significant reduction in sorting operations during decoding.

Pruning probability decreases exponentially with threshold.

Maintains error-correction performance despite pruning.

Abstract

Sorting operation is one of the main bottlenecks for the successive-cancellation list (SCL) decoding. This paper introduces an improvement to the SCL decoding for polar and pre-transformed polar codes that reduces the number of sorting operations without degrading the code's error-correction performance. In an SCL decoding with an optimum metric function we show that, on average, the correct branch's bit-metric value must be equal to the bit-channel capacity, and on the other hand, the average bit-metric value of a wrong branch can be at most zero. This implies that a wrong path's partial path metric value deviates from the bit-channel capacity's partial summation. For relatively reliable bit-channels, the bit metric for a wrong branch becomes very large negative number, which enables us to detect and prune such paths. We prove that, for a threshold lower than the bit-channel cutoff rate, the probability of pruning the correct path decreases exponentially by the given threshold. Based on these findings, we presented a pruning technique, and the experimental results demonstrate a substantial decrease in the amount of sorting procedures required for SCL decoding. In the stack algorithm, a similar technique is used to significantly reduce the average number of paths in the stack.