  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.
