  Short- to medium-block-length polar-like and polarization-adjusted
convolutional (PAC) codes have demonstrated exceptional error-correction
performance through sequential decoding. Successive cancellation list (SCL)
decoding of polar-like and PAC codes can potentially match the performance of
sequential decoding though a relatively large list size is often required. By
benefiting from an optimal metric function, sequential decoding can find the
correct path corresponding to the transmitted data by following almost one path
on average at high Eb/N0 regimes. When considering a large number of paths in
SCL decoding, a main bottleneck emerges that is the need for a rather expensive
sorting operation at each level of decoding of data bits. In this paper, we
propose a method to obtain the optimal metric function for each depth of the
polarization tree through a process that we call polarization of the metric
function. One of the major advantages of the proposed metric function is that
it can be utilized in fast SC-based (FSC) and SCL-based (FSCL) decoders, i.e.,
decoders that opt to skip the so-called rate-1 and rate-0 nodes in the binary
tree representation for significantly more efficient implementation.
Furthermore, based on the average value of the polarized metric function of
FSC-based decoders, we introduce a pruning technique that keeps only the paths
whose metric values are close to the average value. As a result, our proposed
technique significantly reduces the number of required sorting operations for
FSCL-based decoding algorithms. For instance, for a high-rate PAC(128,99) code,
SCL decoding with a list size of 32 achieves error-correction performance
comparable to the Fano algorithm. Our method reduces the number of sorting
operations of FSCL decoding to 33%, further decreasing latency.
