  In successive cancellation list (SCL) decoding, the tree pruning operation
retains the L best paths with respect to metric at every decoding step.
However, the correct path might be among the L worst paths due to imposed
penalties. In this case, the correct path is pruned and the decoding process
fails. In this work, we propose a scheme for additional decoding attempts when
decoding fails, in which the pruning window does not necessarily select the L
best paths, but this window is shifted between positions 1 and 2L in the sorted
list. In the simplest form, the L worst paths are selected at the decoding step
where the probability of elimination of the correct paths is high.
Additionally, we generalize the scheme and propose a number of variants such as
constrained shifting, nested shifting and shifting under segmented decoding,
aiming to reduce the computational complexity. The numerical results for polar
codes of length 512 with code rates 0.5 and 0.8 and list sizes L=2, 8, 32, show
that the shifted-pruning scheme can provide 0.25-0.5 dB gain in error
correction performance, while the average computational complexity approaches
the conventional list decoding complexity at practical FER ranges.
