  Successive cancellation (SC) process is an essential component of various
decoding algorithms used for polar codes and their variants. Rewinding this
process seems trivial if we have access to all intermediate log-likelihood
ratios (LLRs) and partial sums. However, as the block length increases,
retaining all of the intermediate information becomes inefficient and
impractical. Rewinding the SC process in a memory-efficient way is a problem
that we address in this paper. We first explore the properties of the SC
process based on the binary representation of the bit indices by introducing a
new operator used for grouping the bit indices. This special grouping helps us
in finding the closest bit index to the target index for rewinding. We also
analytically prove that this approach gives access to the untouched
intermediate information stored in the memory which is essential in resuming
the SC process. Then, we adapt the proposed approach to multiple rewinds and
apply it on SC-flip decoding and shifted-pruning based list decoding. The
numerical evaluation of the proposed solution shows a significant reduction of
>=50% in the complexity of the additional decoding attempts at medium and high
SNR regimes for SC-flip decoding and less for shifted-pruning based list
decoding.
