Efficient Partial Rewind of Polar Codes' Successive Cancellation-based Decoders for Re-decoding Attempts

TL;DR

This paper introduces a memory-efficient method for rewinding the successive cancellation decoding process of polar codes, enabling multiple re-decoding attempts with significantly reduced complexity, especially at medium and high SNRs.

Contribution

It proposes a novel operator based on binary bit index grouping to efficiently rewind SC decoding, improving re-decoding efficiency for polar codes.

Findings

Reduces complexity of re-decoding attempts by >=50% at medium/high SNRs

Provides a memory-efficient approach for multiple rewinds in SC decoding

Applicable to SC-flip and shifted-pruning list decoding methods

Abstract

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.