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.
翻译:连续取消(SC)进程是用于极地代码及其变异物的各种解码算法的基本组成部分。 如果我们能够获取所有中间日志类比比率(LLLRs)和部分总和, 将这一过程倒转似乎微不足道。 但是, 随着区块长度的增加, 保留所有中间信息变得效率低且不切实际。 以记忆效率高的方式倒转SC进程是我们在本文件中处理的一个问题。 我们首先通过引入用于分组比特指数的新操作员来探索以比特指数二进制表示法为基础的SC进程特性。 这一特殊组合有助于我们找到最接近于倒转目标指数的位指数(LLLRs)和部分总和部分总和内存储存的未保存的中间信息。 然后,我们将拟议方法调整为多重回旋,并将其应用于基于SC-flip 解码的解码和转动驱动列表解码。 对拟议解决方案的数值评估显示,在中和高NSR变换的列表系统的额外解码尝试的复杂性显著降低。