分层临界集上极化码的渐进比特翻转译码
Progressive Bit-Flipping Decoding of Polar Codes Over Layered Critical Sets
摘要：
在连续消除（SC）极化解码中，任何先前未冻结比特的不正确估计可能在随后的解码中带来严重的错误传播，因此期望尽可能早地发现并纠正错误。在本文中，我们首先构造了一个临界集合$S$的解冻位，其中有很高的概率（通常为$>99\%$）包括第一个错误发生的位。然后，我们开发了一个渐进的多级位翻转解码算法，以纠正多个错误的多层关键集，其中每个关键集是使用剩余的未解码的子树与前一层相关联。\emph{level}实际上表示可以纠正的\emph{independent}错误数。我们表明，随着水平的增加，所提出的渐进比特翻转解码器的块出错率（BLER）性能与相应的循环冗余校验（CRC）辅助的连续消除列表（CA-SCL）解码器竞争，例如，第4级逐行位翻转解码器与具有$L=32$的列表大小的CA-SCL解码器相当。此外，该算法的平均复杂度是远远低于SCL解码器（和类似的SC解码）在中到高的信噪比（SNR）。
英文摘要：
In successive cancellation (SC) polar decoding, an incorrect estimate of any prior unfrozen bit may bring about severe error propagation in the following decoding, thus it is desirable to find out and correct an error as early as possible. In this paper, we first construct a critical set $S$ of unfrozen bits, which with high probability (typically $>99\%$) includes the bit where the first error happens. Then we develop a progressive multi-level bit-flipping decoding algorithm to correct multiple errors over the multiple-layer critical sets each of which is constructed using the remaining undecoded subtree associated with the previous layer. The \emph{level} in fact indicates the number of \emph{independent} errors that could be corrected. We show that as the level increases, the block error rate (BLER) performance of the proposed progressive bit flipping decoder competes with the corresponding cyclic redundancy check (CRC) aided successive cancellation list (CA-SCL) decoder, e.g., a level 4 progressive bit-flipping decoder is comparable to the CA-SCL decoder with a list size of $L=32$. Furthermore, the average complexity of the proposed algorithm is much lower than that of a SCL decoder (and is similar to that of SC decoding) at medium to high signal to noise ratio (SNR).
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