Viterbi-Aided Successive-Cancellation Decoding of Polar Codes
Viterbi-Aided Successive-Cancellation Decoding of Polar Codes
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DOI：
10.1109/glocom.2017.8254150
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发表时间：
2017-12
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通讯作者：
Arman Fazeli;Kuangda Tian;A. Vardy
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作者：
Arman Fazeli;Kuangda Tian;A. Vardy
极化码可证明以低编码和解码复杂度实现无记忆对称信道的容量。尽管如此，对于短且中等的块长度，极化码在连续消除解码下不能提供有竞争力的性能。因此，通过增强的解码算法或通过修改码结构或通过这两者，已经致力于改进极化码的性能。CRC辅助的极化码列表解码是沿着这条研究路线的最成功的方法。然而，列表解码需要遵循L个解码路径，如果L很大，则这导致解码复杂度的显著增加。正如Arikan在极化码发明后不久所指出的那样，如果我们有一个精灵，只在连续的消除解码过程中干预几次，以逆转对信息比特的错误判决，那么它们的性能可以得到显着改善。事实上，用于极化码的Tal-Vardy列表解码算法可以被视为实现这种精灵的尝试。在这里，我们介绍了Arikan的精灵的替代实现，它具有比列表解码低得多的复杂性。我们的方法是基于预编码的一些信息位与短卷积码，提供本地纠错能力的代价是一个小的速率损失。该结构允许连续消除极化解码器通过使其通过卷积码的维特比解码器来验证其输出。与传统的CRC辅助列表解码相反，其中仅在到达最后信息位之后才检测到不正确的解码路径被拒绝，维特比解码器在短延迟之后“在运行中”检测不正确的判决。每当检测到不正确的判决时，连续消除解码器被设置回相应的比特信道，然后使用维特比解码器提供的正确比特值重新开始其计算。
Polar codes provably achieve the capacity of memoryless symmetric channels with low encoding and decoding complexity. Nonetheless, for short and moderate blocklengths, polar codes fail to deliver competitive performance under successive cancellation decoding. Consequently, much effort has been devoted to improving the performance of polar codes, either through enhanced decoding algorithms or by modifying the code structure, or both. CRC-aided list decoding of polar codes is the most successful approach along this line of research. However, list decoding requires following L decoding paths, which leads to a significant increase in decoding complexity if L is large. As noted by Arikan shortly after the invention of polar codes, their performance could be improved dramatically if we had a genie that intervenes in the successive cancellation decoding process only a few times to reverse incorrect decisions on information bits. In fact, the Tal-Vardy list-decoding algorithm for polar codes can be regarded as an attempt to implement such a genie. Herein, we introduce an alternative implementation of Arikan's genie, which has much lower complexity than list decoding. Our approach is based on precoding some of the information bits with a short convolutional code that provides local error- correction capability at the expense of a small rate loss. This structure allows the successive cancellation polar decoder to verify its output by running it through a Viterbi decoder for the convolutional code. In contrast to conventional CRC-aided list decoding, wherein incorrect decoding paths are rejected detected only after reaching the last information bit, the Viterbi decoder detects incorrect decisions ``on the fly'' after a short delay. Whenever an incorrect decision is detected, the successive cancellation decoder is set back to the corresponding bit-channel, and then restarts its computation using the correct bit value provided by the Viterbi decoder.