Viterbi-Aided Successive-Cancellation Decoding of Polar Codes

Abstract

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.