CRC (cyclic redundancy check)-aided decoding schemes are proposed to improve the performance of polar codes. A unified description of successive cancellation decoding and its improved version with list or stack is provided and the CRC-aided successive cancellation list/stack (CA-SCL/SCS) decoding schemes are proposed. Simulation results in binaryinput additive white Gaussian noise channel (BI-AWGNC) show that CA-SCL/SCS can provide significant gain of 0.5 dB over the turbo codes used in 3GPP standard with code rate 1/2 and code length 1024 at the block error probability (BLER) of 10 −4 . Moreover, the time complexity of CA-SCS decoder is much lower than that of turbo decoder and can be close to that of successive cancellation (SC) decoder in the high SNR regime.

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A successive cancellation stack (SCS) decoding algorithm is proposed to improve the performance of polar codes. Unlike the conventional successive cancellation decoder which determines the bits successively with a local optimal strategy, the SCS algorithm stores a number of candidate partial paths in an ordered stack and tries to find the global optimal estimation by searching along the best path in the stack. Simulation results in the binary-input additive white Gaussian noise channel show that the SCS algorithm has the same performance as the successive cancellation list (SCL) algorithm and can approach that of the maximum likelihood algorithm. Moreover, the time complexity of the SCS decoder is much lower than that of the SCL and can be very close to that of the SC in the high SNR regime.Introduction: Polar codes (PCs) have been proved to achieve the capacity of symmetric binary input discrete memoryless channels (B-DMCs) under a successive cancellation (SC) decoding [1]. However the finite-length performance under SC is not satisfactory. The belief propagation (BP) decoding algorithm can improve the performance [2, 3], whereas the optimal scheduling of messages in BP is hard to know. In [4], a linear programming (LP) decoder is introduced; unfortunately, it cannot work on channels other than the binary erasure channel (BEC). Moreover, there is a gap between the BP/LP algorithm and the maximum likelihood (ML) algorithm. The successive-cancellation list (SCL) decoder [5] can approach the performance of the ML decoder for a moderate list size L. Nevertheless, the time complexity of the SCL decoder is fixed and slightly high. Inspired by the stack decoding of the convolutional code [6], we propose an alternative decoding strategy called the successive cancellation stack (SCS) algorithm. Compared with the SCL decoder, the SCS algorithm can achieve the same performance and has lower time complexity.

CRC (cyclic redundancy check) concatenated polar codes are superior to the turbo codes under the successive cancellation list (SCL) or successive cancellation stack (SCS) decoding algorithms. But the code length of polar codes is limited to the power of two. In this paper, a family of rate-compatible punctured polar (RCPP) codes is proposed to satisfy the construction with arbitrary code length. We propose a simple qusiuniform puncturing algorithm to generate the puncturing table.And we prove that this method has better row-weight property than that of the random puncturing. Simulation results under the binary input additive white Gaussian noise channels (BI-AWGNs) show that these RCPP codes outperform the performance of turbo codes in WCDMA (Wideband Code Division Multiple Access) or LTE (Long Term Evolution) wireless communication systems in the large range of code lengths. Especially, the RCPP code with CRC-aided SCL/SCS algorithm can provide over 0.7dB performance gain at the block error rate (BLER) of 10 −4 with short code length M = 512 and code rate R = 0.5.

As improved versions of successive cancellation (SC) decoding algorithm, successive cancellation list (SCL) decoding and successive cancellation stack (SCS) decoding are used to improve the finite-length performance of polar codes. Unified descriptions of SC, SCL and SCS decoding algorithms are given as path searching procedures on the code tree of polar codes. Combining the ideas of SCL and SCS, a new decoding algorithm named successive cancellation hybrid (SCH) is proposed, which can achieve a better trade-off between computational complexity and space complexity. Further, to reduce the complexity, a pruning technique is proposed to avoid unnecessary path searching operations. Performance and complexity analysis based on simulations show that, with proper configurations, all the three improved successive cancellation (ISC) decoding algorithms can have a performance very close to that of maximum-likelihood (ML) decoding with acceptable complexity. Moreover, with the help of the proposed pruning technique, the complexities of ISC decoders can be very close to that of SC decoder in the moderate and high signal-to-noise ratio (SNR) regime.Comment: This paper is modified and submitted to IEEE Transactions on Communication