Stack decoding of polar codes

Abstract

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.

Enhanced belief propagation decoding of polar codes by adapting the parity-check matrix

“…2 The Key Laboratory of Information Coding and Transmission, Southwest Jiaotong University, ErHuan Road, Chengdu, China. 3 The School of Computer Science and Technology, Xi'an Technological University, JinHua Road, Xi'an, China. 4 Border Defence Academy, HuanShan Road, Xi'an, China.…”

“…One of the reasons is that the successive cancellation (SC) decoding for polar codes is suboptimal and it may cause error propagation due to the serial decoding architecture. Although there are some improved SC decoders [2,3], the throughput of these decoders is low and the decoding latency is relatively high. Another interesting decoding method for polar codes is belief propagation (BP) decoding [4][5][6][7][8][9][10][11].…”

Design of Rate-Compatible Parallel Concatenated Punctured Polar Codes for IR-HARQ Transmission Schemes

“…The successive cancellation stack (SCS) [36] is proposed to reduce the complexity of SCL in some conditions. The SCL decoding can combine with cyclic redundancy check (CRC) in a concatenated coding fashion to further improve the performance of polar codes [11], which substantially outperformed the state-of-art turbo and LDCP codes.…”

Enhanced Belief Propagation Polar Decoder for Finite Lengths

“…To further improve the performance of polar codes, Niu and Chen showed that, with CRC aided, the performance of SCL decoder becomes comparable to the state-of-the-art LDPC codes [3]. In order to improve the time and space complexity of the SC decoder, Niu proposed successive-cancellation stack (SCS) algorithms [4]. The successive-cancellation hybrid (SCH) algorithm combines the features of SCL and SC and approaches the performance of ML decoding with acceptable complexity [5].…”