Polar codes have gained significant a ttention in recent years due to their superior performance, making them an attractive choice for use in modern communication systems. In this paper, we present a novel approach for implementing a fast decoding method for polar codes with additional nodes. Specifically, we propose a modification of the fast decoding method with bit-flipping capability, called the GSCLAF, which is designed to improve the correction capability of the decoder. To achieve this, we consider additional nodes of five types, which are obtained by a combination of basic generalized nodes, namely information, frozen, SPC, and REP nodes. To evaluate the performance of our proposed algorithm, numerical experiments were conducted using the 5G NR polar code. The results of these experiments demonstrate the effectiveness of GSCLAF relative to other popular polar decoding algorithms. Overall, our proposed algorithm provides a powerful tool for improving the decoding performance of polar codes with additional nodes, making it a promising solution for modern communication systems that require high data rates and reliable communication.
Polar codes have gained significant a ttention in recent years due to their superior performance, making them an attractive choice for use in modern communication systems. In this paper, we present a novel approach for implementing a fast decoding method for polar codes with additional nodes. Specifically, we propose a modification of the fast decoding method with bit-flipping capability, called the GSCLAF, which is designed to improve the correction capability of the decoder. To achieve this, we consider additional nodes of five types, which are obtained by a combination of basic generalized nodes, namely information, frozen, SPC, and REP nodes. To evaluate the performance of our proposed algorithm, numerical experiments were conducted using the 5G NR polar code. The results of these experiments demonstrate the effectiveness of GSCLAF relative to other popular polar decoding algorithms. Overall, our proposed algorithm provides a powerful tool for improving the decoding performance of polar codes with additional nodes, making it a promising solution for modern communication systems that require high data rates and reliable communication.
Multi-kernel polar codes, which are constructed by different sizes of kernels make the length of the traditional polar code more flexible. In this paper, we extend the multi-kernel polar codes to 5×5 kernels including kernel design, code design, and fast decoding. First, we construct a new 5×5 kernel with the maximum polarization rate. The first row of this kernel is an all-one vector, which enable us to find the relation between node modification and distance property of multi-kernel polar codes. Second, we modify the repetition (REP) nodes to the new 5×5 kernel, which can increase the distance property of the constructed polar codes, improve the decoding performance and reduce memory requirements during the fast decoding. In addition, we find our REP node modification can be generalized to multi-kernel polar codes when the first row of the used kernels is all-one vector. Third, we prove the four kinds of basic nodes (Rate-1 node, Rate-0 nodes, Repetition (REP) nodes, and Single-Parity check (SPC) nodes) of fast decoding are suitable for the new kernel. Moreover, we generalize the Generalized Parity-Check (G-PC) nodes and the Generalized Repetition (GREP) nodes, which are suitable for multi-kernel polar codes constructed by any size of kernels and any order of kernels. By simulations, we show that our modification improves the error-rate performance of the fast decoding. Meanwhile, the fast decoding of our multi-kernel polar codes has at least 68.4% latency reduction compared with the traditional SC decoder in all cases considered where code lengths are 80, 135, 400, and 675.
Multi-kernel polar codes, which are constructed by different sizes of kernels make the traditional polar codes have more flexible code length. In this paper, we extend the multi-kernel polar codes to 5×5 kernels including kernel design, code design, and fast decoding. First, we construct a new 5×5 kernel, which has the maximum polarization rate. The first row of this kernel is all-one vector, which enable us to seek the relation between node modification and distance property of multi-kernel polar codes. Second, we modify the repetition (REP) nodes to this kernel, which can increase the distance property of the constructed polar codes, improve the decoding performance and reduce memory requirements during the fast decoding. In addition, we find this REP node modification can be generalized when multi-kernel polar codes constructed by kernels, which the first row is all-one vector. Third, we prove the four kinds of basic nodes (Rate-1 node, Rate-0 nodes, Repetition (REP) nodes, and Single-Parity check (SPC) nodes) of fast decoding are suitable for this kernel. Moreover, we generalize the Generalized Parity-Check (G-PC) nodes and the Generalized Repetition (GREP) nodes, which are suitable for multi-kernel polar codes constructed by any size of kernels and any order of kernels. The G-PC and G-REP nodes can further accelerate the decoding speed. By simulations, we show that our modification improves the error-rate performance of the fast decoding. Meanwhile, the fast decoding of our multi-kernel polar codes has at least 68. 4% reduced latency compared with the traditional SC decoder in all cases considered where frame lengths are (80,135,400,675). Index Terms-Multi-kernel polar codes, node modification, fast decoding, 5×5 kernel matrix
SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct bit-flipping position in SCF decoding limits its improvements. Due to its improved bit-flipping criterion, Thresholded SCF (TSCF) decoding algorithm exhibits a superior error-correction performance and lower computational complexity than SCF decoding. However, the parameters of TSCF decoding depend on multiple channel and code parameters, and are obtained via Monte-Carlo simulations. Our main goal is to realize TSCF decoding as a practical polar decoder implementation. To this end, we first realize an approximated threshold value that is independent of the code parameters and precomputations. The proposed approximation has negligible error-correction performance degradation on the TSCF decoding. Then, we validate an alternative approach for forming a critical set that does not require precomputations, which also paves the way to the implementation of the Fast-TSCF decoder. Compared to the existing fast SCF implementations, the proposed Fast-TSCF decoder has 0.24 to 0.41 dB performance gain at frame error rate of 10−3, without any extra cost. Compared to the TSCF decoding, Fast-TSCF does not depend on precomputations and requires 87% fewer decoding steps. Finally, implementation results in TSMC 65nm CMOS technology show that the Fast-TSCF decoder is 20% and 82% more area-efficient than the state-of-the-art fast SCF and fast SC-List decoder architectures, respectively.
In this paper, an improvement for SC list flip (SCL-Flip) decoding is presented for polar codes. A novel bit-selection metric for critical set (set of information symbols of polar codes being flipped during additional decoding attempts) based on path metric of successive cancellation list (SCL) decoding is suggested. With the proposed metric, the improved SCL scheme based on special nodes (SN) decoders was developed. This decoder will be denoted by GSCLF. The main idea of the proposed decoder is joint using of two approaches: first one is a fast decoding of special nodes in binary tree representation of polar code (e.g., some special nodes in tree representation of polar code that allow efficient list decoding with low complexity) and the second one is an applying of additional decoding attempts (flips) in the case when initial decoding was erroneous. The simultaneous use of these two approaches results in both a significant reduction in spatial complexity and a significant reduction in the number of computations required for decoding whereas keeping excellent performance. Simulation results presented in this paper allow us to conclude that the computational complexity of the proposed GSCLF decoder is from 66% to 80% smaller than the one of SCL-32 decoder.
This paper presents a fast-simplified successive cancellation (SC) flipping (Fast-SSC-Flip) decoding algorithm for polar code.Firstly, by researching the probability distribution of the number of error bits in a node caused by channel noise in simplified-SC (SSC) decoder, a measurement criterion of node reliability is proposed.Under the guidance of the criterion, the most unreliable nodes are firstly located, then the unreliable bits are selected for flipping, so as to realize Fast-SSC-Flip decoding algorithm based on node reliability (NR-Fast-SSC-Flip).Secondly, we extended the proposed NR-Fast-SSC-Flip to multiple node (NR-Fast-SSC-Flipω) by considering dynamic update to measure node reliability, where ω is the order of flipnodes set.The extended algorithm can correct the error bits in multiple nodes, and get good performance at medium and high signal-to-noise (SNR) region.Simulation results show that the proposed NR-Fast-SSC-Flip decoder can obtain 0.27dB and 0.17dB gains, respectively, compared with the traditional Fast-SSC-Flip [14] and the newly proposed two-bit-flipping Fast-SSC (Fast-SSC-2Flip-E2) [18] under the same conditions.Compared with the newly proposed partitioned Fast-SSC-Flip (PA-Fast-SSC-Flip) (𝑠𝑠=4) [18], the proposed NR-Fast-SSC-Flip-ω (ω=2) decoder can obtain about 0.21dB gain, and the FER performance exceeds the cyclic-redundancy-check (CRC) aided SC-list (CRC-SCL) decoder (L=4).
SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct bit-flipping position in SCF decoding limits its improvements. Due to its improved bit-flipping criterion, Thresholded SCF (TSCF) decoding algorithm exhibits a superior error-correction performance and lower computational complexity than SCF decoding. However, the parameters of TSCF decoding depend on multiple channel and code parameters, and are obtained via Monte-Carlo simulations. Our main goal is to realize TSCF decoding as a practical polar decoder implementation. To this end, we first realize an approximated threshold value that is independent of the code parameters and precomputations. The proposed approximation has negligible error-correction performance degradation on the TSCF decoding. Then, we validate an alternative approach for forming a critical set that does not require precomputations, which also paves the way to the implementation of the Fast-TSCF decoder. Compared to the existing fast SCF implementations, the proposed Fast-TSCF decoder has 0.24 to 0.41 dB performance gain at frame error rate of 10-3, without any extra cost. Compared to the TSCF decoding, Fast-TSCF does not depend on precomputations and requires 87% fewer decoding steps. Finally, implementation results in TSMC 65nm CMOS technology show that the Fast-TSCF decoder is 20% and 82% more area-efficient than the state-of-the-art fast SCF and fast SC-List decoder architectures, respectively.