Successive Cancellation Decoding Research Articles

Asynchronous Code Division Multiplexing-Based Visible Light Positioning and Communication Network Using Successive Interference Cancellation Decoding.

In the evolving landscape of sixth-generation wireless communication, the integration of visible light communication (VLC) and visible light positioning (VLP), known as visible light positioning and communication (VLPC), emerges as a pivotal technology. This study addresses the challenges of asynchronous code division multiplexing (ACDM) in VLPC networks, focusing on the enhancement of data transmission quality and positioning accuracy. Firstly, we propose an orthogonal pseudo-random code (OPRC) for ACDM-based VLP systems. Leveraging its excellent correlation properties, VLP signals preserve orthogonality even amidst asynchronous transmissions, achieving sub-centimeter average positioning errors. Next, by combining OPRC with successive interference cancellation decoding (SICD), we propose an enhanced ACDM-based VLPC system that utilizes OPRC for improved signal orthogonality and SICD for progressive elimination of multiple access interference (MAI) among VLPC signals. The results show substantial improvements in bit-error rate (BER) and positioning error (PE), approaching the performance levels observed in synchronized VLPC systems. Specifically, the SICD-OPRC scheme reduces average BER to 4.3 × 10-4 and average PE to 2.7 cm, demonstrating its robustness and superiority in complex asynchronous scenarios.

Polar-coded channel polarization for reducing complexity of soft-decision forward error correction

To reduce the computational complexity of soft-decision (SD) forward error correction (FEC), we propose a polar coding method with a low-complexity successive cancellation decoder. Polar coding induces channel polarization in which two bit-channels with lower and higher reliabilities are polarized. Only the less-reliable bit-channels are protected by SD-FEC, whereas the more-reliable bit-channels are offloaded, reducing the complexity of SD-FEC decoding. The degradation of the bit error ratio (BER) performance can be suppressed by designing the polar encoder structures for the successive cancellation decoder. We numerically demonstrate that the proposed method manages to both reduce the computational complexity by half and suppress the BER performance degradation by less than 0.6 dB, compared with the conventional method using only the SD-FEC.

A Deterministic Algorithm for Computing the Weight Distribution of Polar Code

In this work, we present a deterministic algorithm for computing the entire weight distribution of polar codes. As the first step, we derive an efficient recursive procedure to compute the weight distribution that arises in successive cancellation decoding of polar codes along any decoding path. This solves the open problem recently posed by Polyanskaya, Davletshin, and Polyanskii. Using this recursive procedure, at code length <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> , we can compute the weight distribution of any <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">polar cosets</i> in time <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). We show that any polar code can be represented as a disjoint union of such polar cosets; moreover, this representation extends to polar codes with dynamically frozen bits. However, the number of polar cosets in such representation scales exponentially with a parameter introduced herein, which we call the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mixing factor</i> . To upper bound the complexity of our algorithm for polar codes being decreasing monomial codes, we study the range of their mixing factors. We prove that among all decreasing monomial codes with rates at most 1/2, self-dual Reed-Muller codes have the largest mixing factors. To further reduce the complexity of our algorithm, we make use of the fact that, as decreasing monomial codes, polar codes have a large automorphism group. That automorphism group includes the block lower-triangular affine group (BLTA), which in turn contains the lower-triangular affine group (LTA). We prove that a subgroup of LTA acts transitively on certain subsets of decreasing monomial codes, thereby drastically reducing the number of polar cosets that we need to evaluate. This complexity reduction makes it possible to compute the weight distribution of polar codes at length <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> = 128.

Performance analysis of multi-folded pipelined successive cancellation decoder architecture for polar code

Performance analysis of multi-folded pipelined successive cancellation decoder architecture for polar code

Fast Successive-Cancellation Decoding of Polar Codes With Sequence Nodes

Fast Successive-Cancellation Decoding of Polar Codes With Sequence Nodes

Fast Successive Cancellation Decoding of Polar Codes with Large Kernels

Fast Successive Cancellation Decoding of Polar Codes with Large Kernels

Fast Successive-Cancellation Decoding of 2×2 Kernel Non-Binary Polar Codes

Fast Successive-Cancellation Decoding of 2×2 Kernel Non-Binary Polar Codes

Deep-Reinforcement-Learning-Based NOMA-Aided Slotted ALOHA for LEO Satellite IoT Networks

The low earth orbit (LEO) satellites have received extensive attention as an essential supplement to the terrestrial network for supporting global Internet of Things (IoT) services. Considering the rapid growth of IoT devices and the significant satellite-to-ground latency, proposing low-latency, low-overhead access protocols for LEO satellite IoT systems is challenging. In this paper, we propose a multi-beam random access (RA) framework and deploy the deep reinforcement learning (DRL) algorithm to control the non-orthogonal multiple access (NOMA) aided random access strategy. First, we divide the satellite coverage region into multiple beams and assume that the adjacent beams share parts of regions. Hence, the devices in the sharing region are allowed to transmit packets in two periods allocated for the two beams. Then, packets in multiple beams can be decoded jointly by an inter-slot successive interference cancellation (SIC) decoder. In addition, we consider the heterogeneity among devices and assign different power levels for heterogeneous types of devices, which enables power-domain NOMA and the intra-slot SIC decoder in this system to mitigate the collision resolution. To maximize the average throughput, the deep deterministic policy gradient (DDPG) algorithm is adopted to achieve an online decision to optimize the random access protocol where the packet repetition strategies of devices are adjusted dynamically. The simulation results show that the proposed scheme outperforms the traditional benchmark schemes with significant throughput gain.

Construction of Polar Codes Based on Memetic Algorithm

As an emerging coding technique chosen by the 5th generation wireless systems (5G) standardization process, polar coding has attracted the attention of both academia and industry in recent years. The currently used construction methods of polar code are generally based on the reliability of each polarized sub-channel, which directly correspond to the Successive Cancellation (SC) decoding algorithm. However, much less is known about the optimal construction of polar codes under more sophisticated decoding methods such as the Successive Cancellation List (SCL) decoding. There is currently no perfect theory to derive the optimal construction for the SCL decoding to the best of our knowledge, because finding such optimal construction of SCL is considered to be a hard problem for normal choices of the list size. To address this problem, in this paper we turn to evolutionary computation, and propose a memetic algorithm by incorporating prior knowledge obtained from both the channel estimation of the SC-profile and the codeword weight evaluation of the RM-profile, shorted as MA-SCRM. The potential constructions of polar codes are expressed as binary sequences which are processed as the individuals of the population in MA-SCRM. Based on the prior knowledge obtained from the SC-profile and the Reed-Muller-profile, we design special initialization and evolutional operators for polar codes construction. An elitism archive is also introduced to maintain promising constructions and accelerate the convergence of the algorithm. For the SCL decoding, MA-SCRM obtains polar-coding constructions that are more excellent than the SC decoder construction in the sense of block error probability. Compared with the SC decoding construction method, MA-SCRM can reduce the block error probability by up to 48.78% for the original block error rate around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-2}$</tex-math></inline-formula> , and more improvement can be observed for lower original block error rate.

Recursive Processing Algorithm for Low Complexity Decoding of Polar Codes With Large Kernels

A reduced complexity algorithm is presented for computing the log-likelihood ratios (LLRs) arising in the successive cancellation (SC) decoder for polar codes with large kernels of arbitrary dimension. The proposed algorithm exploits a recursive trellis representation of the codes generated by submatrices of the polarization kernel and enables polar codes based on large kernels to be decoded with lower complexity compared to the codes based on the Arıkan kernel with the same performance. Extensions to the case of non-binary kernels are presented.

Performance Analysis of Successive Cancellation Decoder for Polar Codes with Two Stage Channel Estimator

Nowadays polar codes are becoming one of the most favorable capacity achieving Error Correction Codes (ECC) for their simple low encoding and decoding complexity, have received much attention in recent years; they probably achieve the theoretical capacity of discrete memoryless channels using the low complexity successive cancellation (SC) decoding algorithm. However, among the very few prior successive cancellation polar decoder designs, the required long code length makes the decoding latency high. As a new polar decoder, referred to as 2b-SC-Precomputation decoder, reduce the latency from (2n-1) to ((3n/4)-1) without performance loss, which can reduce the hardware complexity by two stage channel estimators. Furthermore, in our method, the decoding latency decreases rapidly with increasing throughput. Significant latency and throughput reductions are shown by simulation results and report synthesis results for ASIC.

Generalized Constituent Nodes for Simplified Successive-Cancellation Decoding of Multi-Kernel Polar Codes

The decoding latency of the successive-cancellation decoder for polar codes is of great importance in its practical applications, and it can be reduced by implementing multi-bit decision decoders in the constituent nodes of the decoding tree. In this letter, we develop a matrix analysis method to analyze the corresponding parity submatrix of the decoding tree’s internal node. Two generalized constituent nodes are presented for the fast simplified successive-cancellation (fast-SSC) decoding of linear kernels-mixed multi-kernel polar codes. Results show that the proposed method achieves latency reduction and preserves the error-correction performance.

Secure beamforming designs for maximizing secrecy sum rate in MISO-NOMA networks

In this paper, the application of Non-Orthogonal Multiple Access (NOMA) is investigated in a multiple-input single-output network consisting of multiple legitimate users and a potential eavesdropper. To support secure transmissions from legitimate users, two NOMA Secrecy Sum Rate Transmit BeamForming (NOMA-SSR-TBF) schemes are proposed to maximise the SSR of a Base Station (BS) with sufficient and insufficient transmit power. For BS with sufficient transmit power, an artificial jamming beamforming design scheme is proposed to disrupt the potential eavesdropping without impacting the legitimate transmissions. In addition, for BS with insufficient transmit power, a modified successive interference cancellation decoding sequence is used to reduce the impact of artificial jamming on legitimate transmissions. More specifically, iterative algorithm for the successive convex approximation are provided to jointly optimise the vectors of transmit beamforming and artificial jamming. Experimental results demonstrate that the proposed NOMA-SSR-TBF schemes outperforms the existing works, such as the maximized artificial jamming power scheme, the maximized artificial jamming power scheme with artificial jamming beamforming design and maximized secrecy sum rate scheme without artificial jamming beamforming design.

Secure wireless communications for STAR‐RIS‐assisted millimetre‐wave NOMA uplink networks

AbstractThis paper explores the potential application of simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR‐RIS) in improving the physical layer security (PLS) of millimetre wave (mmWave) non‐orthogonal multiple access (NOMA) uplink communications. In particular, the legitimate users on both sides of STAR‐RIS send confidential information simultaneously to the base station (BS) while keeping it secret from the eavesdroppers near the BS by exploiting the STAR‐RIS to proactively regulate the electromagnetic propagation environment. By jointly designing the transmit power, the active beamforming at the BS, and the reflecting/transmitting coefficients at the STAR‐RIS, the authors' goal is to maximize the minimum secrecy capacity subject to the successive interference cancellation decoding order constraints. Due to the non‐convexity of the formulated problem, an efficient algorithm is proposed by capitalizing on alternating optimization, a penalty‐based approach, successive convex approximation, and semi‐definite relaxation. Firstly, a two‐layer iterative algorithm based on the penalty for the joint beamforming optimization sub‐problem is proposed. Then, the non‐convex problem is transformed into a convex positive semi‐definite programming problem for the transmit power sub‐problem. Numerical simulation results reveal that the STAR‐RIS‐aided system has more tremendous advantages and effectiveness in improving the PLS of mmWave NOMA uplink communication compared with the benchmark schemes.

On the improvements of successive cancellation Creeper decoding for polar codes

In this paper, an improvement for successive cancellation (SC) decoding is presented for polar codes. This improvement is based on applying Creeper approach that was used to decode convolutional codes. The proposed decoder combines a stack and a Fano approaches, allowing to significantly decrease complexity of Successive Cancellation Fano decoder at the cost of a slight increase in space complexity. We also show how to combine the SC-Creeper decoding with a bit-flipping approach to further improve the performance of SC-Creeper due to introducing additional decoding attempts.Simulation results show that the proposed SC-Creeper and SC-Creeper Flip decoders with carefully selected parameters have the same performance as both CRC-aided Successive Cancellation List decoder with list size 8 and Fano decoder, while having much smaller complexity.

Wireless Covert Communication with Polarization Dirty Constellation

Wireless covert communication is an emerging communication technique that prevents eavesdroppers. This paper presents a novel approach to wireless covert communication based on polar codes with dirty constellation polarization. The feasibility of dirty constellation polarization is analyzed, and the impact of covert transmission power on undetectability is investigated. We polarize the covert channel and decode the covert information using a successive-cancellation decoder. Simulation results demonstrate that polar codes can significantly improve the undetectability and reliability of covert communication when compared to BCH codes. Additionally, we find that polarized covert channels achieve better undetectability and reliability when using a successive-cancellation list decoder. The proposed algorithm shows significant improvement in the undetectability and reliability of wireless covert communication with dirty constellations. This research provides a promising direction for future development in the field of covert communication, with potential applications in secure communication systems.

Hardware Efficient Successive-Cancellation Polar Decoders Using Approximate Computing

Benefiting for its capacity-achieving property, the polar codes have attracted wide attention in various forward error correction (FEC) codes. Although Successive-Cancellation (SC) decoders have low hardware complexity, their limited thoughput leads to low hardware efficiency. In this paper, two novel processing elements (PE) units for SC decoders are proposed by the reconstruction of key functions. Approximate comparator and adder-subtractor are developed in the proposed PEs to further enhance the hardware efficiency of the SC decoders with neglectable bit error rate (BER) performance degradation. The designs are implemented and evaluated on 28nm CMOS technology. Simulation results indicate that the area efficiency of two designs are 17.758r <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Gb/s/mm^{2}}$ </tex-math></inline-formula> and 14.416r <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Gb/s/mm^{2}}$ </tex-math></inline-formula> with 1024-bit code length and the code rate r, which are 26.7% and 9.7% better than the state-of-the-art SC implementations. Moreover, the low complexity Fast Simplified SC (Fast-SSC) decoder implemented with proposed approximate PEs has 60.3% area efficiency improvement than the prior Fast-SSC decoders with equivalent BER performance.

List-serial pipelined hardware architecture for SCL decoding of polar codes

For polar codes, the performance of successive cancellation list (SCL) decoding is capable of approaching that of maximum likelihood decoding. However, the existing hardware architectures for the SCL decoding suffer from high hardware complexity due to calculating L decoding paths simultaneously, which are unfriendly to the devices with limited logical resources, such as field programmable gate arrays (FPGAs). In this paper, we propose a list-serial pipelined hardware architecture with low complexity for the SCL decoding, where the serial calculation and the pipelined operation are elegantly combined to strike a balance between the complexity and the latency. Moreover, we employ only one successive cancellation (SC) decoder core without L×L crossbars, and reduce the number of inputs of the metric sorter from 2L to L + 2. Finally, the FPGA implementations show that the hardware resource consumption is significantly reduced with negligible decoding performance loss.

Energy-Efficient Backscatter-Assisted Coded Cooperative NOMA for B5G Wireless Communications

In this manuscript, we propose an alternating optimization framework to maximize the energy efficiency of a backscatter-enabled cooperative Non-orthogonal multiple access (NOMA) system by optimizing the transmit power of the source, power allocation coefficients (PAC), and power of the relay node under imperfect successive interference cancellation (SIC) decoding. A three-stage low-complexity energy-efficient alternating optimization algorithm is introduced which optimizes the transmit power, PAC, and relay power by considering the quality of service (QoS), power budget, and cooperation constraints. Subsequently, a joint channel coding framework is introduced to enhance the performance of far user which has no direct communication link with the base station (BS) and has bad channel conditions. In the destination node, the far user data is jointly decoded using a Sum-product algorithm (SPA) based joint iterative decoder realized by jointly-designed Quasi-cyclic Low-density parity-check (QC-LDPC) codes. Simulation results evince that the proposed backscatter-enabled cooperative NOMA system outperforms its counterpart by providing an efficient performance in terms of energy efficiency. Also, proposed jointly-designed QC-LDPC codes provide an excellent bit-error-rate (BER) performance by jointly decoding the far user data for considered BSC cooperative NOMA system with only a few decoding iterations.

A fast computing decoder for polar codes with a neural network

This paper proposes high-speed computing decoders for polar codes based on a neural network. To compensate for the performance gap with the successive cancellation decoder, we propose applying the recurrent neural network to the BP decoder with a modified factor graph to reduce the computational complexity of the decoder without any performance degradation. The results of the performance simulation conducted in this paper reveal that the proposed decoder requires substantially less computational complexity than the conventional decoders to achieve the same bit error rate performance.