Successive Cancellation Research Articles

Convolutional Neural Network-Aided Tree-Based Bit-Flipping Framework for Polar Decoder Using Imitation Learning

Known for their capacity-achieving abilities and low complexity for both encoding and decoding, polar codes have been selected as the control channel coding scheme for 5G communications. To satisfy the needs of high throughput and low latency, belief propagation (BP) is chosen as the decoding algorithm. However, it suffers from worse error performance than that of cyclic redundancy check (CRC)-aided successive cancellation list (CA-SCL). Recently, convolutional neural network-aided bit-flipping (CNN-BF) is applied to BP decoding, which can accurately identify the erroneous bits to achieve a better error rate and lower decoding latency than prior critical-set bit-flipping (CS-BF) mechanism. However, successive BF, having better error correction capability, has not been explored in CNN-BF since the more complicated flipping strategy is out of the scope of supervised learning. In this work, by using imitation learning, a convolutional neural network-aided tree-based multiple-bits BF (CNN-Tree-MBF) mechanism is proposed to explore the benefits of multiple-bits BF. With the CRC information as additional input data, the proposed CNN-BF model can further reduce 5 flipping attempts. Besides, a tree-based flipping strategy is proposed to avoid useless flipping attempts caused by wrongly flipped bits. From the simulation results, our approach can outperform CS-BF and reduce flipping attempts by 89% when code length is 64, code rate is 0.5 and SNR is 1 dB. It also achieves a comparable block error rate (BLER) as CA-SCL.

Improving Polar-Coded SCMA System by Information Coupling and Parity Check.

In this paper, the uplink information-coupled polar-coded sparse code multiple access (PC-SCMA) system is proposed. For this system, we first design the encoding method of systematic joint parity check and CRC-aided (PCCA) polar code. Using the systematic PCCA-polar code as base code, the partially information-coupled (PIC) polar code is constructed. Then, a joint iterative detection and successive cancellation list (SCL)-decoding receiver is proposed for the PC-SCMA system. For the receiver, the coupled polar decoder’s extrinsic messages are calculated by the Bayes rule and soft cancellation (SCAN) algorithm. Based on the extrinsic information transfer (EXIT) idea, the PIC PCCA-polar code is optimized. Simulation results demonstrate that the PIC PCCA-PC-SCMA system outperforms the other polar (or LDPC) coded SCMA systems at various code rates and channel configurations. Additionally, compared with an uncoupled PC-SCMA system with SCL decoder, the complexity of PIC PCCA-PC-SCMA is reduced at a high

A Novel Construction and Block Error Rate Analysis of Polar Codes with Short Messgage Transmission over Different Channels

Polar codes are usually constructed to minimize the upper bound of a block error ratio (BLER). In this paper, we discuss the estimation of the exact BLERs of polar codes as well as the construction of polar codes. Assuming that successive cancellation (SC) decoding is employed, we present a method for estimating the exact BLER of polar codes with the help of Gaussian approximation (GA). A new approach is proposed to construct polar codes over different channels (Awgn and Rayleigh+) with short message transmission scheme , aimed at minimizing the exact BLER, instead of the upper bound of the BLER. Analysis indicates that the new approach less complex than the existing methods. It is also shown that the proposed scheme is outperforms than conventional methods and are visualized in simulation results.

Experimental Demonstration of 9.6 Gbit/s Polar Coded Infrared Light Communication System

A new inter-frame polar coded modulation scheme is proposed and experimentally demonstrated in an infrared light communication (ILC) system. The scheme utilizes the Monte Carlo (MC) method to jointly design an inter-frame polar code with 16-ary quadrature-amplitude modulation (16QAM) and orthogonal frequency-division multiplexing (OFDM). The indoor transmission of 9.6 Gbit/s 16QAM OFDM signal is experimentally achieved over a 3.2 km single-mode fiber and 0.8 m free space. The experiment results show that the proposed scheme employing a polar code of length 1024 and cyclic redundancy check aided successive cancellation list (CA-SCL) decoding with a list size of 2 resulted in no errors over 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> bits. Moreover, the proposed scheme requires negligible extra decoding complexity with respect to its classical counterpart, MC-constructed polar coded modulation. To the best of our knowledge, this is the first experimental demonstration of a polar coded modulation based infrared light communication system.

Improving Image Transmission by Using Polar Codes and Successive Cancellation List Decoding

This paper investigates the transmission of grey scale images encoded with polar codes and de-coded with successive cancellation list (SCL) decoders in the presence of additive white Gaussian noise. Po-lar codes seem a natural choice for this application be-cause of their error-correction efficiency combined with fast decoding. Computer simulations are carried out for evaluating the influence of different code block lengths in the quality of the decoded images. At the encoder a default polar code construction is used in combination with binary phase shift keying modulation. The results are compared with those obtained by using the clas-sic successive cancellation (SC) decoding introduced by Arikan. The quality of the reconstructed images is assessed by using peak signal to noise ratio (PSNR) and the structural similarity (SSIM) index. Curves of PSNR and SSIM versus code block length are presented il-lustrating the improvement in performance of SCL in comparison with SC.

On Polar Coding for Side Information Channels

We propose a successive cancellation list (SCL) encoding and decoding scheme for the Gelfand Pinsker (GP) problem based on the known nested polar coding scheme. It applies SCL encoding for the source coding part, and SCL decoding with a properly defined CRC for the channel coding part. The scheme shows improved performance compared to the existing method. A known issue with nested polar codes for binary dirty paper is the existence of frozen channel code bits that are not frozen in the source code. These bits need to be retransmitted in a second phase of the scheme, thus reducing the rate and increasing the required blocklength. We provide an improved bound on the size of this set, and on its scaling with respect to the blocklength, when the Bhattacharyya parameter of the test channel used for source coding is sufficiently large, or the Bhattacharyya parameter of the channel seen at the decoder is sufficiently small. The result is formulated for an arbitrary binary-input memoryless GP problem, since unlike the previous results, it does not require degradedness of the two channels mentioned above. Finally, we present simulation results for binary dirty paper and noisy write once memory codes.

Reduced-Complexity Low-Latency Logarithmic Successive Cancellation Stack Polar Decoding for 5G New Radio and Its Software Implementation

An efficient Fast logarithmic successive cancellation stack (Log-SCS) polar decoding algorithm is proposed along with its software implementation using single instruction multiple data (SIMD) style processing. Quantitatively, we reduce the decoding complexity by $50\%$ on average, while simultaneously attaining a decoding latency that is only $21\%$ of that of the state-of-the-art Fast successive cancellation list (SCL) polar decoder's software implementation. This is achieved without any loss of error correction performance by applying simplified path-metric (PM) computations for the rate-0, rate-1 and repetition sub-graphs of the proposed Fast Log-SCS decoder. Furthermore, a software implementation of the 32-bit fixed-point Fast Log-SCS polar decoder is conceived for x86 processors, which maintains the same block error ratio (BLER) as the floating-point Log-SCS polar decoder. Additionally, our software implementation is accelerated using SIMD instructions by relying on 512-bit Advanced Vector Extensions (AVX-512) and recursive template meta-programming for the first time, achieving a parallelism of 16, which makes it eminently suitable for the low-latency requirements of software-defined radio systems.

Promising pipelines and hydrocarbon nationalism: the sociality of unbuilt infrastructure in indigenous Siberia

Promising pipelines and hydrocarbon nationalism: the sociality of unbuilt infrastructure in indigenous Siberia

Soft List Decoding of Polar Codes

Soft-output (SO) decoding is proposed for the Logarithmic Successive Cancellation List (Log-SCL) polar decoder for the first time, by exploiting the left-to-right propagation of the Belief Propagation (BP) decoder, which opens new avenues for its employment in powerful turbo-receivers. In the case of decoding a half-rate polar code having a block length of 1024 bits, the proposed soft list polar decoder achieves a 1.5 dB Block Error Ratio (BLER) performance gain, $50\%$ latency improvement and $26\%$ complexity reduction, compared to the state-of-the-art SO Soft Cancellation (SCAN) polar decoder in a polar-coded Multiple-Input Multiple-Output (MIMO) system. Furthermore, we conceive a Memory-Efficient (ME) soft list polar decoder, which requires only $16\%$ of the soft list polar decoder's memory, at the cost of slightly increased latency and complexity.

Neural Successive Cancellation Polar Decoder With Tanh-Based Modified LLR Over FSO Turbulence Channel

The neural successive cancellation (NSC) decoder with tanh-based modified log-likelihood ratio (LLR) is proposed for reducing the decoding latency of polar codes over free space optical (FSO) turbulence channel. The conventional successive cancellation (SC) decoder is partitioned into multiple sub-blocks, which are replaced by multiple sub neural network (NN) decoders with tanh-based modified LLR. The recursive characteristic of the polar sequences reliability ranking given in 5G standard enables the sub-NN decoder to be uniquely determined by code length and the number of information bits. Confirmed by the simulation, the bit error rate (BER) performance of NSC decoder with tanh-based modified LLR is close to the conventional SC decoder over turbulence channel for the practical-length polar codes. Regarding turbulence-stability, the NSC decoder trained in moderate and strong turbulence conditions have stable performance in a wide range of turbulence conditions. Moreover, in comparison of decoding latency, the NSC decoder with tanh-based modified LLR takes less than 25% time steps of SC decoder in the same code length.

Neural Successive Cancellation Flip Decoding of Polar Codes

Dynamic successive cancellation flip (DSCF) decoding of polar codes is a powerful algorithm that can achieve the error correction performance of successive cancellation list (SCL) decoding, with an average complexity that is close to that of successive cancellation (SC) decoding at practical signal-to-noise ratio (SNR) regimes. However, DSCF decoding requires costly transcendental computations to calculate a bit-flipping metric, which adversely affect its implementation complexity. In this paper, we first show that a direct application of common approximation schemes on the conventional DSCF decoding results in a significant error-correction performance loss. We then introduce an additive perturbation parameter and propose an approximation scheme which completely removes the need to perform transcendental computations in DSCF decoding. Machine learning (ML) techniques are then utilized to optimize the perturbation parameter of the proposed scheme. Furthermore, a quantization scheme is developed to enable efficient hardware implementation. Simulation results show that when compared with DSCF decoding, the proposed decoder with quantization scheme only experiences a negligible error-correction performance degradation of less that 0.08 dB at a target frame-error-rate (FER) of 10− 4, for a polar code of length 512 with 256 information bits. In addition, the bit-flipping metric computation of the proposed decoder reduces up to around 31% of the number of additions used by the bit-flipping metric computation of DSCF decoding, without any need to perform costly transcendental computations and multiplications.

Improved Soft Cancellation Decoding of Polar Codes

The soft cancellation decoding of polar codes achieves a better performance than the belief propagation decoding with lower computational time and space complexities. However, because the soft cancellation decoding is based on the successive cancellation decoding, the decoding efficiency and performance with finite-length blocks can be further improved. Exploiting the idea of the successive cancellation list decoding, the soft cancellation decoding can be improved in two aspects: one is by adding branch decoding to the error-prone information bits to increase the accuracy of the soft information, and the other is through using partial iterative decoding to reduce the time and computational complexities. Compared with the original method, the improved soft cancellation decoding makes progress in the error correction performance, increasing the decoding efficiency and reducing the computational complexity, at the cost of a small increase of space complexity.

Efficient stochastic successive cancellation list decoder for polar codes

Polar codes are one of the most favorable capacity-achieving codes owing to their simple structures and low decoding complexity. Successive cancellation list (SCL) decoders with large list sizes achieve performances very close to those of maximum-likelihood (ML) decoders. However, hardware cost is a severe problem because an SCL decoder with list size L consists of L copies of a successive cancellation (SC) decoder. To address this issue, a stochastic SCL (SSCL) polar decoder is proposed. Although stochastic computing can achieve a good hardware reduction compared with the deterministic one, its straightforward application to an SCL decoder is not well-suited owing to the precision loss and severe latency. Therefore, a doubling probability approach and adaptive distributed sorting (DS) are introduced. A corresponding hardware architecture is also developed. Field programmable gate array (FPGA) results demonstrate that the proposed stochastic SCL polar decoder can achieve a good performance and complexity tradeoff.

A 506 Gbit/s Polar Successive Cancellation List Decoder with CRC

A 506 Gbit/s Polar Successive Cancellation List Decoder with CRC

Weight Distributions for Successive Cancellation Decoding of Polar Codes

In this paper, we derive the exact weight distributions that emerge during each stage of successive cancellation decoding of polar codes. Though we do not compute the distance spectrum of polar codes, the results allow us to get an estimate of the decoding error probability and to show a link between the first nonzero components of the weight distribution and the partial order between the synthetic channels. Also, we establish the minimal distance between two cosets associated with two paths that differ in two positions. This can be regarded as a first step toward analyzing the weight distributions for the successive cancellation list decoding.

High-Speed Architecture for Successive Cancellation Decoder With Split-g Node Block

Polar codes are one of the recently developed error correcting codes, and they are popular due to their capacity achieving nature. The architecture of the successive cancellation (SC) decoder algorithm is composed of a recursive processing element (PE). The PE comprises various blocks that include signed adder, subtractor, comparator, multiplexers, and few logic gates. Therefore, the latency of the PE is a primary concern. Hence, a high-speed architecture for implementing the SC decoding algorithm for polar codes is proposed. In the proposed work, a novel restructuring of the 2bit-SC (2b-SC) precomputation decoder architecture is carried out to reduce the latency by 20% while reducing the hardware complexity. Compared to the 2b-SC precomputation decoder, the proposed architecture also has 19% increased throughput for (1024, 512) polar codes with 45% reduction in the gate count.

Super-resolving multiple scatterers detection in synthetic aperture radar tomography assisted by correlation information

This paper proposes a method for detecting multiple scatterers (targets) in the elevation direction for synthetic aperture radar (SAR) tomography. The proposed method can resolve closely spaced targets through a twostep procedure. In the first step, coarse detection is performed with a successive cancellation scheme in which possible locations of targets are marked. Then, in the second step, by searching in the reduced search space which is finely 10 gridded, the accurate location of the targets is found. For estimating the actual number of targets, a model order selection scheme is used in two cases of known and unknown noise variance. Also, by analytical investigation of the probability of detection for the proposed method, the effect of the influential parameters on the detection ability is explicitly demonstrated. Compared to the super-resolution methods based on compressed sensing (CS), the proposed method has a lower computational cost and higher estimation accuracy, especially at low signal-to-noise ratio regime. 15 Simulation results show the superiority of the proposed method in terms of both 3D scatterer reconstruction and detection ability

Design of I-Polar Codes

Recently, a new family of polar codes, termed interleaved polar (i-polar) codes, was proposed. It has been shown that both i-polar codes and polar codes of the same block length generate the same synthesized channels. Therefore, conventional bit channel selection algorithms designed for polar codes can be employed for i-polar codes. However, since most of the bit channel selection algorithms are optimized under successive cancellation (SC) decoding, i-polar codes as well as polar codes are still weak at short to moderate block lengths even under ML decoding. In this letter, we propose a new bit channel selection algorithm for i-polar codes which generates a sequence termed the i-polar sequence (IPS). The IPS can be used to specify the unfrozen bit sets for any code rates. Simulation results show that stand-alone i-polar codes with IPS under SCL decoding outperform the state-of-the-art 5G LDPC codes and 5G polar codes. Also, the performance levels of stand-alone polar codes with IPS are comparable to those of the 5G LDPC codes.

Improved Belief Propagation Polar Decoders With Bit-Flipping Algorithms

Since the inherent serial nature of successive cancellation list (SCL) decoding results in a long latency, belief propagation (BP) decoding for polar codes has drawn attention for high-throughput applications. However, its error correction performance is inferior to that of SCL decoding. Therefore, the bit-flipping strategy has been recently applied to BP decoding, which can approach the SCL decoding performance through multiple additional decoding attempts. The original BP flip (BPF) decoding suffers from an inaccurate identification of erroneous bits by a fixed flip set (FS), which has been improved by the generalized BPF (GBPF) decoding. In this article, the GBPF decoding is extended to support multiple bits being flipped in one decoding attempt. In addition, for two types of decoding errors: detected errors and undetected errors, we propose two novel methods to more effectively identify erroneous bits. For detected errors, the concept of loop sets is defined and a loop-based identification method is introduced based on the study of error patterns of BP decoding. On the other hand, a method to generate a more accurate fixed FS is proposed for undetected errors, which considers the bit error distribution under BP decoding. Combining the two methods, the GBPF with merged sets (GBPF-MS) decoding can achieve the SCL-8 performance and outperforms the state-of-the-art BPF, BP list, and SC flip (SCF) decoding, for polar codes with length 1024 and information rate 1/2. Implemented by 40nm CMOS technology, the proposed GBPF-MS decoder with ten flips exhibits an average throughput of 4.19 Gbps at 2.5 dB, which is $1.6\times $ and $1.72\times $ faster than the state-of-the-art SCL-4 and SCF decoders, respectively.

Design of Short Polar Codes for SCL Decoding

The problem of designing polar-like codes for successive cancellation list (SCL) decoding algorithm is considered. A novel code design algorithm aimed to minimize both successive cancellation (SC) and maximum-likelihood (ML) decoding error probabilities is introduced. The algorithm performs optimization of a precoding matrix for the polarization transformation matrix to guarantee preselected minimum distance and the lowest possible SC decoding error probability to the resulting code. Constructed precoded polar codes are decoded as polar codes with dynamic frozen bits. Numerical results show that the proposed codes of lengths 32 and 64 significantly reduce the frame error rate (FER) compared to the original polar codes under the SCL decoding starting with the list size 4. The gain increases with the list size. The proposed codes have a much lower SC decoding error probability than extended Bose-Chaudhuri-Hocquenghem (e-BCH) codes and their polar subcodes without sacrificing the ML performance. In case of the code length 64, the constructed precoded polar codes demonstrate a FER reduction compared to the polar subcodes of e-BCH codes under the SCL decoding with the list size up to 16 and demonstrate a comparable FER starting with the list size 32.