Decoding Of Polar Codes Research Articles

Improved Automorphism Ensemble Decoder for Polar Codes

Improved Automorphism Ensemble Decoder for Polar Codes

Fast Decoding of Polar Codes for Digital Broadcasting Services in 5G

Fast Decoding of Polar Codes for Digital Broadcasting Services in 5G

Advanced channel coding schemes for B5G/6G networks: State‐of‐the‐art analysis, research challenges and future directions

SummaryAs a consequence of continuing demand for additional capacity and higher quality data transmission, channel coding as a key component of a digital communication network has progressed from a classical single pair, point‐to‐point information theoretic application to a class of coding techniques with diverse parameters. The heterogeneous requirements of B5G/6G networks technology have made flexibility of code parameters the main desired feature while designing channel codes. Owing to this, channel coding techniques have evolved to support enabling applications that depend on different factors such as latency, reliability, energy efficiency and throughput. We review and discuss the application of new techniques, modifications in the design and construction of modern channel coding schemes, including block, convolutional, rateless and space‐time codes. Further, the error correction performance of mainstream channel decoders for LDPC, polar and turbo codes is compared and analysed for their attainable error rate. The aim of this study is to highlight the adaptability of the discussed coding schemes for the forthcoming cellular network landscape. This article also addresses the implementational challenges of high throughput, low latency and machine type communication scenarios. Moreover, some recent studies exploring the role of machine learning for optimisation of B5G/6G networks are classified and discussed. Concluding, research areas pertaining to the scalability of error control coding for next generation networking are addressed.

High-Throughput Polar Code Decoders with Information Bottleneck Quantization.

In digital baseband processing, the forward error correction (FEC) unit belongs to the most demanding components in terms of computational complexity and power consumption. Hence, efficient implementation of FEC decoders is crucial for next-generation mobile broadband standards and an ongoing research topic. Quantization has a significant impact on the decoder area, power consumption and throughput. Thus, lower bit widths are preferred for efficient implementations but degrade the error correction capability. To address this issue, a non-uniform quantization based on the Information Bottleneck (IB) method is proposed that enables a low bit width while maintaining the essential information. Many investigations on the use of the IB method for Low-density parity-check code) LDPC decoders exist and have shown its advantages from an implementation perspective. However, for polar code decoder implementations, there exists only one publication that is not based on the state-of-the-art Fast Simplified Successive-Cancellation (Fast-SSC) decoding algorithm, and only synthesis implementation results without energy estimation are shown. In contrast, our paper presents several optimized Fast-SSC polar code decoder implementations using IB-based quantization with placement and routing results using advanced 12 nm FinFET technology. Gains of up to 16% in area and 13% in energy efficiency are achieved with IB-based quantization at a Frame Error Rate (FER) of 10-7 and a polar code of N=1024,R=0.5 compared to state-of-the-art decoders.

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.

Reducing Complexity of SC-Based Flip Decoding of Polar Codes by Early-Stopping

Reducing Complexity of SC-Based Flip Decoding of Polar Codes by Early-Stopping

Fast Successive-Cancellation Decoding of Polar Codes With Sequence Nodes

Fast Successive-Cancellation Decoding of Polar Codes With Sequence Nodes

Decoding of Polar Codes Using Quadratic Unconstrained Binary Optimization

Decoding of Polar Codes Using Quadratic Unconstrained Binary Optimization

Fast Successive Cancellation Decoding of Polar Codes with Large Kernels

Fast Successive Cancellation Decoding of Polar Codes with Large Kernels

Bidirectional Deep Learning Decoder for Polar Codes in Flat Fading Channels

Bidirectional Deep Learning Decoder for Polar Codes in Flat Fading Channels

Low Complexity Early Stopping Belief Propagation Decoder for Polar Codes

Low Complexity Early Stopping Belief Propagation Decoder for Polar Codes

High-Throughput and Flexible Belief Propagation List Decoder for Polar Codes

High-Throughput and Flexible Belief Propagation List Decoder for Polar Codes

A Critical-Set-Based Multi-Bit Successive Cancellation List Decoder for Polar Codes: Algorithm and Implementation

A Critical-Set-Based Multi-Bit Successive Cancellation List Decoder for Polar Codes: Algorithm and Implementation

Performance of Adaptive Bit-Interleaved Polar Coded Modulation in FSOC System

This paper proposes an adaptive bit-interleaved polar coded modulation (A-BIPCM) method based on minimum logarithmic upper bound weight (MLUW). It is designed to reduce the fading effects and long string of bit error interference caused by atmospheric turbulence in free-space optical communications (FSOC). To assess the effectiveness of this method across turbulent channels of varying intensities, we conducted an evaluation of the bit error rate (BER) performance of polar codes in turbulent channels. The results demonstrate significant performance improvements provided by the A-BIPCM method compared to conventional polar code encoding and decoding. Specifically, under weak, moderate, and strong turbulence conditions, the A-BIPCM method achieves performance gains of 0.96 dB, 1.66 dB, and 1.35 dB, respectively. Additionally, an experimental verification platform for FSOC employing intensity modulation direct detection (IM/DD) with an atmospheric turbulence simulation channel, is established in this work. When the optical power of the detector is −16 dBm, the traditional polar code encoding and decoding performance at BER = 2.36 × 10−5, whereas the A-BIPCM scheme exhibits a significantly higher performance at BER = 2.11 × 10−6. The BER has been improved by representing an order of magnitude.

Design and decoding of polar codes with large kernels: a survey

We present techniques for the construction of polar codes with large kernels and their decoding. A crucial problem in the implementation of the successive cancellation decoding algorithm and its derivatives is kernel processing, i.e., fast evaluation of the log-likelihood ratios for kernel input symbols. We discuss window and recursive trellis processing methods. We consider techniques for evaluation of the reliability of bit subchannels and for obtaining codes with improved distance properties.

Sparse graph neural network aided efficient decoder for polar codes under bursty interference

In this paper, a sparse graph neural network-aided (SGNN-aided) decoder is proposed for improving the decoding performance of polar codes under bursty interference. Firstly, a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding. To further improve the decoding performance, a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network. This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks. Finally, predictions are generated by feeding the embedding vectors into a readout module. Simulation results are shown that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.

Research on different channel coding methods for 5G communication

The implementation of channel coding techniques has the potential to yield coding gains, augment the capacity of the communication system, and significantly enhance the performance of the communication system. The quest for a code possessing a channel capacity surpassing the Shannon limit has been a longstanding pursuit among researchers. The utilization of Polar codes, a coding technique proposed by E. Arikan in 2007, was initially implemented. Theoretical demonstrations have shown that the Shannon limit can be achieved for binary, discrete, memoryless channels through the utilization of a code with a straightforward algorithm. This has resulted in notable progress within the realm of channel coding. As a new coding technology, polar codes have attracted extensive attention in the wireless communication field and become one of the most attractive research hotspots in the coding field. This paper systematically expounds polar codes, analyzes the coding and decoding principles of polar codes, and compares them with Turbo codes and LDPC codes. In this study, polar code coding and decoding are simulated and implemented, and the impact of coding block length, coding rate, and iteration time variations on the performance of polar codes is explored. Through simulation and comparison, the performance, benefits, and drawbacks of these three codes are compared with the polar codes, turbo codes, and LDPC codes.

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.

An Improved Critical Set for List Decoding of Polar Codes

An Improved Critical Set for List Decoding of Polar Codes

Application of Guessing to Sequential Decoding of Polarization-Adjusted Convolutional (PAC) Codes

Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the cutoff rate denotes the region between rates whose average computational complexity of decoding is finite and those which is infinite. In this paper, by benefiting from the polarization and guessing techniques, we prove that the required computation in sequential decoding of pre-transformed polar codes polarizes, and this polarization determines which set of bit positions within the rate profile may result in high computational complexity. Based on this, we propose a technique for taming the Reed-Muller (RM) rate-profile construction, and the performance results demonstrate that the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed-RM rate-profile construction and requires a significantly lower computational complexity than the RM rate-profile construction.