Improved Segmented Belief Propagation List Decoding for Polar Codes with Bit-Flipping

Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.

Deep Learning Aided SCL Decoding of Polar Codes with Shifted-Pruning

Recently,a generalized successive cancellation list(SCL)decoder implemented with shiftedpruning(SP)scheme,namely the SCL-SP-ωdecoder,is presented for polar codes,which is able to shift the pruning window at mostωtimes during each SCL re-decoding attempt to prevent the correct path from being eliminated.The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs.However,the number of exponential/logarithm operations involved in the SCL-SP-ωdecoder grows linearly with the number of information bits and list size,which leads to high computational complexity.In this paper,we present a detailed analysis of the SCL-SP-ωdecoder in terms of the decoding performance and complexity,which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously.Then,we introduce a simplified metric derived from the path metric(PM)domain,and a custom-tailored deep learning(DL)network is further designed to enhance the efficiency of the proposed simplified metric.The proposed metrics are both free of transcendental functions and hence,are more hardware-friendly than the existing metrics.Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.

Belief Propagation List Decoding for Polar Codes:Performance Analysis and Software Implementation on GPU

Belief propagation(BP)decoding outputs soft information and can be naturally used in iterative receivers.BP list(BPL)decoding provides comparable error-correction performance to the successive cancellation list(SCL)decoding.In this paper,we firstly introduce an enhanced code construction scheme for BPL decoding to improve its errorcorrection capability.Then,a GPU-based BPL decoder with adoption of the new code construction is presented.Finally,the proposed BPL decoder is tested on NVIDIA RTX3070 and GTX1060.Experimental results show that the presented BPL decoder with early termination criterion achieves above 1 Gbps throughput on RTX3070 for the code(1024,512)with 32 lists under good channel conditions.

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.

Parallel Implementation of the CCSDS Turbo Decoder on GPU

This paper presents a software turbo decoder on graphics processing units(GPU).Unlike previous works,the proposed decoding architecture for turbo codes mainly focuses on the Consultative Committee for Space Data Systems(CCSDS)standard.However,the information frame lengths of the CCSDS turbo codes are not suitable for flexible sub-frame parallelism design.To mitigate this issue,we propose a padding method that inserts several bits before the information frame header.To obtain low-latency performance and high resource utilization,two-level intra-frame parallelisms and an efficient data structure are considered.The presented Max-Log-Map decoder can be adopted to decode the Long Term Evolution(LTE)turbo codes with only small modifications.The proposed CCSDS turbo decoder at 10 iterations on NVIDIA RTX3070 achieves about 150 Mbps and 50Mbps throughputs for the code rates 1/6 and 1/2,respectively.

Quantized Decoders that Maximize Mutual Information for Polar Codes

In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.

Soft Decoding Scheme of Convolution Code Combined with Huffman Coding

This paper proposes a modification of the soft output Viterbi decoding algorithm (SOVA) which combines convolution code with Huffman coding. The idea is to extract the bit probability information from the Huffman coding and use it to compute the a priori source information which can be used when the channel environment is bad. The suggested scheme does not require changes on the transmitter side. Compared with separate decoding systems, the gain in signal to noise ratio is about 0 5-1.0 dB with a limi...

Recent Advances in Video Coding for Machines Standard and Technologies

To improve the performance of video compression for machine vision analysis tasks,a video coding for machines(VCM)standard working group was established to promote standardization procedures.In this paper,recent advances in video coding for machine standards are presented and comprehensive introductions to the use cases,requirements,evaluation frameworks and corresponding metrics of the VCM standard are given.Then the existing methods are presented,introducing the existing proposals by category and the research progress of the latest VCM conference.Finally,we give conclusions.

Adaptive Hybrid Forward Error Correction Coding Scheme for Video Transmission

This paper proposes an adaptive hybrid forward error correction(AH-FEC)coding scheme for coping with dynamic packet loss events in video and audio transmission.Specifically,the proposed scheme consists of a hybrid Reed-Solomon and low-density parity-check(RS-LDPC)coding system,combined with a Kalman filter-based adaptive algorithm.The hybrid RS-LDPC coding accommodates a wide range of code length requirements,employing RS coding for short codes and LDPC coding for medium-long codes.We delimit the short and medium-length codes by coding performance so that both codes remain in the optimal region.Additionally,a Kalman filter-based adaptive algorithm has been developed to handle dynamic alterations in a packet loss rate.The Kalman filter estimates packet loss rate utilizing observation data and system models,and then we establish the redundancy decision module through receiver feedback.As a result,the lost packets can be perfectly recovered by the receiver based on the redundant packets.Experimental results show that the proposed method enhances the decoding performance significantly under the same redundancy and channel packet loss.

The Confidentiality of Coding Video Games with Cheat Code and Bots for Cheating in a Virtual World

Video games have been around for several decades and have had many advancements from the original start of video games. Video games started as virtual games that were advertised towards children, and these virtual games created a virtual reality of a variety of genres. These genres included sports games, such as tennis, football, baseball, war games, fantasy, puzzles, etc. The start of these games was derived from a sports genre and now has a popularity in multiplayer-online-shooting games. The purpose of this paper is to investigate different types of tools available for cheating in virtual world making players have undue advantage over other players in a competition. With the advancement in technology, these video games have become more expanded in the development aspects of gaming. Video game developers have created long lines of codes to create a new look of video games. As video games have progressed, the coding, bugs, bots, and errors of video games have changed throughout the years. The coding of video games has branched out from the original video games, which have given many benefits to this virtual world, while simultaneously creating more problems such as bots. Analysis of tools available for cheating in a game has disadvantaged normal gamer in a fair contest.

A simplified decoding algorithm for multi-CRC polar codes

Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list(SCL)decoding algorithm.However,the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check(CRC)polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.

Erasure-Correction-Enhanced Iterative Decoding for LDPC-RS Product Codes

Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.

Efficient Soft-Decision Maximum-Likelihood Decoding of BCH Code in the GNSS

Soft-decision decoding of BCH code in the global navigation satellite system( GNSS) is investigated in order to improve the performance of traditional hard-decision decoding. Using the nice structural properties of BCH code,a soft-decision decoding scheme is proposed. It is theoretically shown that the proposed scheme exactly performs maximum-likelihood( ML) decoding,which means the decoding performance is optimal. Moreover,an efficient implementation method of the proposed scheme is designed based on Viterbi algorithm. Simulation results show that the performance of the proposed soft-decision ML decoding scheme is significantly improved compared with the traditional hard-decision decoding method at the expense of moderate complexity increase.

JOINT ITERATIVE DECODING FOR SIMPLE-ENCODING SYSTEMATIC IRREGULAR-LDPC-BASED CODED COOPERATION IN NON-IDEAL RELAY CHANNEL

In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destination which is in accordance with the corresponding joint Tanner graph characterizing two different component LDPC codes used by the source and relay in ideal and non-ideal relay cooperations. The theoretical analysis and simulations show that the coded cooperation scheme obviously outperforms the coded non-cooperation one under the same code rate and decoding complex. The significant performance improvement can be virtually credited to the additional mutual exchange of the extrinsic information resulted by the LDPC code employed by the source and its counterpart used by the relay in both ideal and non-ideal cooperations.

Construction of LDPC Codes for the Layered Decoding Algorithm

Abstract： The layered decoding algorithm has been widely used in the implementation of Low Density Parity Check （LDPC） decoders, due to its high convergence speed. However, the pipeline operation of the layered decoder may introduce memory access conflicts, which heavily deteriorates the decoder throughput. To essentially deal with the issue of memory access conflicts,

Weighted symbol-flipping decoding algorithm for nonbinary LDPC codes with flipping patterns

A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbol vector iteratively in search of a valid codeword in the symbol vector space. Only one symbol is flipped in each iteration, and symbol flipping function, which is employed as the symbol flipping metric, combines the number of failed checks and the reliabilities of the received bits and calculated symbols. A scheme to avoid infinite loops and select one symbol to flip in high order Galois field search is also proposed. The design of flipping pattern＇s order and depth, which is dependent of the computational requirement and error performance, is also proposed and exemplified. Simulation results show that the algorithm achieves an appealing tradeoff between performance and computational requirement over relatively low Galois field for short to medium code length.

NEW ITERATIVE SUPER-TRELLIS DECODING WITH SOURCE A PRIORI INFORMATION FOR VLCS WITH TURBO CODES

A novel Joint Source and Channel Decoding (JSCD) scheme for Variable Length Codes (VLCs) concatenated with turbo codes utilizing a new super-trellis decoding algorithm is presented in this letter. The basic idea of our decoding algorithm is that source a priori information with the form of bit transition probabilities corresponding to the VLC tree can be derived directly from sub-state transitions in new composite-state represented super-trellis. A Maximum Likelihood (ML) decoding algorithm for VLC sequence estimations based on the proposed super-trellis is also described. Simu-lation results show that the new iterative decoding scheme can obtain obvious encoding gain especially for Reversible Variable Length Codes (RVLCs),when compared with the classical separated turbo decoding and the previous joint decoding not considering source statistical characteristics.

Iterative Decoding of Parallel Concatenated Block Codes and Coset Based MAP Decoding Algorithm for F24 Code

A multi dimensional concatenation scheme for block codes is introduced, in which information symbols are interleaved and re encoded for more than once. It provides a convenient platform to design high performance codes with flexible interleaver size. Coset based MAP soft in/soft out decoding algorithms are presented for the F24 code. Simulation results show that the proposed coding scheme can achieve high coding gain with flexible interleaver length and very low decoding complexity.

Jointly-check iterative decoding algorithm for quantum sparse graph codes

For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.

Integrated Joint Source-Channel Symbol-by-Symbol Decoding of Variable-Length Codes Using 3-D MAP Sequence Estimation

Most of multimedia schemes employ variable-length codes （VLCs） like Huffman code as core components in obtaining high compression rates. However VLC methods are very sensitive to channel noise. The goal of this paper is to salvage as many data from the damaged packets as possible for higher audiovisual quality. This paper proposes an integrated joint source-channel decoder （I-JSCD） at a symbol-level using three-dimensional （3-D） trellis representation for first-order Markov sources encoded with VLC source code and convolutional channel code. This method combines source code and channel code state-spaces and bit-lengths to construct a two-dimensional （2-D） state-space, and then develops a 3-D trellis and a maximum a-posterior （MAP） algorithm to estimate the source sequence symbol by symbol. Experiment results demonstrate that our method results in significant improvement in decoding performance, it can salvage at least half of （50%） data in any channel error rate, and can provide additional error resilience to VLC stream like image, audio, video stream over high error rate links.