Novel joint encoding/decoding algorithms of fountain codes for underwater acoustic communication

Fountain codes are considered to be a promising coding technique in underwater acoustic communication（UAC） which is challenged with the unique propagation features of the underwater acoustic channel and the harsh marine environment. And Luby transform（LT） codes are the first codes fully realizing the digital fountain concept. However, in conventional LT encoding/decoding algorithms, due to the imperfect coverage（IC） of input symbols and short cycles in the generator matrix, stopping sets would occur and terminate the decoding. Thus, the recovery probability is reduced,high coding overhead is required and decoding delay is increased.These issues would be disadvantages while applying LT codes in underwater acoustic communication. Aimed at solving those issues, novel encoding/decoding algorithms are proposed. First,a doping and non-uniform selecting（DNS） encoding algorithm is proposed to solve the IC and the generation of short cycles problems. And this can reduce the probability of stopping sets occur during decoding. Second, a hybrid on the fly Gaussian elimination and belief propagation（OFG-BP） decoding algorithm is designed to reduce the decoding delay and efficiently utilize the information of stopping sets. Comparisons via Monte Carlo simulation confirm that the proposed schemes could achieve better overall decoding performances in comparison with conventional schemes.

The Dissemination of Chinese Tea Culture Based on Encoding/Decoding Theory

Tea has a history of thousands of years in China and it plays an important role in the working-life and daily life of people.Tea culture rich in connotation is an important part of Chinese traditional culture,and its existence and development are also of great significance to the diversified development of world culture.Based on Stuart Hall’s encoding/decoding theory,this paper analyzes the problems in the spreading of Chinese tea in and out of the country and provides solutions from the perspective of encoding,communication,and decoding.It is expected to provide a reference for the domestic and international dissemination of Chinese tea culture.

The Dissemination of Intangible Cultural Heritage Along Beijing-Hangzhou Canal Based on Encoding/Decoding Theory

The Beijing-Hangzhou Grand Canal carries a wealth of Chinese cultural symbols,showing the lifestyle and wisdom of working people through ages.The preservation and inheritance of its intangible cultural heritage can help to evoke cultural memories and cultural identification of the Canal and build cultural confidence.This paper applies Stuart Hall’s encoding/decoding theory to analyze the dissemination of intangible heritage tourism culture.On the basis of a practical study of the villages along the Beijing-Hangzhou Grand Canal,this paper analyses the problems in the transmission of its intangible cultural heritage and proposes specific methods to solve them in four processes,encoding,decoding,communication,and secondary encoding,in order to propose references for the transmission of intangible heritage culture at home and abroad.

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.

Decoding topological XYZ^(2) codes with reinforcement learning based on attention mechanisms

Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ^(2) code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ^(2) codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ^(2) codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.

Recurrent neural network decoding of rotated surface codes based on distributed strategy

Quantum error correction is a crucial technology for realizing quantum computers.These computers achieve faulttolerant quantum computing by detecting and correcting errors using decoding algorithms.Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models.In this paper,we use a distributed decoding strategy,which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases.Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder.The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy.Then we test the decoding performance of our distributed strategy decoder,recurrent neural network decoder,and the classic minimum weight perfect matching(MWPM)decoder for rotated surface codes with different code distances under the circuit noise model,the thresholds of these three decoders are about 0.0052,0.0051,and 0.0049,respectively.Our results demonstrate that the distributed strategy decoder outperforms the other two decoders,achieving approximately a 5%improvement in decoding efficiency compared to the MWPM decoder and approximately a 2%improvement compared to the recurrent neural network decoder.

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...

Polar codes: Encoding/decoding and rate-compatible jointly design for HARQ system

Polar coding are the first class of provable capacity-achieving coding techniques for a wide range of channels.With an ideal recursive structure and many elegant mathematical properties,polar codes are inherently implemented with low complexity encoding and decoding algorithms.Since the block length of the original polar construction is limited to powers of two,rate-compatible polar codes(RCPC)are presented to meet the flexible length/rate transmission requirements in practice.The RCPC codes are well-conditioned to combine with the hybrid automatic repeat request(HARQ)system,providing high throughput efficiency and such RCPC-HAPQ scheme is commonly used in delay-insensitive communication system.This paper first gives a survey of both the classical and state-of-the-art encoding/decoding algorithms for polar codes.Then the RCPC construction methods are discussed,including the puncturing,shortening,multi-kernel construction,etc.Finally,we investigate several RCPC-HARQ jointly design systems and discuss their encoding gain and re-transmission diversity gain.

A Denoiser for Correlated Noise Channel Decoding: Gated-Neural Network

This letter proposes a sliced-gated-convolutional neural network with belief propagation(SGCNN-BP) architecture for decoding long codes under correlated noise. The basic idea of SGCNNBP is using Neural Networks(NN) to transform the correlated noise into white noise, setting up the optimal condition for a standard BP decoder that takes the output from the NN. A gate-controlled neuron is used to regulate information flow and an optional operation—slicing is adopted to reduce parameters and lower training complexity. Simulation results show that SGCNN-BP has much better performance(with the largest gap being 5dB improvement) than a single BP decoder and achieves a nearly 1dB improvement compared to Fully Convolutional Networks(FCN).

A highly reliable encoding and decoding communication framework based on semantic information

Increasing research has focused on semantic communication,the goal of which is to convey accurately the meaning instead of transmitting symbols from the sender to the receiver.In this paper,we design a novel encoding and decoding semantic communication framework,which adopts the semantic information and the contextual correlations between items to optimize the performance of a communication system over various channels.On the sender side,the average semantic loss caused by the wrong detection is defined,and a semantic source encoding strategy is developed to minimize the average semantic loss.To further improve communication reliability,a decoding strategy that utilizes the semantic and the context information to recover messages is proposed in the receiver.Extensive simulation results validate the superior performance of our strategies over state-of-the-art semantic coding and decoding policies on different communication channels.

The"Decoding Zhonghua"International Conference on Dialogue among Civilisations Held in Beijing

The"Decoding Zhonghua"International Conference on Dialogue among Civilisations,hosted by China International Public Relations Association,China Ethnic News and Academy of Contemporary China and World Studies was held in Beijing on January 17th.With the theme"Pursing Harmonious Coexistence of Civilisations through Dialogue".

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.