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.

Algebraic-Based Nonbinary LDPC Codes with Flexible Field Orders and Code Rates

In this paper, we study the rank of matrices over GF(2~p),and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all elements of each column of the binary parity-check matrix H corresponding to the original code with the same nonzero element of any field, the first class of nonbinary LDPC codes with flexible field order is proposed. The second method is to replace the nonzero elements of some columns in H with different nonzero field elements in a given field, and then another class of nonbinary LDPC codes with various rates is obtained. Simulation results show that the proposed nonbinary LDPC codes perform well over the AWGN channel with the iterative decoding algorithms.

Construction of Short-Block Nonbinary LDPC Codes Based on Cyclic Codes

In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.

Male, Female, and Nonbinary Differences in UK Twitter Self-descriptions: A Fine-grained Systematic Exploration

Purpose: Although gender identities influence how people present themselves on social media, previous studies have tested pre-specified dimensions of difference, potentially overlooking other differences and ignoring nonbinary users.Design/methodology/approach: Word association thematic analysis was used to systematically check for fine-grained statistically significant gender differences in Twitter profile descriptions between 409,487 UK-based female, male, and nonbinary users in 2020. A series of statistical tests systematically identified 1,474 differences at the individual word level, and a follow up thematic analysis grouped these words into themes.Findings: The results reflect offline variations in interests and in jobs. They also show differences in personal disclosures, as reflected by words, with females mentioning qualifications, relationships, pets, and illnesses much more, nonbinaries discussing sexuality more, and males declaring political and sports affiliations more. Other themes were internally imbalanced, including personal appearance(e.g. male: beardy;female: redhead), selfevaluations(e.g. male: legend;nonbinary: witch;female: feisty), and gender identity(e.g. male: dude;nonbinary: enby;female: queen).Research limitations: The methods are affected by linguistic styles and probably underreport nonbinary differences.Practical implications: The gender differences found may inform gender theory, and aid social web communicators and marketers.Originality/value: The results show a much wider range of gender expression differences than previously acknowledged for any social media site.

Hybrid weighted symbol-flipping decoding for nonbinary LDPC codes

A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorithm （FFT-QSPA）. The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low- eomplexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.

Nonbinary polar coding with low decoding latency and complexity

In this paper,we propose a new class of nonbinary polar codes,where the symbol-level polarization is achieved by using a 2×2 q-ary matrix[10β1]as the kernel.Under bit-level code construction,some partially-frozen symbols exist,where the frozen bits in these symbols can be used as activecheck bits to facilitate the decoder.The encoder/decoder of the proposed codes has a similar structure to the original binary polar codes,admitting an easily configurable and flexible implementation,which is an obvious advantage over the existing nonbinary polar codes based on ReedSolomon(RS)codes.A low-complexity decoding method is also introduced,in which only more competitive symbols are considered rather than the whole q symbols in the finite field.To support high spectral efficiency,we also present,in addition to the single level coded modulation scheme with field-matched modulation order,a mixed multilevel coded modulation scheme with arbitrary modulation in order to trade off the latency against complexity.Simulation results show that our proposed nonbinary polar codes exhibit comparable performance with the RS4-based polar codes and outperform binary polar codes with low decoding latency,suggesting a potential application for future ultra-reliable and low-latency communications(URLLC).

Construction of nonbinary quantum cyclic codes by using graph method

Using the graph method proposed by Schlingemann and Werner, this paper introduces a technique to construct nonbinary quantum cyclic codes and provides a specific example. We also construct the quantum codes [[8, 2, 4]]p and [[n, n - 2, 2]]p for all odd primes p by the graph method.

一种Nonbinary-Turbo-DFH方案及译码算法

一种Nonbinary-Turbo-DFH系统方案,提出了多进制系统递归卷积码类型的G函数及编译码器结构,并给出了相应的软判决迭代译码算法。Nonbinary-Turbo-DFH改进了Turbo-DFH系统的编译码器结构,使用了新的G函数和相应译码算法,解决了Turbo-DFH系统中缺少系统码跳频信息的问题,仿真结果表明,与传统DFH和Turbo-DFH系统相比,Nonbinary-Turbo-DFH系统具有更好的误比特率性能。