Article
Mathematics, Applied
Xiaomeng Zhu, Yangjiang Wei
Summary: In this paper, quaternary linear codes are constructed using simplicial complexes and their weight distributions are determined. Additionally, an infinite family of minimal quaternary linear codes that meet the Griesmer bound is presented.
Article
Mathematics, Applied
Xiaoxiao Li, Minjia Shi
Summary: In this paper, we construct several infinite families of codes over the chain ring R = F-2[u]/< u(k)>, and compute the homogeneous weight distributions of these codes when simplicial complexes are generated by a single maximal element. Through the Gray map, it is determined that some codes are minimal while others are distance optimal. These codes have minimal codewords for inclusion of supports, making them suitable for secret sharing schemes.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Telecommunications
Rongsheng Wu, Minjia Shi
Summary: Mixed alphabet codes are generalizations of classical linear codes over finite fields and rings. The letter introduces a method to construct FpR-additive codes, which are a combination of irreducible cyclic codes over F-p and trace codes over R. By using the Gray map, part of the obtained image codes meets the Greismer bound and can be used to construct new secret sharing schemes.
IEEE COMMUNICATIONS LETTERS
(2021)
Article
Mathematics, Applied
Minjia Shi, Xiaoxiao Li
Summary: In this paper, we construct new families of codes using simplicial complexes and compute their Lee weight distributions. Through the Gray map, we demonstrate that some of these codes are minimal and distance optimal.
FINITE FIELDS AND THEIR APPLICATIONS
(2022)
Article
Mathematics, Applied
Yang Pan, Yan Liu
Summary: This article describes two classes of few-weight ternary codes and computes their minimum weight and weight distribution using mathematical objects called simplicial complexes. One class of codes mentioned here has the same parameters as binary first-order Reed-Muller codes. A class of (optimal) minimal linear codes is also obtained in this correspondence.
Article
Engineering, Electrical & Electronic
Dong Yang, Yinyou Mao, Xingcheng Liu
Summary: Polar codes have gained attention for their excellent performance, but traditional decoding algorithms face time delays. This study proposes a strategy for judging error frames using frozen bits, allowing for early termination of decoding and saving computational resources. Experimental results show that the proposed strategy can recognize at least 85% of erroneously decoded frames.
IET COMMUNICATIONS
(2023)
Article
Engineering, Electrical & Electronic
Mao-Ching Chiu, Yi-Sheng Su
Summary: The performance of a code under the maximum-likelihood decoder is highly influenced by the weight enumerating function. Efficiently computing the weight enumerating function for polar codes or polarization-adjusted convolutional codes remains an open problem. For stand-alone polar code design, we enumerate the number of minimum-weight non-zero codewords and approximate the block error rate using this information. For PAC code design, we average the weight enumerating function over random PAC code ensembles and represent the ML-BLER upper bound as a function of this average. Bit-channel selection algorithms are proposed for polar codes and PAC codes, considering both the polarization effect and ML decoding performance. Simulation results show competitive performance of the proposed stand-alone polar codes for large block lengths and excellent performance of the proposed PAC codes compared to 5G polar codes.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Mathematics, Applied
Shukai Wang, Minjia Shi
Summary: By selecting the down-set appropriately, the weight distribution of the additive code C-L was determined, leading to several infinite families of minimal and optimal few-weight p-codes obtainable through the Gray map, which are applicable in secret sharing schemes.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Computer Science, Information Systems
Hai Q. Dinh, Jamal Laaouine, Mohammed E. Charkani, Warattaya Chinnakum
Summary: This paper investigates the Hamming distance of a certain class of cyclic codes over a specific ring and identifies all maximum distance separable codes among them.
Article
Engineering, Electrical & Electronic
Mohsen Moradi, Amir Mozammel
Summary: This paper introduces an improvement to the SCL decoding that reduces the number of sorting operations without degrading the error-correction performance of the code. By optimizing the metric function, it is found that the correct branch's bit-metric value must be equal to the bit-channel capacity, while the average bit-metric value of a wrong branch can be at most zero. Based on these findings, a pruning technique is presented and experimental results show a substantial decrease in the amount of sorting procedures required for SCL decoding.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Computer Science, Information Systems
Xiaoqiang Wang, Chunming Tang, Cunsheng Ding
Summary: The interplay between coding theory and combinatorial t-designs has been a popular topic of research among combinatorialists and coding theorists for many years. While infinite families of cyclic codes supporting 3-designs have been constructed, no infinite family of negacyclic codes supporting 3-designs has been reported. This paper aims to present an infinite family of cyclic codes and two infinite families of negacyclic codes that support 3-designs. The parameters and weight distributions of these codes are determined, and the subfield subcodes of the negacyclic codes over GF(q) are studied. Three infinite families of almost MDS codes and a constacyclic code supporting a 4-design are also presented.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Telecommunications
Dileep Kumar Soma, Asit Kumar Pradhan, Krishna Narayanan
Summary: This study explores a concatenated soft decision forward error correcting coding scheme with an inner LDGM code and an outer PC code for high-speed optical communications. By comparing different schemes, the study derives an exact expression for errors and erasures decoded by the outer product code, and proposes a method for choosing optimal thresholds for declaring erasures at the output of the inner decoder. It is found that the codeword error rate for the error + erasure iterative decoder outperforms that of error only iterative decoder in the error floor region.
IEEE COMMUNICATIONS LETTERS
(2021)
Article
Telecommunications
Shudi Yang
Summary: By utilizing a proper defining set, a class of linear codes with two or three nonzero weights has been defined and their complete weight enumerators and weight enumerators have been determined using Weil sums. Some of these codes are optimal with respect to the Griesmer bound or Markus Grassl's code tables, making them suitable for applications in strongly regular graphs and secret sharing schemes.
IEEE COMMUNICATIONS LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Mohammad Rowshan, Emanuele Viterbo
Summary: This paper introduces polarization-adjusted convolutional (PAC) codes, which use a one-to-one convolutional transform and polar transform to improve the Hamming distance properties of polar codes, and improve error correction performance by adjusting constraint length, list size, and sorting strategy. Analysis shows that the path sorting complexity in local sorting of the paths in the parallel list Viterbi algorithm (LVA) is significantly lower than global sorting in list decoding.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
(2021)
Article
Computer Science, Information Systems
Maryam Haghighi Ardakani, Muhammad Hanif, Masoud Ardakani, Chintha Tellambura
Summary: Utilizing large size kernels along with binary kernels provides length flexibility in polar codes, but results in high decoding complexity. Size-3 kernels are popular due to their high polarization exponents and low decoding complexity, yet two specific size-3 kernels with optimal polarization have a zero in their last rows causing error-rate performance degradation. Proposed modifications to REP and G-REP nodes aim to improve error-rate performance and reduce memory requirements for fast decoders.
IEEE WIRELESS COMMUNICATIONS LETTERS
(2021)
