• Journal of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.507-521
• /
• 2019

For any $m{\times}n$ nonbinary Boolean matrix A, its spanning column rank is the minimum number of the columns of A that spans its column space. We have a characterization of spanning column rank-1 nonbinary Boolean matrices. We investigate the linear operators that preserve the spanning column ranks of matrices over the nonbinary Boolean algebra. That is, for a linear operator T on $m{\times}n$ nonbinary Boolean matrices, it preserves all spanning column ranks if and only if there exist an invertible nonbinary Boolean matrix P of order m and a permutation matrix Q of order n such that T(A) = PAQ for all $m{\times}n$ nonbinary Boolean matrix A. We also obtain other characterizations of the (spanning) column rank preserver.

• Archives of Plastic Surgery
• /
• v.50 no.1
• /
• pp.63-69
• /
• 2023

Background An increasing number of nonbinary patients are receiving gender-affirming procedures due to improved access to care. However, the preferred treatments for nonbinary patients are underdescribed. The purpose of this study was to investigate the goals and treatments of nonbinary patients. Methods A retrospective study of patients who self-identified as nonbinary from our institutional Gender Health Program was conducted. Patient demographics, clinical characteristics, surgical goals, and operative variables were analyzed. Results Of the 375 patients with gender dysphoria, 67 (18%) were nonbinary. Over half of the nonbinary patients were assigned male at birth (n = 57, 85%) and nearly half preferred the gender pronoun they/them/theirs (n = 33, 49%). A total of 44 patients (66%) received hormone therapy for an average of 2.5±3.6 years, primarily estrogen (n = 39). Most patients (n = 46, 69%) received or are interested in gender-affirming surgery, of which, almost half were previously on hormone therapy (n = 32, 48%). The most common surgeries completed or desired were facial feminization surgery (n = 15, 22%), vaginoplasty (n = 15, 22%), mastectomy (n = 11, 16%), and orchiectomy (n = 9, 13%). Nonbinary patients who were assigned male at birth (NB-AMAB) were more often treated with hormones compared to nonbinary patients assigned female at birth (NB-AFAB) (72% vs. 30%, p = 0.010). Conversely, patients who were AFAB weremore likely to complete or desire surgical intervention than those who were AMAB (100% vs. 63.0%, p < 0.021). Conclusion Majority of nonbinary patients were assigned male at birth. NB-AFAB patients all underwent surgical treatment, whereas NB-AMAB patients were predominantly treated with hormone therapy.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.38C no.10
• /
• pp.852-857
• /
• 2013

In this paper we propose a design algorithm for nonbinary LDPC (low-density parity-check) codes with low error-floors. The proposed algorithm determines the nonbinary values of the nonzero entries in the parity-check matrix in order to maximize the binary minimum distance of the designed nonbinary LDPC codes. We verify the performance of the designed nonbinary LDPC codes in the error-floor region by Monte Carlo simulation and importance sampling over BPSK (binary phase-shift keying) modulation.

• Journal of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.113-123
• /
• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

• Journal of Communications and Networks
• /
• v.15 no.4
• /
• pp.411-421
• /
• 2013

Digital fountain codes are record-breaking codes for erasure channels. They have many potential applications in both wired and wireless communications. Most existing digital fountain codes operate over binary fields using an iterative belief-propagation (BP) decoding algorithm. In this paper, we propose a new iterative decoding algorithm for both binary and nonbinary fields. The basic form of our proposed algorithm considers both degree-1 and degree-2 check nodes (instead of only degree-1 check nodes as in the original BP decoding scheme), and has linear complexity. Extensive simulation demonstrates that it outperforms the original BP decoding scheme, especially for a small number of source packets. The enhanced form of the proposed algorithm combines the basic form of the algorithm and a guess-based algorithm to further improve the decoding performance. Simulation results demonstrate that it can provide better decoding performance than the guess-based algorithm with fewer guesses, and can achieve decoding performance close to that of the maximum likelihood decoder at a much lower decoding complexity. Last, we show that our nonbinary scheme has the potential to outperform the binary scheme when choosing suitable degree distributions, and furthermore it is insensitive to the size of the Galois field.

• Journal of Communications and Networks
• /
• v.14 no.4
• /
• pp.429-433
• /
• 2012

In this paper, we consider nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes and propose a method to design multiple rate codes with either fixed information bit length or block bit length, tailored to different scenarios in wireless applications. We show that the proposed codes achieve good performance over a broad range of code rates.

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.169-179
• /
• 2009

Let P be a (n, n − 1, j)-poset, which is a partially ordered set of cardinality n with n − 1 maximal elements and $j(1{\leq}j{\leq}n-1)$ minimal elements, and $P^*$ the dual poset of P. In this paper, we obtain two types of incidence codes of nonempty proper subset S of P and $P^*$, respectively, by using Bogart's method [1] (see Theorem 3.3).

• Proceedings of the Korean Institute of Communication Sciences Conference
• /
• 1985.10a
• /
• pp.89-92
• /
• 1985

• IEIE Transactions on Smart Processing and Computing
• /
• v.6 no.3
• /
• pp.210-219
• /
• 2017

This paper proposes a modified min-max algorithm (MMMA) for nonbinary quasi-cyclic low-density parity-check (NB-QC-LDPC) codes and an efficient parallel block-layered decoder architecture corresponding to the algorithm on a graphics processing unit (GPU) platform. The algorithm removes multiplications over the Galois field (GF) in the merger step to reduce decoding latency without any performance loss. The decoding implementation on a GPU for NB-QC-LDPC codes achieves improvements in both flexibility and scalability. To perform the decoding on the GPU, data and memory structures suitable for parallel computing are designed. The implementation results for NB-QC-LDPC codes over GF(32) and GF(64) demonstrate that the parallel block-layered decoding on a GPU accelerates the decoding process to provide a faster decoding runtime, and obtains a higher coding gain under a low $10^{-10}$ bit error rate and low $10^{-7}$ frame error rate, compared to existing methods.

• Journal of Korean Institute of Industrial Engineers
• /
• v.23 no.4
• /
• pp.803-816
• /
• 1997

In this paper we propose a new approach far part families considering multiple attributes of parts in the design and operating stage of flexible manufacturing systems. We first represent the relationship of parts and the relative attributes using fuzzy membership function, AHP method and normalization. As a result, more realistic nonbinary data of the relationship is obtained. Then we group parts into part families based on the nonbinary data using fuzzy $\alpha$-cut and new similarity coefficient method. The performance of our method is compared numerically with others.