Deterministic Constructions for Large Girth Protograph LDPC Codes

The bit-error threshold of the standard ensemble of Low Density Parity Check (LDPC) codes is known to be close to capacity, if there is a non-zero fraction of degree-two bit nodes. However, the degree-two bit nodes preclude the possibility of a block-error threshold. Interestingly, LDPC codes constructed using protographs allow the possibility of having both degree-two bit nodes and a block-error threshold. In this paper, we analyze density evolution for protograph LDPC codes over the binary erasure channel and show that their bit-error probability decreases double exponentially with the number of iterations when the erasure probability is below the bit-error threshold and long chain of degree-two variable nodes are avoided in the protograph. We present deterministic constructions of such protograph LDPC codes with girth logarithmic in blocklength, resulting in an exponential fall in bit-error probability below the threshold. We provide optimized protographs, whose block-error thresholds are better than that of the standard ensemble with minimum bit-node degree three. These protograph LDPC codes are theoretically of great interest, and have applications, for instance, in coding with strong secrecy over wiretap channels.Comment: 5 pages, 2 figures; To appear in ISIT 2013; Minor changes in presentatio

The Trend of Leadership Research in Higher Education: A Bibliometric Overview and Visualization

This study examines leadership research in higher education from 2008 to 2022. A total of 268 important publications were systematically retrieved and bibliometrically analyzed from the Scopus database. The present study employed Bibliometrix to analyse leadership research trends. To represent the general pattern and structure of leadership research in higher education, the final analysis incorporates bibliometric indicators, e.g., annual scientific production, most prolific journal, most prolific author, country and institutions, most influential articles, co-citation, and author’s keywords. This bibliometric investigation revealed that the US, Australia, and the UK produce the most relevant publications. It is also observed that there is still a severe manque of leadership research in higher education, and there is no appreciable growth in this field from 2008 to 2022. To give more in-depth information about the trend topics and important fields of leadership research in higher education, co-citation, and the author’s keyword analysis are also employed. The study offers valuable insight into leadership research in higher education for theoretical and practical advancements for further studies

Quaternary-Binary Message-Passing Decoder for Quantum LDPC Codes

We introduce a low-complexity message-passing quantum error correction algorithm for decoding Quantum Low-Density Parity-Check (QLDPC) stabilizer codes. The proposed decoder operates on the quaternary stabilizer graph but only exchanges binary messages. This leads to a significantly reduced complexity compared to other quaternary belief propagation (BP) algorithms that pass floating-point messages. The efficacy of the proposed decoder is evaluated by providing decoding examples, performance metrics using Monte-Carlo simulations, and complexity analysis. Despite its reduced complexity, the performance loss of the proposed decoder is modest compared to floating-point parallel quaternary decoders for a Calderbank-Shor-Steane (CSS) code family. In particular, experiments obtained over the [[1054, 140, 20]] lifted product (LP) Tanner code demonstrated that for low error rates (< 0.01), the proposed quaternary-binary message-passing decoder approaches the performance of quaternary BP by converging in almost the same number of iterations while requiring less complex operations. Additionally, for non-CSS codes, our decoder performs similarly as quaternary floating-point decoders despite its lower complexity.NSFImmediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]