Mutual Information-Maximizing Quantized Belief Propagation Decoding of Regular LDPC Codes

In mutual information-maximizing lookup table (MIM-LUT) decoding of low-density parity-check (LDPC) codes, table lookup operations are used to replace arithmetic operations. In practice, large tables need to be decomposed into small tables to save the memory consumption, at the cost of degraded error performance. In this paper, we propose a method, called mutual information-maximizing quantized belief propagation (MIM-QBP) decoding, to remove the lookup tables used for MIM-LUT decoding. Our method leads to a very efficient decoder, namely the MIM-QBP decoder, which can be implemented based only on simple mappings and fixed-point additions. Simulation results show that the MIM-QBP decoder can always considerably outperform the state-of-the-art MIM-LUT decoder, mainly because it can avoid the performance loss due to table decomposition. Furthermore, the MIM-QBP decoder with only 3 bits per message can outperform the floating-point belief propagation (BP) decoder at high signal-to-noise ratio (SNR) regions when testing on high-rate codes with a maximum of 10-30 iterations

Understanding Electronic-commerce platforms’ Role in Indirect Patent Infringement: Law Enforcers in the United States and Notice Enforcers in China

More and more bad faith complaints about indirect patent infringement are filed to e-commerce platforms in China The roles that e-commerce platforms play in indirect patent infringement are different law enforcers in the United States and notice enforcers in China In the context of indirect patent infringement the e-commerce platform operators can take down the allegedly infringing listings only if the right holder can provide the court order enjoining the sales of the patented items In contrast the platforms in China seem to remove the allegedly infringing products when they receive the notice from the patentee This paper examines IP policies between eBay and Alibaba the largest e-commerce platforms in the U S and China respectively It also compares cases and statutes on the issue of indirect patent infringement occurring on e-commerce platforms to explore the different roles of e-commerce platforms in China and the US Learning from the United States the paper concludes with legislative and collaborative governance suggestions to pave the way for e-commerce platform governance in the context of indirect patent infringemen

Development of Students’ Digital Capability under the Context of New Liberal Arts Construction

The construction of the new liberal arts puts forward new requirements and expectations for the training of liberal arts students. This paper demonstrates the importance of enhancing students’ digital capability in the context of new liberal arts construction in our country, and discusses the three challenges that liberal arts students face in improving their digital ability, namely, poor grasp of mathematics, self-psychological exclusion, and lack of opportunities for digital ability and communication. Based on this, this paper puts forward three measures to promote the basic ability of mathematics, the psychological construction of mathematics learning, and the digital resource system of arts, in order to provide reference basis for promoting the construction of new liberal arts

Generalized Reed-Solomon Codes with Sparsest and Balanced Generator Matrices

We prove that for any positive integers $n$ and $k$ such that $n\!\geq\! k\!\geq\! 1$, there exists an $[n,k]$ generalized Reed-Solomon (GRS) code that has a sparsest and balanced generator matrix (SBGM) over any finite field of size $q\!\geq\! n\!+\!\lceil\frac{k(k-1)}{n}\rceil$, where sparsest means that each row of the generator matrix has the least possible number of nonzeros, while balanced means that the number of nonzeros in any two columns differ by at most one. Previous work by Dau et al (ISIT'13) showed that there always exists an MDS code that has an SBGM over any finite field of size $q\geq {n-1\choose k-1}$, and Halbawi et al (ISIT'16, ITW'16) showed that there exists a cyclic Reed-Solomon code (i.e., $n=q-1$) with an SBGM for any prime power $q$. Hence, this work extends both of the previous results

Basis-Finding Algorithm for Decoding Fountain Codes for DNA-Based Data Storage

In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in the DNA-based data storage systems where the inner code decoding, which generally has undetectable errors, is performed before the outer fountain code decoding. We propose a novel and efficient decoding algorithm, namely the basis-finding algorithm (BFA). The key idea of the BFA is to find a basis of the received symbols, and then use the most reliable basis elements to recover the source symbols with the inactivation decoding. Gaussian elimination is used to find the basis and to identify the most reliable basis elements. As a result, the BFA has polynomial time complexity. For random fountain codes, we are able to derive some theoretical bounds for the frame error rate (FER) of the BFA. Extensive simulations with Luby transform (LT) codes show that for the scenario we consider, the BFA has significantly better FER than the belief propagation (BP) algorithm except when the overhead is extremely large.Comment: 13 page

Bridged [2.2.1] bicyclic phosphine oxide facilitates catalytic γ-umpolung addition-Wittig olefination.

A novel bridged [2.2.1] bicyclic phosphine oxide, devised to circumvent the waste generation and burdens of purification that are typical of reactions driven by the generation of phosphine oxides, has been prepared in three steps from commercially available cyclopent-3-ene-1-carboxylic acid. The performance of this novel phosphine oxide was superior to those of current best-in-class counterparts, as verified experimentally through kinetic analysis of its silane-mediated reduction. It has been applied successfully in halide-/base-free catalytic γ-umpolung addition-Wittig olefinations of allenoates and 2-amidobenzaldehydes to produce 1,2-dihydroquinolines with good efficiency. One of the 1,2-dihydroquinoline products was converted to known antitubercular furanoquinolines