Erasure List-Decodable Codes from Random and Algebraic Geometry Codes

Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure errors. The contributions of this paper are two-fold. Firstly, we show that, for arbitrary $00$ ($R$ and $\epsilon$ are independent), with high probability a random linear code is an erasure list decodable code with constant list size $2^{O(1/\epsilon)}$ that can correct a fraction $1-R-\epsilon$ of erasures, i.e., a random linear code achieves the information-theoretic optimal trade-off between information rate and fraction of erasure errors. Secondly, we show that algebraic geometry codes are good erasure list-decodable codes. Precisely speaking, for any $0<R<1$ and $\epsilon>0$, a $q$-ary algebraic geometry code of rate $R$ from the Garcia-Stichtenoth tower can correct $1-R-\frac{1}{\sqrt{q}-1}+\frac{1}{q}-\epsilon$ fraction of erasure errors with list size $O(1/\epsilon)$. This improves the Johnson bound applied to algebraic geometry codes. Furthermore, list decoding of these algebraic geometry codes can be implemented in polynomial time

Optimal Throughput Fairness Trade-offs for Downlink Non-Orthogonal Multiple Access over Fading Channels

Recently, non-orthogonal multiple access (NOMA) has attracted considerable interest as one of the 5G-enabling techniques. However, users with better channel conditions in downlink communications intrinsically benefits from NOMA thanks to successive decoding, judicious designs are required to guarantee user fairness. In this paper, a two-user downlink NOMA system over fading channels is considered. For delay-tolerant transmission, the average sum-rate is maximized subject to both average and peak power constraints as well as a minimum average user rate constraint. The optimal resource allocation is obtained using Lagrangian dual decomposition under full channel state information at the transmitter (CSIT), while an effective power allocation policy under partial CSIT is also developed based on analytical results. In parallel, for delay-limited transmission, the sum of delay-limited throughput (DLT) is maximized subject to a maximum allowable user outage constraint under full CSIT, and the analysis for the sum of DLT is also performed under partial CSIT. Furthermore, an optimal orthogonal multiple access (OMA) scheme is also studied as a benchmark to prove the superiority of NOMA over OMA under full CSIT. Finally, the theoretical analysis is verified by simulations via different trade-offs for the average sum-rate (sum-DLT) versus the minimum (maximum) average user rate (outage) requirement.Comment: 35 pages, 10 figures, 3 tables, the longer version of the paper with the same titl

A World of Difference: Divergent Word Interpretations among People

Divergent word usages reflect differences among people. In this paper, we present a novel angle for studying word usage divergence -- word interpretations. We propose an approach that quantifies semantic differences in interpretations among different groups of people. The effectiveness of our approach is validated by quantitative evaluations. Experiment results indicate that divergences in word interpretations exist. We further apply the approach to two well studied types of differences between people -- gender and region. The detected words with divergent interpretations reveal the unique features of specific groups of people. For gender, we discover that certain different interests, social attitudes, and characters between males and females are reflected in their divergent interpretations of many words. For region, we find that specific interpretations of certain words reveal the geographical and cultural features of different regions.Comment: 4 pages, 1 figure, published at ICWSM'1

In situ structures of the segmented genome and RNA polymerase complex inside a dsRNA virus.

Viruses in the Reoviridae, like the triple-shelled human rotavirus and the single-shelled insect cytoplasmic polyhedrosis virus (CPV), all package a genome of segmented double-stranded RNAs (dsRNAs) inside the viral capsid and carry out endogenous messenger RNA synthesis through a transcriptional enzyme complex (TEC). By direct electron-counting cryoelectron microscopy and asymmetric reconstruction, we have determined the organization of the dsRNA genome inside quiescent CPV (q-CPV) and the in situ atomic structures of TEC within CPV in both quiescent and transcribing (t-CPV) states. We show that the ten segmented dsRNAs in CPV are organized with ten TECs in a specific, non-symmetric manner, with each dsRNA segment attached directly to a TEC. The TEC consists of two extensively interacting subunits: an RNA-dependent RNA polymerase (RdRP) and an NTPase VP4. We find that the bracelet domain of RdRP undergoes marked conformational change when q-CPV is converted to t-CPV, leading to formation of the RNA template entry channel and access to the polymerase active site. An amino-terminal helix from each of two subunits of the capsid shell protein (CSP) interacts with VP4 and RdRP. These findings establish the link between sensing of environmental cues by the external proteins and activation of endogenous RNA transcription by the TEC inside the virus