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Reed-Solomon (RS) codes are widely used to correct errors in storage systems. Finding the error locator polynomial is one of the key steps in the error correction procedure of RS codes. Modular Approach (MA) is an effective algorithm for solving the Welch-Berlekamp (WB) key-equation problem to find the error locator polynomial that needs $2t$ steps, where $t$ is the error correction capability. In this paper, we first present a new MA algorithm that only requires $2e$ steps and then propose two fast decoding algorithms for RS codes based on our MA algorithm, where $e$ is the number of errors and $e\leq t$. We propose Improved-Frequency Domain Modular Approach (I-FDMA) algorithm that needs $2e$ steps to solve the error locator polynomial and present our first decoding algorithm based on the I-FDMA algorithm. We show that, compared with the existing methods based on MA algorithms, our I-FDMA algorithm can effectively reduce the decoding complexity of RS codes when $e

Length generalization failure problem, namely the large language model (LLM) fails to generalize to texts longer than its maximum training length, greatly restricts the application of LLM in the scenarios with streaming long inputs. To address this problem, the existing methods either require substantial costs or introduce precision loss. In this paper, we empirically find that the accuracy of the LLM's prediction is highly correlated to its certainty. Based on this, we propose an efficient training free framework, named XL3M (it means extra-long large language model), which enables the LLMs trained on short sequences to reason extremely long sequence without any further training or fine-tuning. Under the XL3M framework, the input context will be firstly decomposed into multiple short sub-contexts, where each sub-context contains an independent segment and a common ``question'' which is a few tokens from the end of the original context. Then XL3M gives a method to measure the relevance between each segment and the ``question'', and constructs a concise key context by splicing all the relevant segments in chronological order. The key context is further used instead of the original context to complete the inference task. Evaluations on comprehensive benchmarks show the superiority of XL3M. Using our framework, a Llama2-7B model is able to reason 20M long sequences on an 8-card Huawei Ascend 910B NPU machine with 64GB memory per card., Comment: 11 pages, 5 figures

Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization level being one, however, they require large repair bandwidth defined as the total amount of symbols downloaded from other surviving nodes during single-node failure/repair. In this paper, we present the {\em set transformation}, which can transform any MDS code into set transformed code such that (i) the sub-packetization level is flexible and ranges from 2 to $(n-k)^{\lfloor\frac{n}{n-k}\rfloor}$ in which $n$ is the number of nodes and $k$ is the number of data nodes, (ii) the new code is MDS code, (iii) the new code has lower repair bandwidth for any single-node failure. We show that our set transformed codes have both lower repair bandwidth and lower field size than the existing related MDS array codes, such as elastic transformed codes \cite{10228984}. Specifically, our set transformed codes have $2\%-6.6\%$ repair bandwidth reduction compared with elastic transformed codes \cite{10228984} for the evaluated typical parameters.

Recommendation systems are widely used in e-commerce websites and online platforms to address information overload. However, existing systems primarily rely on historical data and user feedback, making it difficult to capture user intent transitions. Recently, Knowledge Base (KB)-based models are proposed to incorporate expert knowledge, but it struggle to adapt to new items and the evolving e-commerce environment. To address these challenges, we propose a novel Large Language Model based Complementary Knowledge Enhanced Recommendation System (LLM-KERec). It introduces an entity extractor that extracts unified concept terms from item and user information. To provide cost-effective and reliable prior knowledge, entity pairs are generated based on entity popularity and specific strategies. The large language model determines complementary relationships in each entity pair, constructing a complementary knowledge graph. Furthermore, a new complementary recall module and an Entity-Entity-Item (E-E-I) weight decision model refine the scoring of the ranking model using real complementary exposure-click samples. Extensive experiments conducted on three industry datasets demonstrate the significant performance improvement of our model compared to existing approaches. Additionally, detailed analysis shows that LLM-KERec enhances users' enthusiasm for consumption by recommending complementary items. In summary, LLM-KERec addresses the limitations of traditional recommendation systems by incorporating complementary knowledge and utilizing a large language model to capture user intent transitions, adapt to new items, and enhance recommendation efficiency in the evolving e-commerce landscape., Comment: 9 pages, 5 figures

Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve both smaller repair bandwidth and smaller repair locality than traditional MDS codes in repairing single-node erasure. In this paper, we propose {\em generalized simple regenerating codes} (GSRCs) that can support much more parameters than that of SRCs. We show that there is a trade-off between sub-packetization and fault tolerance in our GSRCs, and SRCs achieve a special point of the trade-off of GSRCs. We show that the fault tolerance of our GSRCs increases when the sub-packetization increases linearly. We also show that our GSRCs can locally repair any singe-symbol erasure and any single-node erasure, and the repair bandwidth of our GSRCs is smaller than that of the existing related codes.

High-rate minimum storage regenerating (MSR) codes are known to require a large sub-packetization level, which can make meta-data management difficult and hinder implementation in practical systems. A few maximum distance separable (MDS) array code constructions have been proposed to attain a much smaller sub-packetization level by sacrificing a bit of repair bandwidth. However, to the best of our knowledge, only one construction by Guruswami et al. can support the repair of a failed node without contacting all the surviving nodes. This construction is certainly of theoretical interest but not yet practical due to its requirement for very large code parameters. In this paper, we propose a generic transformation that can convert any $(\overline{n}, \overline{k})$ MSR code with a repair degree of $\overline{d}<\overline{n}-1$ into another $(n=s\overline{n},k)$ MDS array code that supports $d

We study the Belle reaction $\Xi_c^+ \to \Xi^- \pi^+ \pi^+$ looking at the mass distribution of $\pi^+ \Xi$, where clear signals for the $\Xi(1620)$ and $\Xi(1690)$ resonances are seen. These two resonances are generated dynamically from the interaction in coupled channels of $\pi \Xi, \bar K \Lambda, \bar K \Sigma$ and $\eta \Xi$ within the chiral unitary approach. Yet, the weak decay process at the quark level, together with the hadronization to produce pairs of mesons, does not produce the $\pi \pi \Xi$ final state. In order to produce this state one must make transitions from the $\bar K \Lambda, \bar K \Sigma$ and $\eta \Xi$ components to $\pi \Xi$, and this interaction is what produces the resonances. So, the reaction offers a good test for the molecular picture of these resonances. Adding the contribution of the $\Xi^*(1530)$ and some background we are able to get a good reproduction of the mass distribution showing the signatures of the two resonances as found in the experiment., Comment: 15 pages, 8 figures, 2 tables; v2: discussion added, references added, version to appear in Eur.Phys.J.C

A popular branch of stochastic network calculus (SNC) utilizes moment-generating functions (MGFs) to characterize arrivals and services, which enables end-to-end performance analysis. However, existing traffic models for SNC cannot effectively represent the complicated nature of real-world network traffic such as dramatic burstiness. To conquer this challenge, we propose an adaptive spatial-temporal traffic model: dMAPAR-HMM. Specifically, we model the temporal on-off switching process as a dual Markovian arrival process (dMAP) and the arrivals during the on phases as an autoregressive hidden Markov model (AR-HMM). The dMAPAR-HMM model fits in with the MGF-SNC analysis framework, unifies various state-of-the-art arrival models, and matches real-world data more closely. We perform extensive experiments with real-world traces under different network topologies and utilization levels. Experimental results show that dMAPAR-HMM significantly outperforms prevailing models in MGF-SNC.

The recently proposed learned indexes have attracted much attention as they can adapt to the actual data and query distributions to attain better search efficiency. Based on this technique, several existing works build up indexes for multi-dimensional data and achieve improved query performance. A common paradigm of these works is to (i) map multi-dimensional data points to a one-dimensional space using a fixed space-filling curve (SFC) or its variant and (ii) then apply the learned indexing techniques. We notice that the first step typically uses a fixed SFC method, such as row-major order and z-order. It definitely limits the potential of learned multi-dimensional indexes to adapt variable data distributions via different query workloads. In this paper, we propose a novel idea of learning a space-filling curve that is carefully designed and actively optimized for efficient query processing. We also identify innovative offline and online optimization opportunities common to SFC-based learned indexes and offer optimal and/or heuristic solutions. Experimental results demonstrate that our proposed method, LMSFC, outperforms state-of-the-art non-learned or learned methods across three commonly used real-world datasets and diverse experimental settings., Comment: Extended Version. Accepted by VLDB 2023

The conventional direction-of-arrival (DoA) estimation approaches only be effective when the line-of-sight (LoS) link exists, while in the case of the non-line-of-sight (NLoS) situation, the spatial angle can not be captured and thus the DoA estimation performance would be significantly degraded. To address this challenge, a novel reconfigurable intelligent surface (RIS)- enabled gridless DoA estimation approach is proposed, where the RIS can establish the virtual LoS link between the base station (BS) and the targets. For extracting the statistics of the signal, the RIS-enabled signal model in the covariance domain is proposed. Then we estimate the noise variance by constraining the Frobenius norm of the measurement error matrix to obtain the RIS-enabled covariance matrix free of noise nuisance. Additionally, we reconstruct the Hermitian Toeplitz matrix by addressing the atom norm minimization (ANM) problem. To ease the calculation burden, an efficient iterative approach finally is designed to solve the ANM problem via the alternating direction method of multipliers (ADMM). Numerical experiments validate the robustness of the proposed method against the benchmark in terms of computational efficiency and multi-source DoA estimation precision.

Abundant high-rate (n, k) minimum storage regenerating (MSR) codes have been reported in the literature. However, most of them require contacting all the surviving nodes during a node repair process, resulting in a repair degree of d=n-1. In practical systems, it may not always be feasible to connect and download data from all surviving nodes, as some nodes may be unavailable. Therefore, there is a need for MSR code constructions with a repair degree of dk, and has a smaller sub-packetization level or finite field than some existing constructions. Additionally, in conjunction with a previous generic transformation to reduce the sub-packetization level, we obtain an MDS array code with a small sub-packetization level and $(1+\epsilon)$-optimal repair bandwidth (i.e., $(1+\epsilon)$ times the optimal repair bandwidth) for repair degree d=n-1. This code outperforms some existing ones in terms of either the sub-packetization level or the field size., Comment: Submitted to the IEEE Transactions on Communications

This paper proposes a super-resolution harmonic retrieval method for uncorrelated strictly non-circular signals, whose covariance and pseudo-covariance present Toeplitz and Hankel structures, respectively. Accordingly, the augmented covariance matrix constructed by the covariance and pseudo-covariance matrices is not only low rank but also jointly Toeplitz-Hankel structured. To efficiently exploit such a desired structure for high estimation accuracy, we develop a low-rank Toeplitz-Hankel covariance reconstruction (LRTHCR) solution employed over the augmented covariance matrix. Further, we design a fitting error constraint to flexibly implement the LRTHCR algorithm without knowing the noise statistics. In addition, performance analysis is provided for the proposed LRTHCR in practical settings. Simulation results reveal that the LRTHCR outperforms the benchmark methods in terms of lower estimation errors.

Partial maximum distance separable (PMDS) codes are a kind of erasure codes where the nodes are divided into multiple groups with each forming an MDS code with a smaller code length, thus they allow repairing a failed node with only a few helper nodes and can correct all erasure patterns that are information-theoretically correctable. However, the repair of a failed node of PMDS codes still requires a large amount of communication if the group size is large. Recently, PMDS array codes with each local code being an MSR code were introduced to reduce the repair bandwidth further. However, they require extensive rebuilding access and unavoidably a significant sub packetization level. In this paper, we first propose two constructions of PMDS array codes with two global parities that have smaller sub-packetization levels and much smaller finite fields than the existing one. One construction can support an arbitrary number of local parities and has $(1+\epsilon)$-optimal repair bandwidth (i.e., $(1+\epsilon)$ times the optimal repair bandwidth), while the other one is limited to two local parities but has significantly smaller rebuilding access and its sub packetization level is only $2$. In addition, we present a construction of PMDS array code with three global parities, which has a smaller sub-packetization level as well as $(1+\epsilon)$-optimal repair bandwidth, the required finite field is significantly smaller than existing ones., Comment: Accepted for publication in the IEEE Transactions on Information Theory

Many network applications can be formulated as NP-hard combinatorial optimization problems of community detection (CD). Due to the NP-hardness, to balance the CD quality and efficiency remains a challenge. Most existing CD methods are transductive, which are independently optimized only for the CD on a single graph. Some of these methods use advanced machine learning techniques to obtain high-quality CD results but usually have high complexity. Other approaches use fast heuristic approximation to ensure low runtime but may suffer from quality degradation. In contrast to these transductive methods, we propose an alternative inductive community detection (ICD) method across graphs of a system or scenario to alleviate the NP-hard challenge. ICD first conducts the offline training of an adversarial dual GNN on historical graphs to capture key properties of the system. The trained model is then directly generalized to new unseen graphs for online CD without additional optimization, where a better trade-off between quality and efficiency can be achieved. ICD can also capture the permutation invariant community labels in the offline training and tackle the online CD on new graphs with non-fixed number of nodes and communities. Experiments on a set of benchmarks demonstrate that ICD can achieve a significant trade-off between quality and efficiency over various baselines.

Motivated by applications in computing and telecommunication systems, we investigate the problem of estimating p-quantile of steady-state sojourn times in a single-server multi-class queueing system with non-preemptive priorities for p close to 1. The main challenge in this problem lies in efficient sampling from the tail event. To address this issue, we develop a regenerative simulation algorithm with importance sampling. In addition, we establish a central limit theorem for the estimator to construct the confidence interval. Numerical experiments show that our algorithm outperforms benchmark simulation methods. Our result contributes to the literature on rare event simulation for queueing systems.

Quantum random number generators (QRNGs) are able to generate numbers that are certifiably random, even to an agent who holds some side-information. Such systems typically require that the elements being used are precisely calibrated and validly certified for a credible security analysis. However, this can be experimentally challenging and result in potential side-channels which could compromise the security of the QRNG. In this work, we propose, design and experimentally demonstrate a QRNG protocol that completely removes the calibration requirement for the measurement device. Moreover, our protocol is secure against quantum side-information. We also take into account the finite-size effects and remove the independent and identically distributed requirement for the measurement side. More importantly, our QRNG scheme features a simple implementation which uses only standard optical components and are readily implementable on integrated-photonic platforms. To validate the feasibility and practicability of the protocol, we set up a fibre-optical experimental system with a home-made homodyne detector with an effective efficiency of 91.7% at 1550nm. The system works at a rate of 2.5MHz, and obtains a net randomness expansion rate of 4.98kbits/s at 1E10 rounds. Our results pave the way for an integrated QRNG with self-testing feature and provable security., Comment: This is a preliminary draft, comments and suggestions are welcomed!

The disentanglement of StyleGAN latent space has paved the way for realistic and controllable image editing, but does StyleGAN know anything about temporal motion, as it was only trained on static images? To study the motion features in the latent space of StyleGAN, in this paper, we hypothesize and demonstrate that a series of meaningful, natural, and versatile small, local movements (referred to as "micromotion", such as expression, head movement, and aging effect) can be represented in low-rank spaces extracted from the latent space of a conventionally pre-trained StyleGAN-v2 model for face generation, with the guidance of proper "anchors" in the form of either short text or video clips. Starting from one target face image, with the editing direction decoded from the low-rank space, its micromotion features can be represented as simple as an affine transformation over its latent feature. Perhaps more surprisingly, such micromotion subspace, even learned from just single target face, can be painlessly transferred to other unseen face images, even those from vastly different domains (such as oil painting, cartoon, and sculpture faces). It demonstrates that the local feature geometry corresponding to one type of micromotion is aligned across different face subjects, and hence that StyleGAN-v2 is indeed "secretly" aware of the subject-disentangled feature variations caused by that micromotion. We present various successful examples of applying our low-dimensional micromotion subspace technique to directly and effortlessly manipulate faces, showing high robustness, low computational overhead, and impressive domain transferability. Our codes are available at https://github.com/wuqiuche/micromotion-StyleGAN., Comment: 13 pages, 8 figures