arXiv - MATH - Information Theory最新文献_第4页

Compute-Update Federated Learning: A Lattice Coding Approach 计算-更新联合学习：网格编码方法

arXiv - MATH - Information Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06343

Seyed Mohammad Azimi-Abarghouyi, Lav R. Varshney

引用次数: 0

New constructions of DNA codes under multiple constraints and parallel searching algorithms 多约束条件下 DNA 代码的新构造和并行搜索算法

arXiv - MATH - Information Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06519

Guodong Wang, Hongwei Liu, Xueyan Chen

{"title":"New constructions of DNA codes under multiple constraints and parallel searching algorithms","authors":"Guodong Wang, Hongwei Liu, Xueyan Chen","doi":"arxiv-2409.06519","DOIUrl":"https://doi.org/arxiv-2409.06519","url":null,"abstract":"DNA codes have garnered significant interest due to their utilization in\u0000digital media storage, cryptography, and DNA computing. In this paper, we first\u0000extend the results of constructing reversible group codes cite{Cengellenmis}\u0000and reversible composite group codes cite{Korban5} to general even-order\u0000finite groups. By using these results, we give parallel searching algorithms to\u0000find some new DNA codes with better parameters. Secondly, by mapping codes over\u0000$mathbb{F}_4$ to DNA codes, we establish a relationship between the\u0000$GC$-weight enumerator of DNA codes and the Hamming weight enumerator of their\u0000trace codes, which greatly improves the computational efficiency of searching\u0000for DNA codes. Based on this relationship, we propose an efficient algorithm\u0000for generating DNA codes with $50%$ $GC$-content. Furthermore, we find that\u0000there is no direct connection between the $GC$-weight enumerator of a DNA code\u0000and the $GC$-weight enumerator of its dual code. Finally, we present algorithms\u0000for determining whether a DNA code is free from secondary structures or\u0000conflict-free, and some new DNA codes with better parameters under multiple\u0000constraints are obtained, which are listed in Tables 1 and 4.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"110 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized Approximate Message-Passing for Compressed Sensing with Sublinear Sparsity 亚线性稀疏性压缩传感的广义近似信息传递

arXiv - MATH - Information Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06320

Keigo Takeuchi

{"title":"Generalized Approximate Message-Passing for Compressed Sensing with Sublinear Sparsity","authors":"Keigo Takeuchi","doi":"arxiv-2409.06320","DOIUrl":"https://doi.org/arxiv-2409.06320","url":null,"abstract":"This paper addresses the reconstruction of an unknown signal vector with\u0000sublinear sparsity from generalized linear measurements. Generalized\u0000approximate message-passing (GAMP) is proposed via state evolution in the\u0000sublinear sparsity limit, where the signal dimension $N$, measurement dimension\u0000$M$, and signal sparsity $k$ satisfy $log k/log Nto gammain[0, 1)$ and\u0000$M/{klog (N/k)}todelta$ as $N$ and $k$ tend to infinity. While the overall\u0000flow in state evolution is the same as that for linear sparsity, each proof\u0000step for inner denoising requires stronger assumptions than those for linear\u0000sparsity. The required new assumptions are proved for Bayesian inner denoising.\u0000When Bayesian outer and inner denoisers are used in GAMP, the obtained state\u0000evolution recursion is utilized to evaluate the prefactor $delta$ in the\u0000sample complexity, called reconstruction threshold. If and only if $delta$ is\u0000larger than the reconstruction threshold, Bayesian GAMP can achieve\u0000asymptotically exact signal reconstruction. In particular, the reconstruction\u0000threshold is finite for noisy linear measurements when the support of non-zero\u0000signal elements does not include a neighborhood of zero. As numerical examples,\u0000this paper considers linear measurements and 1-bit compressed sensing.\u0000Numerical simulations for both cases show that Bayesian GAMP outperforms\u0000existing algorithms for sublinear sparsity in terms of the sample complexity.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Design of Threshold-Constrained Indirect Quantizers 设计阈值受限的间接量化器

arXiv - MATH - Information Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06839

Ariel Doubchak, Tal Philosof, Uri Erez, Amit Berman

引用次数: 0

Universal tester for multiple independence testing and classical-quantum arbitrarily varying multiple access channel 用于多重独立性测试和经典量子任意变化多重接入信道的通用测试仪

arXiv - MATH - Information Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05619

Ayanava Dasgupta, Naqueeb Ahmad Warsi, Masahito Hayashi

{"title":"Universal tester for multiple independence testing and classical-quantum arbitrarily varying multiple access channel","authors":"Ayanava Dasgupta, Naqueeb Ahmad Warsi, Masahito Hayashi","doi":"arxiv-2409.05619","DOIUrl":"https://doi.org/arxiv-2409.05619","url":null,"abstract":"We study two kinds of different problems. One is the multiple independence\u0000testing, which can be considered as a kind of generalization of quantum Stein's\u0000lemma. We test whether the quantum system is correlated to the classical system\u0000or is independent of it. Here, the null hypothesis is composed of states having\u0000the quantum system is correlated to the classical system in an arbitrarily\u0000varying form. The second problem is the problem of reliable communication over\u0000classical-quantum arbitrarily varying multiple access channels (CQ-AVMAC) and\u0000establishing its capacity region by giving multiple achievability techniques.\u0000We prove that each of these techniques is optimal by proving a converse.\u0000Further, for both these techniques, the decoder designed is a emph{universal}\u0000decoder and can achieve any rate pair in the capacity region without time\u0000sharing and also these decoders do not depend on the channel and therefore they\u0000are universal. Our result covers the case when the channel parameter is\u0000continuous, which has not been studied even in the classical case. Further,\u0000both these techniques can be easily generalized to the case when there are $T\u0000(T>2)$ senders. The design of each of these decoders is based on the study of\u0000multiple independence testing. This approach allows us to study the problem of\u0000reliable communication over CQ-AVMAC from the point of view of hypothesis\u0000testing. Further, we also give a necessary and sufficient condition for the\u0000deterministic code capacity region of CQ-AVMAC to be non-empty.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tele-LLMs: A Series of Specialized Large Language Models for Telecommunications Tele-LLMs：电信专用大型语言模型系列

arXiv - MATH - Information Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05314

Ali Maatouk, Kenny Chirino Ampudia, Rex Ying, Leandros Tassiulas

{"title":"Tele-LLMs: A Series of Specialized Large Language Models for Telecommunications","authors":"Ali Maatouk, Kenny Chirino Ampudia, Rex Ying, Leandros Tassiulas","doi":"arxiv-2409.05314","DOIUrl":"https://doi.org/arxiv-2409.05314","url":null,"abstract":"The emergence of large language models (LLMs) has significantly impacted\u0000various fields, from natural language processing to sectors like medicine and\u0000finance. However, despite their rapid proliferation, the applications of LLMs\u0000in telecommunications remain limited, often relying on general-purpose models\u0000that lack domain-specific specialization. This lack of specialization results\u0000in underperformance, particularly when dealing with telecommunications-specific\u0000technical terminology and their associated mathematical representations. This\u0000paper addresses this gap by first creating and disseminating Tele-Data, a\u0000comprehensive dataset of telecommunications material curated from relevant\u0000sources, and Tele-Eval, a large-scale question-and-answer dataset tailored to\u0000the domain. Through extensive experiments, we explore the most effective\u0000training techniques for adapting LLMs to the telecommunications domain, ranging\u0000from examining the division of expertise across various telecommunications\u0000aspects to employing parameter-efficient techniques. We also investigate how\u0000models of different sizes behave during adaptation and analyze the impact of\u0000their training data on this behavior. Leveraging these findings, we develop and\u0000open-source Tele-LLMs, the first series of language models ranging from 1B to\u00008B parameters, specifically tailored for telecommunications. Our evaluations\u0000demonstrate that these models outperform their general-purpose counterparts on\u0000Tele-Eval while retaining their previously acquired capabilities, thus avoiding\u0000the catastrophic forgetting phenomenon.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

OciorCOOL: Faster Byzantine Agreement and Reliable Broadcast OciorCOOL：更快的拜占庭协议和可靠广播

arXiv - MATH - Information Theory Pub Date : 2024-09-09 DOI: arxiv-2409.06008

Jinyuan Chen

引用次数: 0

Decoding up to Hartmann-Tzeng and Roos bounds for rank codes 阶码的哈特曼-曾和鲁斯边界解码

arXiv - MATH - Information Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05534

José Manuel Muñoz

引用次数: 0

The Error Probability of Spatially Coupled Sparse Regression Codes over Memoryless Channels 无记忆信道上空间耦合稀疏回归编码的错误概率

arXiv - MATH - Information Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05745

Yuhao Liu, Yizhou Xu, Tianqi Hou