Yiping Zuo, Jiajia Guo, Weicong Chen, Weibei Fan, Biyun Sheng, Fu Xiao, Shi Jin
The current integrated sensing, communication, and computing (ISCC) systems face significant challenges in both efficiency and resource utilization. To tackle these issues, we propose a novel fluid antenna (FA)-enabled ISCC system, specifically designed for vehicular networks. We develop detailed models for the communication and sensing processes to support this architecture. An integrated latency optimization problem is formulated to jointly optimize computing resources, receive combining matrices, and antenna positions. To tackle this complex problem, we decompose it into three sub-problems and analyze each separately. A mixed optimization algorithm is then designed to address the overall problem comprehensively. Numerical results demonstrate the rapid convergence of the proposed algorithm. Compared with baseline schemes, the FA-enabled vehicle ISCC system significantly improves resource utilization and reduces latency for communication, sensing, and computation.
当前的集成传感、通信和计算（ISCC）系统在效率和资源利用方面都面临着巨大挑战。为了解决这些问题，我们提出了一种新型流体天线（FA）支持的 ISCC 系统，专门为车载网络而设计。我们为通信和传感过程建立了详细的模型，以支持这种架构。我们提出了一个综合延迟优化问题，以联合优化计算资源、接收组合矩阵和天线位置。为了解决这一复杂问题，我们将其分解为三个子问题，并分别进行分析。然后设计了一种混合优化算法来全面解决整个问题。数值结果证明了所提算法的快速收敛性。与基线方案相比，支持 FA 的车辆 ISCC 系统显著提高了资源利用率，减少了通信、传感和计算的延迟。
{"title":"Fluid Antenna-enabled Integrated Sensing, Communication, and Computing Systems","authors":"Yiping Zuo, Jiajia Guo, Weicong Chen, Weibei Fan, Biyun Sheng, Fu Xiao, Shi Jin","doi":"arxiv-2409.11622","DOIUrl":"https://doi.org/arxiv-2409.11622","url":null,"abstract":"The current integrated sensing, communication, and computing (ISCC) systems\u0000face significant challenges in both efficiency and resource utilization. To\u0000tackle these issues, we propose a novel fluid antenna (FA)-enabled ISCC system,\u0000specifically designed for vehicular networks. We develop detailed models for\u0000the communication and sensing processes to support this architecture. An\u0000integrated latency optimization problem is formulated to jointly optimize\u0000computing resources, receive combining matrices, and antenna positions. To\u0000tackle this complex problem, we decompose it into three sub-problems and\u0000analyze each separately. A mixed optimization algorithm is then designed to\u0000address the overall problem comprehensively. Numerical results demonstrate the\u0000rapid convergence of the proposed algorithm. Compared with baseline schemes,\u0000the FA-enabled vehicle ISCC system significantly improves resource utilization\u0000and reduces latency for communication, sensing, and computation.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268474","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}
Feistel Boomerang Connectivity Table (FBCT) is an important cryptanalytic technique on analysing the resistance of the Feistel network-based ciphers to power attacks such as differential and boomerang attacks. Moreover, the coefficients of FBCT are closely related to the second-order zero differential spectra of the function $F(x)$ over the finite fields with even characteristic and the Feistel boomerang uniformity is the second-order zero differential uniformity of $F(x)$. In this paper, by computing the number of solutions of specific equations over finite fields, we determine explicitly the second-order zero differential spectra of power functions $x^{2^m+3}$ and $x^{2^m+5}$ with $m>2$ being a positive integer over finite field with even characteristic, and $x^{p^k+1}$ with integer $kgeq1$ over finite field with odd characteristic $p$. It is worth noting that $x^{2^m+3}$ is a permutation over $mathbb{F}_{2^n}$ and only when $m$ is odd, $x^{2^m+5}$ is a permutation over $mathbb{F}_{2^n}$, where integer $n=2m$. As a byproduct, we find $F(x)=x^4$ is a PN and second-order zero differentially $0$-uniform function over $mathbb{F}_{3^n}$ with odd $n$. The computation of these entries and the cardinalities in each table aimed to facilitate the analysis of differential and boomerang cryptanalysis of S-boxes when studying distinguishers and trails.
{"title":"On the second-order zero differential properties of several classes of power functions over finite fields","authors":"Huan Zhou, Xiaoni Du, Xingbin Qiao, Wenping Yuan","doi":"arxiv-2409.11693","DOIUrl":"https://doi.org/arxiv-2409.11693","url":null,"abstract":"Feistel Boomerang Connectivity Table (FBCT) is an important cryptanalytic\u0000technique on analysing the resistance of the Feistel network-based ciphers to\u0000power attacks such as differential and boomerang attacks. Moreover, the\u0000coefficients of FBCT are closely related to the second-order zero differential\u0000spectra of the function $F(x)$ over the finite fields with even characteristic\u0000and the Feistel boomerang uniformity is the second-order zero differential\u0000uniformity of $F(x)$. In this paper, by computing the number of solutions of\u0000specific equations over finite fields, we determine explicitly the second-order\u0000zero differential spectra of power functions $x^{2^m+3}$ and $x^{2^m+5}$ with\u0000$m>2$ being a positive integer over finite field with even characteristic, and\u0000$x^{p^k+1}$ with integer $kgeq1$ over finite field with odd characteristic\u0000$p$. It is worth noting that $x^{2^m+3}$ is a permutation over\u0000$mathbb{F}_{2^n}$ and only when $m$ is odd, $x^{2^m+5}$ is a permutation over\u0000$mathbb{F}_{2^n}$, where integer $n=2m$. As a byproduct, we find $F(x)=x^4$ is\u0000a PN and second-order zero differentially $0$-uniform function over\u0000$mathbb{F}_{3^n}$ with odd $n$. The computation of these entries and the\u0000cardinalities in each table aimed to facilitate the analysis of differential\u0000and boomerang cryptanalysis of S-boxes when studying distinguishers and trails.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268739","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}
In this paper, we assume an error such that a single insertion occurs and then a single deletion occurs. Under such an error model, this paper provides a decoding algorithm for non-binary quantum codes constructed by Matsumoto and Hagiwara.
{"title":"Decoding Algorithm Correcting Single-Insertion Plus Single-Deletion for Non-binary Quantum Codes","authors":"Ken Nakamura, Takayuki Nozaki","doi":"arxiv-2409.10924","DOIUrl":"https://doi.org/arxiv-2409.10924","url":null,"abstract":"In this paper, we assume an error such that a single insertion occurs and\u0000then a single deletion occurs. Under such an error model, this paper provides a\u0000decoding algorithm for non-binary quantum codes constructed by Matsumoto and\u0000Hagiwara.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268471","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}
This paper evaluates the geometrically averaged performance of a wireless communication network assisted by a multitude of distributed reconfigurable intelligent surfaces (RISs), where the RIS locations are randomly dropped obeying a homogeneous Poisson point process. By exploiting stochastic geometry and then averaging over the random locations of RISs as well as the serving user, we first derive a closed-form expression for the spatially ergodic rate in the presence of phase errors at the RISs in practice. Armed with this closed-form characterization, we then optimize the RIS deployment under a reasonable and fair constraint of a total number of RIS elements per unit area. The optimal configurations in terms of key network parameters, including the RIS deployment density and the array sizes of RISs, are disclosed for the spatially ergodic rate maximization. Our findings suggest that deploying larger-size RISs with reduced deployment density is theoretically preferred to support extended RIS coverages, under the cases of bounded phase shift errors. However, when dealing with random phase shifts, the reflecting elements are recommended to spread out as much as possible, disregarding the deployment cost. Furthermore, the spatially ergodic rate loss due to the phase shift errors is quantitatively characterized. For bounded phase shift errors, the rate loss is eventually upper bounded by a constant as $Nrightarrowinfty$, where $N$ is the number of reflecting elements at each RIS. While for random phase shifts, this rate loss scales up in the order of $log N$. These analytical observations are validated through numerical results.
{"title":"On Performance of Distributed RIS-aided Communication in Random Networks","authors":"Jindan Xu, Wei Xu, Chau Yuen","doi":"arxiv-2409.11156","DOIUrl":"https://doi.org/arxiv-2409.11156","url":null,"abstract":"This paper evaluates the geometrically averaged performance of a wireless\u0000communication network assisted by a multitude of distributed reconfigurable\u0000intelligent surfaces (RISs), where the RIS locations are randomly dropped\u0000obeying a homogeneous Poisson point process. By exploiting stochastic geometry\u0000and then averaging over the random locations of RISs as well as the serving\u0000user, we first derive a closed-form expression for the spatially ergodic rate\u0000in the presence of phase errors at the RISs in practice. Armed with this\u0000closed-form characterization, we then optimize the RIS deployment under a\u0000reasonable and fair constraint of a total number of RIS elements per unit area.\u0000The optimal configurations in terms of key network parameters, including the\u0000RIS deployment density and the array sizes of RISs, are disclosed for the\u0000spatially ergodic rate maximization. Our findings suggest that deploying\u0000larger-size RISs with reduced deployment density is theoretically preferred to\u0000support extended RIS coverages, under the cases of bounded phase shift errors.\u0000However, when dealing with random phase shifts, the reflecting elements are\u0000recommended to spread out as much as possible, disregarding the deployment\u0000cost. Furthermore, the spatially ergodic rate loss due to the phase shift\u0000errors is quantitatively characterized. For bounded phase shift errors, the\u0000rate loss is eventually upper bounded by a constant as $Nrightarrowinfty$,\u0000where $N$ is the number of reflecting elements at each RIS. While for random\u0000phase shifts, this rate loss scales up in the order of $log N$. These\u0000analytical observations are validated through numerical results.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268740","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}
Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $mathcal{C}$, $mathcal{D}$ satisfying $mathcal{C}^{perp} subset mathcal{C} subset mathcal{D}$ through the Calderbank-Shor-Steane (CSS) code construction. In this work, we establish connections between quantum synchronizable codes, subsystem codes, and hybrid codes constructed from the same pair of classical cyclic codes. We also propose a method to construct a synchronizable hybrid subsystem code which can correct both Pauli and synchronization errors, is resilient to gauge errors by virtue of the subsystem structure, and can transmit both classical and quantum information, all at the same time. The trade-offs between the number of synchronization errors that the code can correct, the number of gauge qubits, and the number of logical classical bits of the code are also established. In addition, we propose general methods to construct hybrid and hybrid subsystem codes of CSS type from classical codes, which cover relevant codes from our main construction.
{"title":"Synchronizable hybrid subsystem codes","authors":"Theerapat Tansuwannont, Andrew Nemec","doi":"arxiv-2409.11312","DOIUrl":"https://doi.org/arxiv-2409.11312","url":null,"abstract":"Quantum synchronizable codes are quantum error correcting codes that can\u0000correct not only Pauli errors but also errors in block synchronization. The\u0000code can be constructed from two classical cyclic codes $mathcal{C}$,\u0000$mathcal{D}$ satisfying $mathcal{C}^{perp} subset mathcal{C} subset\u0000mathcal{D}$ through the Calderbank-Shor-Steane (CSS) code construction. In\u0000this work, we establish connections between quantum synchronizable codes,\u0000subsystem codes, and hybrid codes constructed from the same pair of classical\u0000cyclic codes. We also propose a method to construct a synchronizable hybrid\u0000subsystem code which can correct both Pauli and synchronization errors, is\u0000resilient to gauge errors by virtue of the subsystem structure, and can\u0000transmit both classical and quantum information, all at the same time. The\u0000trade-offs between the number of synchronization errors that the code can\u0000correct, the number of gauge qubits, and the number of logical classical bits\u0000of the code are also established. In addition, we propose general methods to\u0000construct hybrid and hybrid subsystem codes of CSS type from classical codes,\u0000which cover relevant codes from our main construction.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268470","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}
We investigate linear network coding in the context of robust function computation, where a sink node is tasked with computing a target function of messages generated at multiple source nodes. In a previous work, a new distance measure was introduced to evaluate the error tolerance of a linear network code for function computation, along with a Singleton-like bound for this distance. In this paper, we first present a minimum distance decoder for these linear network codes. We then focus on the sum function and the identity function, showing that in any directed acyclic network there are two classes of linear network codes for these target functions, respectively, that attain the Singleton-like bound. Additionally, we explore the application of these codes in distributed computing and design a distributed gradient coding scheme in a heterogeneous setting, optimizing the trade-off between straggler tolerance, computation cost, and communication cost. This scheme can also defend against Byzantine attacks.
{"title":"Linear Network Coding for Robust Function Computation and Its Applications in Distributed Computing","authors":"Hengjia Wei, Min Xu, Gennian Ge","doi":"arxiv-2409.10854","DOIUrl":"https://doi.org/arxiv-2409.10854","url":null,"abstract":"We investigate linear network coding in the context of robust function\u0000computation, where a sink node is tasked with computing a target function of\u0000messages generated at multiple source nodes. In a previous work, a new distance\u0000measure was introduced to evaluate the error tolerance of a linear network code\u0000for function computation, along with a Singleton-like bound for this distance.\u0000In this paper, we first present a minimum distance decoder for these linear\u0000network codes. We then focus on the sum function and the identity function,\u0000showing that in any directed acyclic network there are two classes of linear\u0000network codes for these target functions, respectively, that attain the\u0000Singleton-like bound. Additionally, we explore the application of these codes\u0000in distributed computing and design a distributed gradient coding scheme in a\u0000heterogeneous setting, optimizing the trade-off between straggler tolerance,\u0000computation cost, and communication cost. This scheme can also defend against\u0000Byzantine attacks.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268476","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}
The relation between stabilizer codes and binary codes provided by Gottesman and Calderbank et al. is a celebrated result, as it allows the lifting of classical codes to quantum codes. An equivalent way to state this result is that the work allows us to lift decoders for classical codes over the Hamming metric to decoders for stabilizer quantum codes. A natural question to consider: Can we do something similar with decoders for classical codes considered over other metrics? i.e., Can we lift decoders for classical codes over other metrics to obtain decoders for stabilizer quantum codes? In our current work, we answer this question in the affirmative by considering classical codes over the symbol-pair metric. In particular, we present a relation between the symplectic weight and the symbol-pair weight and use it to improve the error correction capability of CSS-codes (a well-studied class of stabilizer codes) obtained from cyclic codes.
{"title":"A Symbol-Pair Decoder for CSS Codes","authors":"Vatsal Pramod Jha, Udaya Parampalli, Abhay Kumar Singh","doi":"arxiv-2409.10979","DOIUrl":"https://doi.org/arxiv-2409.10979","url":null,"abstract":"The relation between stabilizer codes and binary codes provided by Gottesman\u0000and Calderbank et al. is a celebrated result, as it allows the lifting of\u0000classical codes to quantum codes. An equivalent way to state this result is\u0000that the work allows us to lift decoders for classical codes over the Hamming\u0000metric to decoders for stabilizer quantum codes. A natural question to\u0000consider: Can we do something similar with decoders for classical codes\u0000considered over other metrics? i.e., Can we lift decoders for classical codes\u0000over other metrics to obtain decoders for stabilizer quantum codes? In our\u0000current work, we answer this question in the affirmative by considering\u0000classical codes over the symbol-pair metric. In particular, we present a\u0000relation between the symplectic weight and the symbol-pair weight and use it to\u0000improve the error correction capability of CSS-codes (a well-studied class of\u0000stabilizer codes) obtained from cyclic codes.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268472","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}
In multistage group testing, the tests within the same stage are considered nonadaptive, while those conducted across different stages are adaptive. Specifically, when the pools within the same stage are disjoint, meaning that the entire set is divided into several disjoint subgroups, it is referred to as a multistage group partition testing problem, denoted as the (n, d, s) problem, where n, d, and s represent the total number of items, defectives, and stages respectively. This paper presents exact solutions for the (n, 1, s) and (n, d, 2) problems for the first time. Additionally, a general dynamic programming approach is developed for the (n, d, s) problem. Significantly I give the sharp upper and lower bounds estimates. If the defective number in unknown but bounded, I can provide an algorithm with an optimal competitive ratio in the asymptotic sense. While assuming the prior distribution of the defective items, I also establish a well performing upper and lower bound estimate to the expectation of optimal strategy
{"title":"Estimates for Optimal Multistage Group Partition Testing","authors":"Guojiang Shao","doi":"arxiv-2409.10410","DOIUrl":"https://doi.org/arxiv-2409.10410","url":null,"abstract":"In multistage group testing, the tests within the same stage are considered\u0000nonadaptive, while those conducted across different stages are adaptive.\u0000Specifically, when the pools within the same stage are disjoint, meaning that\u0000the entire set is divided into several disjoint subgroups, it is referred to as\u0000a multistage group partition testing problem, denoted as the (n, d, s) problem,\u0000where n, d, and s represent the total number of items, defectives, and stages\u0000respectively. This paper presents exact solutions for the (n, 1, s) and (n, d,\u00002) problems for the first time. Additionally, a general dynamic programming\u0000approach is developed for the (n, d, s) problem. Significantly I give the sharp\u0000upper and lower bounds estimates. If the defective number in unknown but\u0000bounded, I can provide an algorithm with an optimal competitive ratio in the\u0000asymptotic sense. While assuming the prior distribution of the defective items,\u0000I also establish a well performing upper and lower bound estimate to the\u0000expectation of optimal strategy","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"173 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268480","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}
We settle the problem of determining the asymptotic behavior of the parameters of optimal difference systems of sets, or DSSes for short, which were originally introduced for computationally efficient frame synchronization under the presence of additive noise. We prove that the lowest achievable redundancy of a DSS asymptotically attains Levenshtein's lower bound for any alphabet size and relative index, answering the question of Levenshtein posed in 1971. Our proof is probabilistic and gives a linear-time randomized algorithm for constructing asymptotically optimal DSSes with high probability for any alphabet size and information rate. This provides efficient self-synchronizing codes with strong noise resilience. We also point out an application of DSSes to phase detection.
{"title":"The Asymptotics of Difference Systems of Sets for Synchronization and Phase Detection","authors":"Yu Tsunoda, Yuichiro Fujiwara","doi":"arxiv-2409.10646","DOIUrl":"https://doi.org/arxiv-2409.10646","url":null,"abstract":"We settle the problem of determining the asymptotic behavior of the\u0000parameters of optimal difference systems of sets, or DSSes for short, which\u0000were originally introduced for computationally efficient frame synchronization\u0000under the presence of additive noise. We prove that the lowest achievable\u0000redundancy of a DSS asymptotically attains Levenshtein's lower bound for any\u0000alphabet size and relative index, answering the question of Levenshtein posed\u0000in 1971. Our proof is probabilistic and gives a linear-time randomized\u0000algorithm for constructing asymptotically optimal DSSes with high probability\u0000for any alphabet size and information rate. This provides efficient\u0000self-synchronizing codes with strong noise resilience. We also point out an\u0000application of DSSes to phase detection.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268475","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}
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class of codes may also be seen as a stricter variant of what are known as locally thin families in combinatorics. Originally, weak superimposed codes were introduced in the context of multimedia content protection against illegal distribution of copies under the assumption that a coalition of malicious users may employ the averaging attack with adversarial noise. As in many other kinds of codes in information theory, it is of interest and importance in the study of weak superimposed codes to find the highest achievable rate in the asymptotic regime and give an efficient construction that produces an infinite sequence of codes that achieve it. Here, we prove a tighter lower bound than the sharpest known one on the rate of optimal weak superimposed codes and give a polynomial-time randomized construction algorithm for codes that asymptotically attain our improved bound with high probability. Our probabilistic approach is versatile and applicable to many other related codes and arrays.
{"title":"Weak Superimposed Codes of Improved Asymptotic Rate and Their Randomized Construction","authors":"Yu Tsunoda, Yuichiro Fujiwara","doi":"arxiv-2409.10511","DOIUrl":"https://doi.org/arxiv-2409.10511","url":null,"abstract":"Weak superimposed codes are combinatorial structures related closely to\u0000generalized cover-free families, superimposed codes, and disjunct matrices in\u0000that they are only required to satisfy similar but less stringent conditions.\u0000This class of codes may also be seen as a stricter variant of what are known as\u0000locally thin families in combinatorics. Originally, weak superimposed codes\u0000were introduced in the context of multimedia content protection against illegal\u0000distribution of copies under the assumption that a coalition of malicious users\u0000may employ the averaging attack with adversarial noise. As in many other kinds\u0000of codes in information theory, it is of interest and importance in the study\u0000of weak superimposed codes to find the highest achievable rate in the\u0000asymptotic regime and give an efficient construction that produces an infinite\u0000sequence of codes that achieve it. Here, we prove a tighter lower bound than\u0000the sharpest known one on the rate of optimal weak superimposed codes and give\u0000a polynomial-time randomized construction algorithm for codes that\u0000asymptotically attain our improved bound with high probability. Our\u0000probabilistic approach is versatile and applicable to many other related codes\u0000and arrays.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268478","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}
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