Qi Li, Jinhong Yuan, Min Qiu, Shuangyang Li, Yixuan Xie
Recently, orthogonal time frequency space (OTFS) modulation has garnered considerable attention due to its robustness against doubly-selective wireless channels. In this paper, we propose a low-complexity iterative successive interference cancellation based minimum mean squared error (SIC-MMSE) detection algorithm for zero-padded OTFS (ZP-OTFS) modulation. In the proposed algorithm, signals are detected based on layers processed by multiple SIC-MMSE linear filters for each sub-channel, with interference on the targeted signal layer being successively canceled either by hard or soft information. To reduce the complexity of computing individual layer filter coefficients, we also propose a novel filter coefficients recycling approach in place of generating the exact form of MMSE filter weights. Moreover, we design a joint detection and decoding algorithm for ZP-OTFS to enhance error performance. Compared to the conventional SIC-MMSE detection, our proposed algorithms outperform other linear detectors, e.g., maximal ratio combining (MRC), for ZP-OTFS with up to 3 dB gain while maintaining comparable computation complexity.
{"title":"Low Complexity Turbo SIC-MMSE Detection for Orthogonal Time Frequency Space Modulation","authors":"Qi Li, Jinhong Yuan, Min Qiu, Shuangyang Li, Yixuan Xie","doi":"arxiv-2401.11058","DOIUrl":"https://doi.org/arxiv-2401.11058","url":null,"abstract":"Recently, orthogonal time frequency space (OTFS) modulation has garnered\u0000considerable attention due to its robustness against doubly-selective wireless\u0000channels. In this paper, we propose a low-complexity iterative successive\u0000interference cancellation based minimum mean squared error (SIC-MMSE) detection\u0000algorithm for zero-padded OTFS (ZP-OTFS) modulation. In the proposed algorithm,\u0000signals are detected based on layers processed by multiple SIC-MMSE linear\u0000filters for each sub-channel, with interference on the targeted signal layer\u0000being successively canceled either by hard or soft information. To reduce the\u0000complexity of computing individual layer filter coefficients, we also propose a\u0000novel filter coefficients recycling approach in place of generating the exact\u0000form of MMSE filter weights. Moreover, we design a joint detection and decoding\u0000algorithm for ZP-OTFS to enhance error performance. Compared to the\u0000conventional SIC-MMSE detection, our proposed algorithms outperform other\u0000linear detectors, e.g., maximal ratio combining (MRC), for ZP-OTFS with up to 3\u0000dB gain while maintaining comparable computation complexity.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559166","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}
Cristina Fernández-Córdoba, Adrián Torres, Carlos Vela, Mercè Villanueva
The Zps-additive codes of length n are subgroups of Zps^n , and can be seen as a generalization of linear codes over Z2, Z4, or more general over Z2s . In this paper, we show two methods for computing a parity-check matrix of a Zps-additive code from a generator matrix of the code in standard form. We also compare the performance of our results implemented in Magma with the current available function in Magma for codes over finite rings in general. A time complexity analysis is also shown.
长度为 n 的 Zps-additive 码是 Zps^n 的子群，可以看作是 Z2、Z4 或更广义的 Z2s 上线性码的广义化。在本文中，我们展示了从标准形式的 Zps-additive 码生成矩阵计算该码奇偶校验矩阵的两种方法。我们还比较了我们在 Magma 中实现的结果与 Magma 中针对有限环上的一般代码的当前可用函数的性能。我们还展示了时间复杂性分析。
{"title":"Computing efficiently a parity-check matrix for Zps-additive codes","authors":"Cristina Fernández-Córdoba, Adrián Torres, Carlos Vela, Mercè Villanueva","doi":"arxiv-2401.05247","DOIUrl":"https://doi.org/arxiv-2401.05247","url":null,"abstract":"The Zps-additive codes of length n are subgroups of Zps^n , and can be seen\u0000as a generalization of linear codes over Z2, Z4, or more general over Z2s . In\u0000this paper, we show two methods for computing a parity-check matrix of a\u0000Zps-additive code from a generator matrix of the code in standard form. We also\u0000compare the performance of our results implemented in Magma with the current\u0000available function in Magma for codes over finite rings in general. A time\u0000complexity analysis is also shown.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139421235","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}
Luca BarlettaShitz, Alex DytsoShitz, Shlomo ShamaiShitz
This work considers a discrete-time Poisson noise channel with an input amplitude constraint $mathsf{A}$ and a dark current parameter $lambda$. It is known that the capacity-achieving distribution for this channel is discrete with finitely many points. Recently, for $lambda=0$, a lower bound of order $sqrt{mathsf{A}}$ and an upper bound of order $mathsf{A} log^2(mathsf{A})$ have been demonstrated on the cardinality of the support of the optimal input distribution. In this work, we improve these results in several ways. First, we provide upper and lower bounds that hold for non-zero dark current. Second, we produce a sharper upper bound with a far simpler technique. In particular, for $lambda=0$, we sharpen the upper bound from the order of $mathsf{A} log^2(mathsf{A})$ to the order of $mathsf{A}$. Finally, some other additional information about the location of the support is provided.
{"title":"Improved Bounds on the Number of Support Points of the Capacity-Achieving Input for Amplitude Constrained Poisson Channels","authors":"Luca BarlettaShitz, Alex DytsoShitz, Shlomo ShamaiShitz","doi":"arxiv-2401.05045","DOIUrl":"https://doi.org/arxiv-2401.05045","url":null,"abstract":"This work considers a discrete-time Poisson noise channel with an input\u0000amplitude constraint $mathsf{A}$ and a dark current parameter $lambda$. It is\u0000known that the capacity-achieving distribution for this channel is discrete\u0000with finitely many points. Recently, for $lambda=0$, a lower bound of order\u0000$sqrt{mathsf{A}}$ and an upper bound of order $mathsf{A} log^2(mathsf{A})$\u0000have been demonstrated on the cardinality of the support of the optimal input\u0000distribution. In this work, we improve these results in several ways. First, we provide\u0000upper and lower bounds that hold for non-zero dark current. Second, we produce\u0000a sharper upper bound with a far simpler technique. In particular, for\u0000$lambda=0$, we sharpen the upper bound from the order of $mathsf{A}\u0000log^2(mathsf{A})$ to the order of $mathsf{A}$. Finally, some other\u0000additional information about the location of the support is provided.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422503","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 two-part paper, we investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. In Part I, we revisit the information geometry approach (IGA) for massive MIMO-OFDM channel estimation. By using the constant magnitude property of the entries of the measurement matrix in the massive MIMO-OFDM channel estimation and the asymptotic analysis, we find that the second-order natural parameters of the distributions on all the auxiliary manifolds are equivalent to each other at each iteration of IGA, and the first-order natural parameters of the distributions on all the auxiliary manifolds are asymptotically equivalent to each other at the fixed point of IGA. Motivated by these results, we simplify the iterative process of IGA and propose a simplified IGA for massive MIMO-OFDM channel estimation. It is proved that at the fixed point, the a posteriori mean obtained by the simplified IGA is asymptotically optimal. The simplified IGA allows efficient implementation with fast Fourier transformation (FFT). Simulations confirm that the simplified IGA can achieve near the optimal performance with low complexity in a limited number of iterations.
本文由两部分组成，研究大规模多输入多输出正交频分复用（MIMO-OFDM）系统的信道估计。在第一部分中，我们重温了用于大规模 MIMO-OFDM 信道估计的信息几何方法（IGA）。通过利用大规模 MIMO-OFDM 信道估计中测量矩阵项的恒定幅度特性和渐近分析，我们发现在 IGA 的每次迭代中，所有辅助流形上分布的二阶自然参数彼此相等，而在 IGA 的定点处，所有辅助流形上分布的一阶自然参数彼此渐近相等。受这些结果的启发，我们简化了 IGA 的迭代过程，并提出了用于大规模 MIMO-OFDM 信道估计的简化 IGA。实验证明，在定点处，简化 IGA 所获得的后验均值是渐近最优的。简化 IGA 允许使用快速傅立叶变换 (FFT) 高效实现。仿真证实，简化 IGA 可以在有限的迭代次数中以较低的复杂度达到接近最优的性能。
{"title":"Simplified Information Geometry Approach for Massive MIMO-OFDM Channel Estimation -- Part I: Algorithm and Fixed Point Analysis","authors":"Jiyuan Yang, Yan Chen, An-An Lu, Wen Zhong, Xiqi Gao, Xiaohu You, Xiang-Gen Xia, Dirk Slock","doi":"arxiv-2401.02035","DOIUrl":"https://doi.org/arxiv-2401.02035","url":null,"abstract":"In this two-part paper, we investigate the channel estimation for massive\u0000multiple-input multiple-output orthogonal frequency division multiplexing\u0000(MIMO-OFDM) systems. In Part I, we revisit the information geometry approach\u0000(IGA) for massive MIMO-OFDM channel estimation. By using the constant magnitude\u0000property of the entries of the measurement matrix in the massive MIMO-OFDM\u0000channel estimation and the asymptotic analysis, we find that the second-order\u0000natural parameters of the distributions on all the auxiliary manifolds are\u0000equivalent to each other at each iteration of IGA, and the first-order natural\u0000parameters of the distributions on all the auxiliary manifolds are\u0000asymptotically equivalent to each other at the fixed point of IGA. Motivated by\u0000these results, we simplify the iterative process of IGA and propose a\u0000simplified IGA for massive MIMO-OFDM channel estimation. It is proved that at\u0000the fixed point, the a posteriori mean obtained by the simplified IGA is\u0000asymptotically optimal. The simplified IGA allows efficient implementation with\u0000fast Fourier transformation (FFT). Simulations confirm that the simplified IGA\u0000can achieve near the optimal performance with low complexity in a limited\u0000number of iterations.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139104116","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}
Christoph Hofmeister, Luis Maßny, Eitan Yaakobi, Rawad Bitar
We consider gradient coding in the presence of an adversary controlling so-called malicious workers trying to corrupt the computations. Previous works propose the use of MDS codes to treat the responses from malicious workers as errors and correct them using the error-correction properties of the code. This comes at the expense of increasing the replication, i.e., the number of workers each partial gradient is computed by. In this work, we propose a way to reduce the replication to $s+1$ instead of $2s+1$ in the presence of $s$ malicious workers. Our method detects erroneous inputs from the malicious workers, transforming them into erasures. This comes at the expense of $s$ additional local computations at the main node and additional rounds of light communication between the main node and the workers. We define a general framework and give fundamental limits for fractional repetition data allocations. Our scheme is optimal in terms of replication and local computation and incurs a communication cost that is asymptotically, in the size of the dataset, a multiplicative factor away from the derived bound. We furthermore show how additional redundancy can be exploited to reduce the number of local computations and communication cost, or, alternatively, tolerate straggling workers.
{"title":"Byzantine-Resilient Gradient Coding through Local Gradient Computations","authors":"Christoph Hofmeister, Luis Maßny, Eitan Yaakobi, Rawad Bitar","doi":"arxiv-2401.02380","DOIUrl":"https://doi.org/arxiv-2401.02380","url":null,"abstract":"We consider gradient coding in the presence of an adversary controlling\u0000so-called malicious workers trying to corrupt the computations. Previous works\u0000propose the use of MDS codes to treat the responses from malicious workers as\u0000errors and correct them using the error-correction properties of the code. This\u0000comes at the expense of increasing the replication, i.e., the number of workers\u0000each partial gradient is computed by. In this work, we propose a way to reduce\u0000the replication to $s+1$ instead of $2s+1$ in the presence of $s$ malicious\u0000workers. Our method detects erroneous inputs from the malicious workers,\u0000transforming them into erasures. This comes at the expense of $s$ additional\u0000local computations at the main node and additional rounds of light\u0000communication between the main node and the workers. We define a general\u0000framework and give fundamental limits for fractional repetition data\u0000allocations. Our scheme is optimal in terms of replication and local\u0000computation and incurs a communication cost that is asymptotically, in the size\u0000of the dataset, a multiplicative factor away from the derived bound. We\u0000furthermore show how additional redundancy can be exploited to reduce the\u0000number of local computations and communication cost, or, alternatively,\u0000tolerate straggling workers.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"117 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139104550","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 Part II of this two-part paper, we prove the convergence of the simplified information geometry approach (SIGA) proposed in Part I. For a general Bayesian inference problem, we first show that the iteration of the common second-order natural parameter (SONP) is separated from that of the common first-order natural parameter (FONP). Hence, the convergence of the common SONP can be checked independently. We show that with the initialization satisfying a specific but large range, the common SONP is convergent regardless of the value of the damping factor. For the common FONP, we establish a sufficient condition of its convergence and prove that the convergence of the common FONP relies on the spectral radius of a particular matrix related to the damping factor. We give the range of the damping factor that guarantees the convergence in the worst case. Further, we determine the range of the damping factor for massive MIMO-OFDM channel estimation by using the specific properties of the measurement matrices. Simulation results are provided to confirm the theoretical results.
{"title":"Simplified Information Geometry Approach for Massive MIMO-OFDM Channel Estimation -- Part II: Convergence Analysis","authors":"Jiyuan Yang, Yan Chen, Mingrui Fan, Xiqi Gao, Xiang-Gen Xia, Dirk Slock","doi":"arxiv-2401.02037","DOIUrl":"https://doi.org/arxiv-2401.02037","url":null,"abstract":"In Part II of this two-part paper, we prove the convergence of the simplified\u0000information geometry approach (SIGA) proposed in Part I. For a general Bayesian\u0000inference problem, we first show that the iteration of the common second-order\u0000natural parameter (SONP) is separated from that of the common first-order\u0000natural parameter (FONP). Hence, the convergence of the common SONP can be\u0000checked independently. We show that with the initialization satisfying a\u0000specific but large range, the common SONP is convergent regardless of the value\u0000of the damping factor. For the common FONP, we establish a sufficient condition\u0000of its convergence and prove that the convergence of the common FONP relies on\u0000the spectral radius of a particular matrix related to the damping factor. We\u0000give the range of the damping factor that guarantees the convergence in the\u0000worst case. Further, we determine the range of the damping factor for massive\u0000MIMO-OFDM channel estimation by using the specific properties of the\u0000measurement matrices. Simulation results are provided to confirm the\u0000theoretical results.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139104227","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}
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of cyclotomic cosets in cyclic groups are presented as key tools in the study of such linear intersection pairs. Characterization and constructions of two cyclic codes of a fixed intersecting dimension are given in terms of their generator polynomials and cyclotomic cosets. In some cases, constructions of two cyclic codes of a fixed intersecting subcode are presented as well. Based on the theoretical characterization, some numerical examples of linear intersection pairs of cyclic codes with good parameters are illustrated.
{"title":"Characterizations and Constructions of Linear Intersection Pairs of Cyclic Codes over Finite Fields","authors":"Somphong Jitman","doi":"arxiv-2401.02077","DOIUrl":"https://doi.org/arxiv-2401.02077","url":null,"abstract":"Linear intersection pairs of linear codes have become of interest due to\u0000their nice algebraic properties and wide applications. In this paper, we focus\u0000on linear intersection pairs of cyclic codes over finite fields. Some\u0000properties of cyclotomic cosets in cyclic groups are presented as key tools in\u0000the study of such linear intersection pairs. Characterization and constructions\u0000of two cyclic codes of a fixed intersecting dimension are given in terms of\u0000their generator polynomials and cyclotomic cosets. In some cases, constructions\u0000of two cyclic codes of a fixed intersecting subcode are presented as well.\u0000Based on the theoretical characterization, some numerical examples of linear\u0000intersection pairs of cyclic codes with good parameters are illustrated.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"461 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139104064","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}
Wireless embedded edge devices are ubiquitous in our daily lives, enabling them to gather immense data via onboard sensors and mobile applications. This offers an amazing opportunity to train machine learning (ML) models in the realm of wireless devices for decision-making. Training ML models in a wireless setting necessitates transmitting datasets collected at the edge to a cloud parameter server, which is infeasible due to bandwidth constraints, security, and privacy issues. To tackle these challenges, Federated Learning (FL) has emerged as a distributed optimization approach to the decentralization of the model training process. In this work, we present a novel prototype to examine FL's effectiveness over bandwidth-constrained wireless channels. Through a novel design consisting of Zigbee and NI USRP devices, we propose a configuration that allows clients to broadcast synergistically local ML model updates to a central server to obtain a generalized global model. We assess the efficacy of this prototype using metrics such as global model accuracy and time complexity under varying conditions of transmission power, data heterogeneity and local learning.
无线嵌入式边缘设备在我们的日常生活中无处不在，使它们能够通过板载传感器和移动应用程序收集大量数据。这为在无线设备中训练机器学习（ML）模型以进行决策提供了绝佳的机会。在无线环境中训练 ML 模型需要将在边缘收集的数据集传输到云参数服务器，但由于带宽限制、安全和隐私问题，这种做法并不可行。为了应对这些挑战，联邦学习（FL）作为一种分布式优化方法应运而生，它可以实现模型训练过程的去中心化。在这项工作中，我们提出了一个新颖的原型，以检验联邦学习在带宽受限的无线信道中的有效性。通过一个由 Zigbee 和 NI USRP 设备组成的新颖设计，我们提出了一种配置，允许客户端向中央服务器协同广播本地 ML 模型更新，从而获得一个广义的全局模型。我们在不同的传输功率、数据异构性和本地学习条件下，使用全局模型准确性和时间复杂性等指标来评估该原型的有效性。
{"title":"Federated Learning for Wireless Applications: A Prototype","authors":"Varun Laxman Muttepawar, Arjun Mehra, Zubair Shaban, Ranjitha Prasad, Harshan Jagadeesh","doi":"arxiv-2312.08577","DOIUrl":"https://doi.org/arxiv-2312.08577","url":null,"abstract":"Wireless embedded edge devices are ubiquitous in our daily lives, enabling\u0000them to gather immense data via onboard sensors and mobile applications. This\u0000offers an amazing opportunity to train machine learning (ML) models in the\u0000realm of wireless devices for decision-making. Training ML models in a wireless\u0000setting necessitates transmitting datasets collected at the edge to a cloud\u0000parameter server, which is infeasible due to bandwidth constraints, security,\u0000and privacy issues. To tackle these challenges, Federated Learning (FL) has\u0000emerged as a distributed optimization approach to the decentralization of the\u0000model training process. In this work, we present a novel prototype to examine\u0000FL's effectiveness over bandwidth-constrained wireless channels. Through a\u0000novel design consisting of Zigbee and NI USRP devices, we propose a\u0000configuration that allows clients to broadcast synergistically local ML model\u0000updates to a central server to obtain a generalized global model. We assess the\u0000efficacy of this prototype using metrics such as global model accuracy and time\u0000complexity under varying conditions of transmission power, data heterogeneity\u0000and local learning.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138689190","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 addresses an uplink localization problem in which a base station (BS) aims to locate a remote user with the help of reconfigurable intelligent surfaces (RISs). We propose a strategy in which the user transmits pilots sequentially and the BS adaptively adjusts the sensing vectors, including the BS beamforming vector and multiple RIS reflection coefficients based on the observations already made, to eventually produce an estimated user position. This is a challenging active sensing problem for which finding an optimal solution involves searching through a complicated functional space whose dimension increases with the number of measurements. We show that the long short-term memory (LSTM) network can be used to exploit the latent temporal correlation between measurements to automatically construct scalable state vectors. Subsequently, the state vector is mapped to the sensing vectors for the next time frame via a deep neural network (DNN). A final DNN is used to map the state vector to the estimated user position. Numerical result illustrates the advantage of the active sensing design as compared to non-active sensing methods. The proposed solution produces interpretable results and is generalizable in the number of sensing stages. Remarkably, we show that a network with one BS and multiple RISs can outperform a comparable setting with multiple BSs.
{"title":"Localization with Reconfigurable Intelligent Surface: An Active Sensing Approach","authors":"Zhongze Zhang, Tao Jiang, Wei Yu","doi":"arxiv-2312.09002","DOIUrl":"https://doi.org/arxiv-2312.09002","url":null,"abstract":"This paper addresses an uplink localization problem in which a base station\u0000(BS) aims to locate a remote user with the help of reconfigurable intelligent\u0000surfaces (RISs). We propose a strategy in which the user transmits pilots\u0000sequentially and the BS adaptively adjusts the sensing vectors, including the\u0000BS beamforming vector and multiple RIS reflection coefficients based on the\u0000observations already made, to eventually produce an estimated user position.\u0000This is a challenging active sensing problem for which finding an optimal\u0000solution involves searching through a complicated functional space whose\u0000dimension increases with the number of measurements. We show that the long\u0000short-term memory (LSTM) network can be used to exploit the latent temporal\u0000correlation between measurements to automatically construct scalable state\u0000vectors. Subsequently, the state vector is mapped to the sensing vectors for\u0000the next time frame via a deep neural network (DNN). A final DNN is used to map\u0000the state vector to the estimated user position. Numerical result illustrates\u0000the advantage of the active sensing design as compared to non-active sensing\u0000methods. The proposed solution produces interpretable results and is\u0000generalizable in the number of sensing stages. Remarkably, we show that a\u0000network with one BS and multiple RISs can outperform a comparable setting with\u0000multiple BSs.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138689194","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 the effect of the well-known Mycielski construction on the Shannon capacity of graphs and on one of its most prominent upper bounds, the (complementary) Lov'asz theta number. We prove that if the Shannon capacity of a graph, the distinguishability graph of a noisy channel, is attained by some finite power, then its Mycielskian has strictly larger Shannon capacity than the graph itself. For the complementary Lov'asz theta function we show that its value on the Mycielskian of a graph is completely determined by its value on the original graph, a phenomenon similar to the one discovered for the fractional chromatic number by Larsen, Propp and Ullman. We also consider the possibility of generalizing our results on the Sperner capacity of directed graphs and on the generalized Mycielsky construction. Possible connections with what Zuiddam calls the asymptotic spectrum of graphs are discussed as well.
{"title":"Shannon capacity, Lovász theta number and the Mycielski construction","authors":"Bence Csonka, Gábor Simonyi","doi":"arxiv-2312.09224","DOIUrl":"https://doi.org/arxiv-2312.09224","url":null,"abstract":"We investigate the effect of the well-known Mycielski construction on the\u0000Shannon capacity of graphs and on one of its most prominent upper bounds, the\u0000(complementary) Lov'asz theta number. We prove that if the Shannon capacity of\u0000a graph, the distinguishability graph of a noisy channel, is attained by some\u0000finite power, then its Mycielskian has strictly larger Shannon capacity than\u0000the graph itself. For the complementary Lov'asz theta function we show that\u0000its value on the Mycielskian of a graph is completely determined by its value\u0000on the original graph, a phenomenon similar to the one discovered for the\u0000fractional chromatic number by Larsen, Propp and Ullman. We also consider the\u0000possibility of generalizing our results on the Sperner capacity of directed\u0000graphs and on the generalized Mycielsky construction. Possible connections with\u0000what Zuiddam calls the asymptotic spectrum of graphs are discussed as well.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138693114","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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