Pub Date : 2023-11-01DOI: 10.1109/JSAIT.2023.3328476
Jun Wu;Mathias Drton
Recursive linear structural equation models and the associated directed acyclic graphs (DAGs) play an important role in causal discovery. The classic identifiability result for this class of models states that when only observational data is available, each DAG can be identified only up to a Markov equivalence class. In contrast, recent work has shown that the DAG can be uniquely identified if the errors in the model are homoscedastic, i.e., all have the same variance. This equal variance assumption yields methods that, if appropriate, are highly scalable and also sheds light on fundamental information-theoretic limits and optimality in causal discovery. In this paper, we fill the gap that exists between the two previously considered cases, which assume the error variances to be either arbitrary or all equal. Specifically, we formulate a framework of partial homoscedasticity, in which the variables are partitioned into blocks and each block shares the same error variance. For any such groupwise equal variances assumption, we characterize when two DAGs give rise to identical Gaussian linear structural equation models. Furthermore, we show how the resulting distributional equivalence classes may be represented using a completed partially directed acyclic graph (CPDAG), and we give an algorithm to efficiently construct this CPDAG. In a simulation study, we demonstrate that greedy search provides an effective way to learn the CPDAG and exploit partial knowledge about homoscedasticity of errors in structural equation models.
递归线性结构方程模型和相关的有向无环图（DAG）在因果发现中发挥着重要作用。这类模型的经典可识别性结果表明，当只有观测数据时，每个 DAG 只能识别到马尔可夫等价类。相反，最近的研究表明，如果模型中的误差是同方差的，即所有误差都具有相同的方差，那么 DAG 就可以唯一地识别出来。这种等方差假设产生的方法，如果合适，具有很强的可扩展性，同时也揭示了因果发现中基本的信息论极限和最优性。在本文中，我们填补了之前考虑的两种情况之间的空白，即假设误差方差要么任意，要么全部相等。具体来说，我们提出了一个部分同方差的框架，在这个框架中，变量被划分成块，每个块共享相同的误差方差。对于任何这样的分组等方差假设，我们都会描述两个 DAG 何时会产生相同的高斯线性结构方程模型。此外，我们还展示了如何用一个完整的部分有向无环图（CPDAG）来表示所产生的分布等价类，并给出了一种高效构建 CPDAG 的算法。在模拟研究中，我们证明了贪婪搜索是学习 CPDAG 和利用结构方程模型中误差同方差性部分知识的有效方法。
{"title":"Partial Homoscedasticity in Causal Discovery With Linear Models","authors":"Jun Wu;Mathias Drton","doi":"10.1109/JSAIT.2023.3328476","DOIUrl":"10.1109/JSAIT.2023.3328476","url":null,"abstract":"Recursive linear structural equation models and the associated directed acyclic graphs (DAGs) play an important role in causal discovery. The classic identifiability result for this class of models states that when only observational data is available, each DAG can be identified only up to a Markov equivalence class. In contrast, recent work has shown that the DAG can be uniquely identified if the errors in the model are homoscedastic, i.e., all have the same variance. This equal variance assumption yields methods that, if appropriate, are highly scalable and also sheds light on fundamental information-theoretic limits and optimality in causal discovery. In this paper, we fill the gap that exists between the two previously considered cases, which assume the error variances to be either arbitrary or all equal. Specifically, we formulate a framework of partial homoscedasticity, in which the variables are partitioned into blocks and each block shares the same error variance. For any such groupwise equal variances assumption, we characterize when two DAGs give rise to identical Gaussian linear structural equation models. Furthermore, we show how the resulting distributional equivalence classes may be represented using a completed partially directed acyclic graph (CPDAG), and we give an algorithm to efficiently construct this CPDAG. In a simulation study, we demonstrate that greedy search provides an effective way to learn the CPDAG and exploit partial knowledge about homoscedasticity of errors in structural equation models.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"639-650"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10304270","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135360763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1109/JSAIT.2023.3329034
Kumar Saurav;Rahul Vaze
We consider a node where packets of fixed size (inbits) are generated at arbitrary intervals. The node is required to maintain the peak age of information (AoI) at the monitor below a threshold by transmitting potentially a subset of the generated packets. At any time, depending on the packet availability and the current AoI, the node can choose which packet to transmit, and at what transmission speed (in bits per second). Power consumption is a monotonically increasing convex function of the transmission speed. In this paper, for any given time horizon, the objective is to find a causal policy that minimizes the total energy consumption while satisfying the peak AoI constraint. We consider competitive ratio as the performance metric, that is defined as the ratio of the expected cost of a causal policy, and the expected cost of an optimal offline policy that knows the input (packet generation times) in advance. We first derive a lower bound on the competitive ratio of all causal policies, in terms of the system parameters (such as power function, packet size and peak AoI threshold), and then propose a particular policy for which we show that its competitive ratio has similar order of dependence on the system parameters as the derived lower bound.
{"title":"Online Energy Minimization Under a Peak Age of Information Constraint","authors":"Kumar Saurav;Rahul Vaze","doi":"10.1109/JSAIT.2023.3329034","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3329034","url":null,"abstract":"We consider a node where packets of fixed size (inbits) are generated at arbitrary intervals. The node is required to maintain the peak age of information (AoI) at the monitor below a threshold by transmitting potentially a subset of the generated packets. At any time, depending on the packet availability and the current AoI, the node can choose which packet to transmit, and at what transmission speed (in bits per second). Power consumption is a monotonically increasing convex function of the transmission speed. In this paper, for any given time horizon, the objective is to find a causal policy that minimizes the total energy consumption while satisfying the peak AoI constraint. We consider competitive ratio as the performance metric, that is defined as the ratio of the expected cost of a causal policy, and the expected cost of an optimal offline policy that knows the input (packet generation times) in advance. We first derive a lower bound on the competitive ratio of all causal policies, in terms of the system parameters (such as power function, packet size and peak AoI threshold), and then propose a particular policy for which we show that its competitive ratio has similar order of dependence on the system parameters as the derived lower bound.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"579-590"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138431090","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}
Pub Date : 2023-10-31DOI: 10.1109/JSAIT.2023.3328766
Markus Fidler;Jaya Prakash Champati;Joerg Widmer;Mahsa Noroozi
This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limited and random service outages and congestion cause buffering that impairs the age-of-information. The parallel use of independent channels promises a remedy, since outages on one channel may be compensated for by another. Surprisingly, for the well-known case of $text{M}mid text{M}mid 1$ queues we find the opposite: pooling capacity in one channel performs better than a parallel system with the same total capacity. A generalization is not possible since there are no solutions for other types of parallel queues at hand. In this work, we prove a dual representation of age-of-information in min-plus algebra that connects to queueing models known from the theory of effective bandwidth/capacity and the stochastic network calculus. Exploiting these methods, we derive tail bounds of the age-of-information of $text{G}mid text{G}mid 1$ queues. Tail bounds of the age-of-information of independent parallel queues follow readily. In addition to parallel classical queues, we investigate Markov channels where, depending on the memory of the channel, we show the true advantage of parallel systems. We continue to investigate this new finding and provide insight into when capacity should be pooled in one channel or when independent parallel channels perform better. We complement our analysis with simulation results and evaluate different update policies, scheduling policies, and the use of heterogeneous channels that is most relevant for latest multi-band networks.
{"title":"Statistical Age-of-Information Bounds for Parallel Systems: When Do Independent Channels Make a Difference?","authors":"Markus Fidler;Jaya Prakash Champati;Joerg Widmer;Mahsa Noroozi","doi":"10.1109/JSAIT.2023.3328766","DOIUrl":"10.1109/JSAIT.2023.3328766","url":null,"abstract":"This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limited and random service outages and congestion cause buffering that impairs the age-of-information. The parallel use of independent channels promises a remedy, since outages on one channel may be compensated for by another. Surprisingly, for the well-known case of \u0000<inline-formula> <tex-math>$text{M}mid text{M}mid 1$ </tex-math></inline-formula>\u0000 queues we find the opposite: pooling capacity in one channel performs better than a parallel system with the same total capacity. A generalization is not possible since there are no solutions for other types of parallel queues at hand. In this work, we prove a dual representation of age-of-information in min-plus algebra that connects to queueing models known from the theory of effective bandwidth/capacity and the stochastic network calculus. Exploiting these methods, we derive tail bounds of the age-of-information of \u0000<inline-formula> <tex-math>$text{G}mid text{G}mid 1$ </tex-math></inline-formula>\u0000 queues. Tail bounds of the age-of-information of independent parallel queues follow readily. In addition to parallel classical queues, we investigate Markov channels where, depending on the memory of the channel, we show the true advantage of parallel systems. We continue to investigate this new finding and provide insight into when capacity should be pooled in one channel or when independent parallel channels perform better. We complement our analysis with simulation results and evaluate different update policies, scheduling policies, and the use of heterogeneous channels that is most relevant for latest multi-band networks.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"591-606"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10302220","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a consistent and highly scalable local approach to learn the causal structure of a linear Gaussian polytree using data from interventional experiments with known intervention targets. Our methods first learn the skeleton of the polytree and then orient its edges. The output is a CPDAG representing the interventional equivalence class of the polytree of the true underlying distribution. The skeleton and orientation recovery procedures we use rely on second order statistics and low-dimensional marginal distributions. We assess the performance of our methods under different scenarios in synthetic data sets and apply our algorithm to learn a polytree in a gene expression interventional data set. Our simulation studies demonstrate that our approach is fast, has good accuracy in terms of structural Hamming distance, and handles problems with thousands of nodes.
{"title":"Learning Linear Gaussian Polytree Models With Interventions","authors":"Daniele Tramontano;L. Waldmann;M. Drton;Eliana Duarte","doi":"10.1109/JSAIT.2023.3328429","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3328429","url":null,"abstract":"We present a consistent and highly scalable local approach to learn the causal structure of a linear Gaussian polytree using data from interventional experiments with known intervention targets. Our methods first learn the skeleton of the polytree and then orient its edges. The output is a CPDAG representing the interventional equivalence class of the polytree of the true underlying distribution. The skeleton and orientation recovery procedures we use rely on second order statistics and low-dimensional marginal distributions. We assess the performance of our methods under different scenarios in synthetic data sets and apply our algorithm to learn a polytree in a gene expression interventional data set. Our simulation studies demonstrate that our approach is fast, has good accuracy in terms of structural Hamming distance, and handles problems with thousands of nodes.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"569-578"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795150","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}
Pub Date : 2023-10-12DOI: 10.1109/JSAIT.2023.3322077
Kumar Saurav;Rahul Vaze
Finding an optimal/near-optimal scheduling algorithm to minimize the age of information (AoI) in a multi-source G/G/1 system is well-known to be a hard problem, more so if there is a transmission (energy) cost. In this paper, we consider a multi-source G/G/1 system and the goal is to minimize a weighted sum of the AoI of all sources, subject to an energy cost constraint. We propose a novel doubly randomized non-preemptive scheduling algorithm and show that in the non-preemptive setting, where an update under transmission cannot be preempted, the competitive ratio of the proposed algorithm is at most 3 plus the maximum of the ratio of the variance and the mean of the update inter-generation time distribution of sources. Notably, the competitive ratio is independent of the number of sources, or their service time distributions, and is at most 4 for several common update inter-generation time distributions such as exponential, uniform and Rayleigh. For preemptive setting, where an update under transmission can be preempted, we consider a multi-source G/M/1 system and show that the proposed non-preemptive algorithm has competitive ratio at most 5 plus the maximum of the ratio of the variance and the mean of the update inter-generation time distribution of sources.
{"title":"Scheduling to Minimize Age of Information With Multiple Sources","authors":"Kumar Saurav;Rahul Vaze","doi":"10.1109/JSAIT.2023.3322077","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3322077","url":null,"abstract":"Finding an optimal/near-optimal scheduling algorithm to minimize the age of information (AoI) in a multi-source G/G/1 system is well-known to be a hard problem, more so if there is a transmission (energy) cost. In this paper, we consider a multi-source G/G/1 system and the goal is to minimize a weighted sum of the AoI of all sources, subject to an energy cost constraint. We propose a novel doubly randomized non-preemptive scheduling algorithm and show that in the non-preemptive setting, where an update under transmission cannot be preempted, the competitive ratio of the proposed algorithm is at most 3 plus the maximum of the ratio of the variance and the mean of the update inter-generation time distribution of sources. Notably, the competitive ratio is independent of the number of sources, or their service time distributions, and is at most 4 for several common update inter-generation time distributions such as exponential, uniform and Rayleigh. For preemptive setting, where an update under transmission can be preempted, we consider a multi-source G/M/1 system and show that the proposed non-preemptive algorithm has competitive ratio at most 5 plus the maximum of the ratio of the variance and the mean of the update inter-generation time distribution of sources.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"539-550"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"109157409","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}
Pub Date : 2023-10-06DOI: 10.1109/JSAIT.2023.3322620
Md Kamran Chowdhury Shisher;Bo Ji;I-Hong Hou;Yin Sun
In this paper, we consider a remote inference system, where a neural network is used to infer a time-varying target (e.g., robot movement), based on features (e.g., video clips) that are progressively received from a sensing node (e.g., a camera). Each feature is a temporal sequence of sensory data. The inference error is determined by (i) the timeliness and (ii) the sequence length of the feature, where we use Age of Information (AoI) as a metric for timeliness. While a longer feature can typically provide better inference performance, it often requires more channel resources for sending the feature. To minimize the time-averaged inference error, we study a learning and communication co-design problem that jointly optimizes feature length selection and transmission scheduling. When there is a single sensor-predictor pair and a single channel, we develop low-complexity optimal co-designs for both the cases of time-invariant and time-variant feature length. When there are multiple sensor-predictor pairs and multiple channels, the co-design problem becomes a restless multi-arm multi-action bandit problem that is PSPACE-hard. For this setting, we design a low-complexity algorithm to solve the problem. Trace-driven evaluations demonstrate the potential of these co-designs to reduce inference error by up to 10000 times.
{"title":"Learning and Communications Co-Design for Remote Inference Systems: Feature Length Selection and Transmission Scheduling","authors":"Md Kamran Chowdhury Shisher;Bo Ji;I-Hong Hou;Yin Sun","doi":"10.1109/JSAIT.2023.3322620","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3322620","url":null,"abstract":"In this paper, we consider a remote inference system, where a neural network is used to infer a time-varying target (e.g., robot movement), based on features (e.g., video clips) that are progressively received from a sensing node (e.g., a camera). Each feature is a temporal sequence of sensory data. The inference error is determined by (i) the timeliness and (ii) the sequence length of the feature, where we use Age of Information (AoI) as a metric for timeliness. While a longer feature can typically provide better inference performance, it often requires more channel resources for sending the feature. To minimize the time-averaged inference error, we study a learning and communication co-design problem that jointly optimizes feature length selection and transmission scheduling. When there is a single sensor-predictor pair and a single channel, we develop low-complexity optimal co-designs for both the cases of time-invariant and time-variant feature length. When there are multiple sensor-predictor pairs and multiple channels, the co-design problem becomes a restless multi-arm multi-action bandit problem that is PSPACE-hard. For this setting, we design a low-complexity algorithm to solve the problem. Trace-driven evaluations demonstrate the potential of these co-designs to reduce inference error by up to 10000 times.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"524-538"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354744","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}
Pub Date : 2023-09-29DOI: 10.1109/JSAIT.2023.3320068
Shailja Agrawal;K. V. Sushena Sree;Prasad Krishnan;Abhinav Vaishya;Srikar Kale
We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called cache ) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. One of the chief drawbacks of many of these existing constructions is the large subpacketization level, which denotes the number of times a file should be split for the schemes to provide coding gain. In this work, using a new binary matrix model, we present several novel constructions for coded caching based on the various types of combinatorial designs and their $q$ -analogs, which are also called subspace designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement, they provide a rate that is either constant or decreasing, and moreover require competitively small levels of subpacketization, which is an extremely important feature in practical applications of coded caching. We also apply our constructions to the distributed computing framework of MapReduce, which consists of three phases, the Map phase, the Shuffle phase and the Reduce phase. Using our binary matrix framework, we present a new simple generic coded data shuffling scheme. Employing our designs-based constructions in conjunction with this new shuffling scheme, we obtain new coded computing schemes which have low file complexity, with marginally higher communication load compared to the optimal scheme for equivalent parameters. We show that our schemes can neatly extend to the scenario with full and partial stragglers also.
{"title":"Cache-Aided Communication Schemes via Combinatorial Designs and Their q-Analogs","authors":"Shailja Agrawal;K. V. Sushena Sree;Prasad Krishnan;Abhinav Vaishya;Srikar Kale","doi":"10.1109/JSAIT.2023.3320068","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3320068","url":null,"abstract":"We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called \u0000<italic>cache</i>\u0000) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. One of the chief drawbacks of many of these existing constructions is the large subpacketization level, which denotes the number of times a file should be split for the schemes to provide coding gain. In this work, using a new binary matrix model, we present several novel constructions for coded caching based on the various types of combinatorial designs and their \u0000<inline-formula> <tex-math>$q$ </tex-math></inline-formula>\u0000-analogs, which are also called subspace designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement, they provide a rate that is either constant or decreasing, and moreover require competitively small levels of subpacketization, which is an extremely important feature in practical applications of coded caching. We also apply our constructions to the distributed computing framework of MapReduce, which consists of three phases, the Map phase, the Shuffle phase and the Reduce phase. Using our binary matrix framework, we present a new simple generic coded data shuffling scheme. Employing our designs-based constructions in conjunction with this new shuffling scheme, we obtain new coded computing schemes which have low file complexity, with marginally higher communication load compared to the optimal scheme for equivalent parameters. We show that our schemes can neatly extend to the scenario with full and partial stragglers also.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"551-568"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795149","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}
Pub Date : 2023-09-22DOI: 10.1109/JSAIT.2023.3317941
Xuan Guang;Raymond W. Yeung
We consider linear network erro correction (LNEC) coding when errors may occur on the edges of a communication network of which the topology is known. In this paper, we first present a framework of additive adversarial network for LNEC coding, and then prove the equivalence of two well-known LNEC coding approaches, which can be unified under this framework. Furthermore, by developing a graph-theoretic approach, we obtain a significantly enhanced characterization of the error correction capability of LNEC codes in terms of the minimum distances at the sink nodes. Specifically, in order to ensure that an LNEC code can correct up to $r$ errors at a sink node $t$ , it suffices to ensure that this code can correct every error vector in a reduced set of error vectors; and on the other hand, this LNEC code in fact can correct every error vector in an enlarged set of error vectors. In general, the size of this reduced set is considerably smaller than the number of error vectors with Hamming weight not larger than $r$ , and the size of this enlarged set is considerably larger than the same number. This result has the important implication that the computational complexities for decoding and for code construction can be significantly reduced.
{"title":"A Revisit of Linear Network Error Correction Coding","authors":"Xuan Guang;Raymond W. Yeung","doi":"10.1109/JSAIT.2023.3317941","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3317941","url":null,"abstract":"We consider linear network erro correction (LNEC) coding when errors may occur on the edges of a communication network of which the topology is known. In this paper, we first present a framework of additive adversarial network for LNEC coding, and then prove the equivalence of two well-known LNEC coding approaches, which can be unified under this framework. Furthermore, by developing a graph-theoretic approach, we obtain a significantly enhanced characterization of the error correction capability of LNEC codes in terms of the minimum distances at the sink nodes. Specifically, in order to ensure that an LNEC code can correct up to \u0000<inline-formula> <tex-math>$r$ </tex-math></inline-formula>\u0000 errors at a sink node \u0000<inline-formula> <tex-math>$t$ </tex-math></inline-formula>\u0000, it suffices to ensure that this code can correct every error vector in a reduced set of error vectors; and on the other hand, this LNEC code in fact can correct every error vector in an enlarged set of error vectors. In general, the size of this reduced set is considerably smaller than the number of error vectors with Hamming weight not larger than \u0000<inline-formula> <tex-math>$r$ </tex-math></inline-formula>\u0000, and the size of this enlarged set is considerably larger than the same number. This result has the important implication that the computational complexities for decoding and for code construction can be significantly reduced.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"514-523"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354743","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}
Pub Date : 2023-09-19DOI: 10.1109/JSAIT.2023.3317094
Coleman DeLude;Rakshith S. Srinivasa;Santhosh Karnik;Christopher Hood;Mark A. Davenport;Justin Romberg
In this paper we consider the problem of localizing a set of broadband sources from a finite window of measurements. In the case of narrowband sources this can be reduced to the problem of spectral line estimation, where our goal is simply to estimate the active frequencies from a weighted mixture of pure sinusoids. There exists a plethora of modern and classical methods that effectively solve this problem. However, for a wide variety of applications the underlying sources are not narrowband and can have an appreciable amount of bandwidth. In this work, we extend classical greedy algorithms for sparse recovery (e.g., orthogonal matching pursuit) to localize broadband sources. We leverage models for samples of broadband signals based on a union of Slepian subspaces, which are more aptly suited for dealing with spectral leakage and dynamic range disparities. We show that by using these models, our adapted algorithms can successfully localize broadband sources under a variety of adverse operating scenarios. Furthermore, we show that our algorithms outperform complementary methods that use more standard Fourier models. We also show that we can perform estimation from compressed measurements with little loss in fidelity as long as the number of measurements are on the order of the signal’s implicit degrees of freedom. We conclude with an in-depth application of these ideas to the problem of localization in multi-sensor arrays.
{"title":"Iterative Broadband Source Localization","authors":"Coleman DeLude;Rakshith S. Srinivasa;Santhosh Karnik;Christopher Hood;Mark A. Davenport;Justin Romberg","doi":"10.1109/JSAIT.2023.3317094","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3317094","url":null,"abstract":"In this paper we consider the problem of localizing a set of broadband sources from a finite window of measurements. In the case of narrowband sources this can be reduced to the problem of spectral line estimation, where our goal is simply to estimate the active frequencies from a weighted mixture of pure sinusoids. There exists a plethora of modern and classical methods that effectively solve this problem. However, for a wide variety of applications the underlying sources are not narrowband and can have an appreciable amount of bandwidth. In this work, we extend classical greedy algorithms for sparse recovery (e.g., orthogonal matching pursuit) to localize broadband sources. We leverage models for samples of broadband signals based on a union of Slepian subspaces, which are more aptly suited for dealing with spectral leakage and dynamic range disparities. We show that by using these models, our adapted algorithms can successfully localize broadband sources under a variety of adverse operating scenarios. Furthermore, we show that our algorithms outperform complementary methods that use more standard Fourier models. We also show that we can perform estimation from compressed measurements with little loss in fidelity as long as the number of measurements are on the order of the signal’s implicit degrees of freedom. We conclude with an in-depth application of these ideas to the problem of localization in multi-sensor arrays.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"453-469"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354740","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}
Pub Date : 2023-09-14DOI: 10.1109/JSAIT.2023.3315585
Anthony Gómez-Fonseca;Roxana Smarandache;David G. M. Mitchell
In this paper, we present an efficient strategy to enumerate the number of $k$ -cycles, $gleq k < 2g$ , in the Tanner graph of a quasi-cyclic low-density parity-check (QC-LDPC) code with girth $g$ using its polynomial parity-check matrix $H$ . This strategy works for both $(d_{v},d_{c})$ -regular and irregular QC-LDPC codes. In this approach, we note that the $m$ th power of the polynomial adjacency matrix can be used to describe walks of length $m$ in the protograph and can therefore be sufficiently described by the matrices $B_{m}(H) triangleq (HH^{mathsf {T}})^{lfloor {m/2}rfloor }H^{(mmod 2)}$ , where $mgeq 0$ . We provide formulas for the number of $k$ -cycles, $mathcal {N}_{k}$ , by just taking into account repetitions in some multisets constructed from the matrices $B_{m}(H)$ . This approach is shown to have low complexity. For example, in the case of QC-LDPC codes based on the $3times n_{v}$ fully-connected protograph, the complexity of determining $mathcal {N}_{k}$ , for $k=4,6,8,10$ and 12, is $O(n_{v}^{2}log (N))$ , $O(n_{v}^{2}log (n_{v})log (N))$ , $O(n_{v}^{4}log ^{4}(n_{v})log (N))$ , $O(n_{v}^{4}log (n_{v})log (N))$ and $O(n_{v}^{6}log ^{6}(n_{v})log (N))$ , respectively. The complexity, depending logarithmically on the lifting factor $N$ , gives our approach, to the best of our knowledge, a significant advantage over previous works on the cycle distribution of QC-LDPC codes.
{"title":"An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes","authors":"Anthony Gómez-Fonseca;Roxana Smarandache;David G. M. Mitchell","doi":"10.1109/JSAIT.2023.3315585","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3315585","url":null,"abstract":"In this paper, we present an efficient strategy to enumerate the number of \u0000<inline-formula> <tex-math>$k$ </tex-math></inline-formula>\u0000-cycles, \u0000<inline-formula> <tex-math>$gleq k < 2g$ </tex-math></inline-formula>\u0000, in the Tanner graph of a quasi-cyclic low-density parity-check (QC-LDPC) code with girth \u0000<inline-formula> <tex-math>$g$ </tex-math></inline-formula>\u0000 using its polynomial parity-check matrix \u0000<inline-formula> <tex-math>$H$ </tex-math></inline-formula>\u0000. This strategy works for both \u0000<inline-formula> <tex-math>$(d_{v},d_{c})$ </tex-math></inline-formula>\u0000-regular and irregular QC-LDPC codes. In this approach, we note that the \u0000<inline-formula> <tex-math>$m$ </tex-math></inline-formula>\u0000th power of the polynomial adjacency matrix can be used to describe walks of length \u0000<inline-formula> <tex-math>$m$ </tex-math></inline-formula>\u0000 in the protograph and can therefore be sufficiently described by the matrices \u0000<inline-formula> <tex-math>$B_{m}(H) triangleq (HH^{mathsf {T}})^{lfloor {m/2}rfloor }H^{(mmod 2)}$ </tex-math></inline-formula>\u0000, where \u0000<inline-formula> <tex-math>$mgeq 0$ </tex-math></inline-formula>\u0000. We provide formulas for the number of \u0000<inline-formula> <tex-math>$k$ </tex-math></inline-formula>\u0000-cycles, \u0000<inline-formula> <tex-math>$mathcal {N}_{k}$ </tex-math></inline-formula>\u0000, by just taking into account repetitions in some multisets constructed from the matrices \u0000<inline-formula> <tex-math>$B_{m}(H)$ </tex-math></inline-formula>\u0000. This approach is shown to have low complexity. For example, in the case of QC-LDPC codes based on the \u0000<inline-formula> <tex-math>$3times n_{v}$ </tex-math></inline-formula>\u0000 fully-connected protograph, the complexity of determining \u0000<inline-formula> <tex-math>$mathcal {N}_{k}$ </tex-math></inline-formula>\u0000, for \u0000<inline-formula> <tex-math>$k=4,6,8,10$ </tex-math></inline-formula>\u0000 and 12, is \u0000<inline-formula> <tex-math>$O(n_{v}^{2}log (N))$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$O(n_{v}^{2}log (n_{v})log (N))$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$O(n_{v}^{4}log ^{4}(n_{v})log (N))$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$O(n_{v}^{4}log (n_{v})log (N))$ </tex-math></inline-formula>\u0000 and \u0000<inline-formula> <tex-math>$O(n_{v}^{6}log ^{6}(n_{v})log (N))$ </tex-math></inline-formula>\u0000, respectively. The complexity, depending logarithmically on the lifting factor \u0000<inline-formula> <tex-math>$N$ </tex-math></inline-formula>\u0000, gives our approach, to the best of our knowledge, a significant advantage over previous works on the cycle distribution of QC-LDPC codes.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"499-513"},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354741","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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