Pub Date : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174259
Shouvik Ganguly, Lele Wang, Young-Han Kim
Codes are developed for two-user multiple access and broadcast channels starting from Gelfand-Pinsker codes with known block lengths, rates, and error performances. Guarantees are provided on the block error rates of the MAC and BC codes in terms of the parameters of the constituent Gelfand- Pinsker codes. These guarantees hold as long as the constituent codes satisfy the assumed properties on rate, codeword weights, and performances, irrespective of the basic structure and other properties.
{"title":"A Functional Construction of Codes for Multiple Access and Broadcast Channels","authors":"Shouvik Ganguly, Lele Wang, Young-Han Kim","doi":"10.1109/ISIT44484.2020.9174259","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174259","url":null,"abstract":"Codes are developed for two-user multiple access and broadcast channels starting from Gelfand-Pinsker codes with known block lengths, rates, and error performances. Guarantees are provided on the block error rates of the MAC and BC codes in terms of the parameters of the constituent Gelfand- Pinsker codes. These guarantees hold as long as the constituent codes satisfy the assumed properties on rate, codeword weights, and performances, irrespective of the basic structure and other properties.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133631919","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174356
Tyler Sypherd, Mario Díaz, L. Sankar, Gautam Dasarathy
We analyze the optimization landscape of a recently introduced tunable class of loss functions called α-loss, α ∈ (0, ∞], in the logistic model. This family encapsulates the exponential loss (α = 1/2), the log-loss (α = 1), and the 0-1 loss (α = ∞) and contains compelling properties that enable the practitioner to discern among a host of operating conditions relevant to emerging learning methods. Specifically, we study the evolution of the optimization landscape of α-loss with respect to α using tools drawn from the study of strictly-locally-quasi-convex functions in addition to geometric techniques. We interpret these results in terms of optimization complexity via normalized gradient descent.
{"title":"On the α-loss Landscape in the Logistic Model","authors":"Tyler Sypherd, Mario Díaz, L. Sankar, Gautam Dasarathy","doi":"10.1109/ISIT44484.2020.9174356","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174356","url":null,"abstract":"We analyze the optimization landscape of a recently introduced tunable class of loss functions called α-loss, α ∈ (0, ∞], in the logistic model. This family encapsulates the exponential loss (α = 1/2), the log-loss (α = 1), and the 0-1 loss (α = ∞) and contains compelling properties that enable the practitioner to discern among a host of operating conditions relevant to emerging learning methods. Specifically, we study the evolution of the optimization landscape of α-loss with respect to α using tools drawn from the study of strictly-locally-quasi-convex functions in addition to geometric techniques. We interpret these results in terms of optimization complexity via normalized gradient descent.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134526658","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174071
Alex Dytso, H. Poor, S. Shamai
This paper provides a general derivative identity for the conditional mean estimator of an arbitrary vector signal in Gaussian noise with an arbitrary covariance matrix. This new identity is used to recover and generalize many known identities in the literature and derive some new identities. For example, a new identity is discovered, which shows that an arbitrary higher-order conditional moment is completely determined by the first conditional moment.Several applications of the identities are shown. For instance, by using one of the identities, a simple proof of the uniqueness of the conditional mean estimator as a function of the distribution of the signal is shown. Moreover, one of the identities is used to extend the notion of empirical Bayes to higher-order conditional moments. Specifically, based on a random sample of noisy observations, a consistent estimator for a conditional expectation of any order is derived.
{"title":"A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications","authors":"Alex Dytso, H. Poor, S. Shamai","doi":"10.1109/ISIT44484.2020.9174071","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174071","url":null,"abstract":"This paper provides a general derivative identity for the conditional mean estimator of an arbitrary vector signal in Gaussian noise with an arbitrary covariance matrix. This new identity is used to recover and generalize many known identities in the literature and derive some new identities. For example, a new identity is discovered, which shows that an arbitrary higher-order conditional moment is completely determined by the first conditional moment.Several applications of the identities are shown. For instance, by using one of the identities, a simple proof of the uniqueness of the conditional mean estimator as a function of the distribution of the signal is shown. Moreover, one of the identities is used to extend the notion of empirical Bayes to higher-order conditional moments. Specifically, based on a random sample of noisy observations, a consistent estimator for a conditional expectation of any order is derived.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130365254","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174461
Hanxu Hou, P. Lee, Y. Han
Modern data centers often organize storage nodes in racks, in which the cross-rack communication cost is typically much higher than the intra-rack communication cost. Rack-aware regenerating codes have recently been proposed to achieve the optimal trade-off between storage redundancy and cross-rack repair bandwidth, subject to the condition that the original data can be reconstructed from a sufficient number of any non-failed nodes. In this paper, we present a coding framework that transforms any minimum-storage regenerating (MSR) code to a minimum-storage rack-aware regenerating (MSRR) code, such that the cross-rack repair bandwidth is minimized subject to the minimum storage redundancy. To this end, we can construct a family of exact-repair constructions for the MSRR codes for all admissible parameters. Furthermore, our constructions achieve low sub-packetization, which is critical for mitigating the I/O overhead during repair.
{"title":"Minimum Storage Rack-Aware Regenerating Codes with Exact Repair and Small Sub-Packetization","authors":"Hanxu Hou, P. Lee, Y. Han","doi":"10.1109/ISIT44484.2020.9174461","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174461","url":null,"abstract":"Modern data centers often organize storage nodes in racks, in which the cross-rack communication cost is typically much higher than the intra-rack communication cost. Rack-aware regenerating codes have recently been proposed to achieve the optimal trade-off between storage redundancy and cross-rack repair bandwidth, subject to the condition that the original data can be reconstructed from a sufficient number of any non-failed nodes. In this paper, we present a coding framework that transforms any minimum-storage regenerating (MSR) code to a minimum-storage rack-aware regenerating (MSRR) code, such that the cross-rack repair bandwidth is minimized subject to the minimum storage redundancy. To this end, we can construct a family of exact-repair constructions for the MSRR codes for all admissible parameters. Furthermore, our constructions achieve low sub-packetization, which is critical for mitigating the I/O overhead during repair.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115334617","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174282
P. Trifonov
Recursive trellis decoding of polar codes is considered. Polar codes are shown to have much lower recursive trellis decoding complexity compared to similar Reed-Muller codes. Furthermore, a low-latency decoding algorithm, which combines recursive trellis and successive cancellation decoding methods, is presented.
{"title":"Recursive Trellis Decoding Techniques of Polar Codes","authors":"P. Trifonov","doi":"10.1109/ISIT44484.2020.9174282","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174282","url":null,"abstract":"Recursive trellis decoding of polar codes is considered. Polar codes are shown to have much lower recursive trellis decoding complexity compared to similar Reed-Muller codes. Furthermore, a low-latency decoding algorithm, which combines recursive trellis and successive cancellation decoding methods, is presented.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114777905","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174145
Jinwen Shi, Cong Ling, O. Simeone, J. Kliewer
The uplink of a Cloud Radio Access Network (C-RAN) architecture is studied, where decoding in the cloud takes place at distributed decoding processors. To mitigate the impact of straggling decoders in the cloud, the cloud re-encodes the received frames via a linear code before distributing them to the decoding processors, which estimate linear combinations of the codewords. Focusing on Gaussian channels, and assuming the use of lattice codes at the users, we derive the computational rates and frame error probabilities at the cloud. The approach differs from Compute-and-Forward in that the combination of codewords is not caused by the channel but purposefully created in the cloud by encoding the received signals to reduce the decoding delay.
{"title":"Coded Computation Against Straggling Channel Decoders in the Cloud for Gaussian Channels","authors":"Jinwen Shi, Cong Ling, O. Simeone, J. Kliewer","doi":"10.1109/ISIT44484.2020.9174145","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174145","url":null,"abstract":"The uplink of a Cloud Radio Access Network (C-RAN) architecture is studied, where decoding in the cloud takes place at distributed decoding processors. To mitigate the impact of straggling decoders in the cloud, the cloud re-encodes the received frames via a linear code before distributing them to the decoding processors, which estimate linear combinations of the codewords. Focusing on Gaussian channels, and assuming the use of lattice codes at the users, we derive the computational rates and frame error probabilities at the cloud. The approach differs from Compute-and-Forward in that the combination of codewords is not caused by the channel but purposefully created in the cloud by encoding the received signals to reduce the decoding delay.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114802806","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9173939
Heedong Do, N. Lee, A. Lozano
We establish an upper bound on the informationtheoretic capacity of line-of-sight (LOS) multiantenna channels with arbitrary antenna arrangements and identify array structures that, properly configured, can attain at least 96.6% of such capacity at every signal-to-noise ratio (SNR). In the process, we determine how to configure the arrays as a function of the SNR. At low- and high-SNR specifically, the configured arrays revert to simpler structures and become capacity-achieving.
{"title":"Capacity of Line-of-Sight MIMO Channels","authors":"Heedong Do, N. Lee, A. Lozano","doi":"10.1109/ISIT44484.2020.9173939","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9173939","url":null,"abstract":"We establish an upper bound on the informationtheoretic capacity of line-of-sight (LOS) multiantenna channels with arbitrary antenna arrangements and identify array structures that, properly configured, can attain at least 96.6% of such capacity at every signal-to-noise ratio (SNR). In the process, we determine how to configure the arrays as a function of the SNR. At low- and high-SNR specifically, the configured arrays revert to simpler structures and become capacity-achieving.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"15 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114085667","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174100
Wei Zhao, K. Shum, Shenghao Yang
A locally repairable code (LRC) with locality r allows for the recovery of any erased symbol of a codeword by accessing only r other symbols of the same codeword. The LRCs achieving the Singleton-like bound are said to be optimal. In this paper, we completely characterize the locality of any constacyclic codes of length ps over finite fields. Using this characterization, we determine all the optimal constacyclic LRCs of prime power lengths over finite fields, i.e., there are no other optimal constacyclic LRCs of prime power length except for those we characterized in this paper. We classify all the optimal constacyclic LRCs into seven classes. The first six classes of constacyclic LRCs classified in this paper have unbounded length, and can achieve smaller locality comparing to those codes constructed by Luo, Xing and Yuan, which also provide unbounded length.
{"title":"Optimal Locally Repairable Constacyclic Codes of Prime Power Lengths","authors":"Wei Zhao, K. Shum, Shenghao Yang","doi":"10.1109/ISIT44484.2020.9174100","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174100","url":null,"abstract":"A locally repairable code (LRC) with locality r allows for the recovery of any erased symbol of a codeword by accessing only r other symbols of the same codeword. The LRCs achieving the Singleton-like bound are said to be optimal. In this paper, we completely characterize the locality of any constacyclic codes of length ps over finite fields. Using this characterization, we determine all the optimal constacyclic LRCs of prime power lengths over finite fields, i.e., there are no other optimal constacyclic LRCs of prime power length except for those we characterized in this paper. We classify all the optimal constacyclic LRCs into seven classes. The first six classes of constacyclic LRCs classified in this paper have unbounded length, and can achieve smaller locality comparing to those codes constructed by Luo, Xing and Yuan, which also provide unbounded length.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116147795","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174396
Sourya Basu, Daewon Seo, L. Varshney
We consider two problems in multiterminal source coding under maximal distortion: distributed coding for computing and successive refinement. In distributed coding for computing, we propose a hypergraph-based coding scheme which matches the sum-rate bound of the Berger-Tung inner bound. Further, this scheme matches the entire Berger-Tung inner region when the sources are independent and it outperforms existing graph-based coding schemes. For successive refinement, we propose a hypergraph-based scheme that attains the entire rate region.
{"title":"Hypergraph-based Coding Schemes for Two Source Coding Problems under Maximal Distortion","authors":"Sourya Basu, Daewon Seo, L. Varshney","doi":"10.1109/ISIT44484.2020.9174396","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174396","url":null,"abstract":"We consider two problems in multiterminal source coding under maximal distortion: distributed coding for computing and successive refinement. In distributed coding for computing, we propose a hypergraph-based coding scheme which matches the sum-rate bound of the Berger-Tung inner bound. Further, this scheme matches the entire Berger-Tung inner region when the sources are independent and it outperforms existing graph-based coding schemes. For successive refinement, we propose a hypergraph-based scheme that attains the entire rate region.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123332417","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 : 2020-06-01DOI: 10.1109/ISIT44484.2020.9174528
Mansi Sood, Osman Yağan
Random key predistribution schemes serve as a viable solution for facilitating secure communication in Wireless Sensor Networks (WSNs). We analyze reliable connectivity of a heterogeneous WSN under the random pairwise key predistribution scheme of Chan et al. According to this scheme, each of the n sensor nodes is classified as type-1 (respectively, type-2) with probability μ (respectively, 1 − μ) where 0 < μ < 1. Each type-1 (respectively, type-2) node is paired with 1 (respectively, Kn) other node selected uniformly at random; each pair is then assigned a unique pairwise key so that they can securely communicate with each other. A main question in the design of secure and heterogeneous WSNs is how should the parameters n, μ, and Kn be selected such that resulting network exhibits certain desirable properties with high probability. Of particular interest is the strength of connectivity often studied in terms of k-connectivity; i.e., with k = 1, 2, …, the property that the network remains connected despite the removal of any k − 1 nodes or links. In this paper, we answer this question by analyzing the inhomogeneous random K-out graph model naturally induced under the heterogeneous pairwise scheme. It was recently established that this graph is 1-connected asymptotically almost surely (a.a.s.) if and only if Kn = ω(1). Here, we show that for k = 2, 3, …, we need to set ${K_n} = frac{1}{{1 - mu }}left( {log n + (k - 2)log log n + omega (1)} right)$ for the network to be k-connected a.a.s. The result is given in the form of a zero-one law indicating that the network is a.a.s. not k-connected when ${K_n} = frac{1}{{1 - mu }}left( {log n + (k - 2)log log n - omega (1)} right)$. We present simulation results to demonstrate the usefulness of the results in the finite node regime.
随机密钥预分配方案是实现无线传感器网络安全通信的可行方案。本文分析了Chan等人提出的随机密钥对预分配方案下异构WSN的可靠连通性。根据该方案，n个传感器节点中的每一个都被分类为类型1(分别为，类型2)，其概率为μ(分别为，1−μ)，其中0 < μ < 1。每个1型(分别，2型)节点与随机均匀选择的1个(分别，Kn)其他节点配对;然后为每对配对分配一个唯一的配对密钥，以便它们可以安全地相互通信。在设计安全的异构WSNs时，一个主要问题是如何选择n、μ和Kn参数，使网络高概率地表现出某些期望的特性。特别有趣的是连通性的强度，通常用k-连通性来研究;即，当k = 1,2，…时，尽管移除任何k−1个节点或链路，网络仍保持连接的性质。本文通过对非齐次随机K-out图模型的分析，回答了这一问题。最近证明，当且仅当Kn = ω(1)时，此图是渐近几乎肯定的1连通。这里，我们表明，当k = 2,3，…时，我们需要设置${K_n} = frac{1}{{1 - mu }}left( {log n + (k - 2)log log n + omega (1)} right)$使网络a.a.s.为k连通。结果以0 - 1定律的形式给出，表明当${K_n} = frac{1}{{1 - mu }}left( {log n + (k - 2)log log n - omega (1)} right)$时网络a.a.s.为非k连通。我们给出了仿真结果来证明结果在有限节点状态下的有效性。
{"title":"k-Connectivity in Random Graphs induced by Pairwise Key Predistribution Schemes","authors":"Mansi Sood, Osman Yağan","doi":"10.1109/ISIT44484.2020.9174528","DOIUrl":"https://doi.org/10.1109/ISIT44484.2020.9174528","url":null,"abstract":"Random key predistribution schemes serve as a viable solution for facilitating secure communication in Wireless Sensor Networks (WSNs). We analyze reliable connectivity of a heterogeneous WSN under the random pairwise key predistribution scheme of Chan et al. According to this scheme, each of the n sensor nodes is classified as type-1 (respectively, type-2) with probability μ (respectively, 1 − μ) where 0 < μ < 1. Each type-1 (respectively, type-2) node is paired with 1 (respectively, Kn) other node selected uniformly at random; each pair is then assigned a unique pairwise key so that they can securely communicate with each other. A main question in the design of secure and heterogeneous WSNs is how should the parameters n, μ, and Kn be selected such that resulting network exhibits certain desirable properties with high probability. Of particular interest is the strength of connectivity often studied in terms of k-connectivity; i.e., with k = 1, 2, …, the property that the network remains connected despite the removal of any k − 1 nodes or links. In this paper, we answer this question by analyzing the inhomogeneous random K-out graph model naturally induced under the heterogeneous pairwise scheme. It was recently established that this graph is 1-connected asymptotically almost surely (a.a.s.) if and only if Kn = ω(1). Here, we show that for k = 2, 3, …, we need to set ${K_n} = frac{1}{{1 - mu }}left( {log n + (k - 2)log log n + omega (1)} right)$ for the network to be k-connected a.a.s. The result is given in the form of a zero-one law indicating that the network is a.a.s. not k-connected when ${K_n} = frac{1}{{1 - mu }}left( {log n + (k - 2)log log n - omega (1)} right)$. We present simulation results to demonstrate the usefulness of the results in the finite node regime.","PeriodicalId":159311,"journal":{"name":"2020 IEEE International Symposium on Information Theory (ISIT)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122908141","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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