Pub Date : 2015-04-01DOI: 10.1109/ITW.2015.7133124
G. Brassard, Benno Salwey, S. Wolf
Besides being one of the most puzzling aspects of quantum information theory, non-locality has been recognised as a valuable resource for various cryptographic protocols. We study the phenomenon of distillation of non-locality, which is the ability to generate a stronger instance of non-locality from weaker ones. We construct an eavesdropping third party who gains knowledge about the outputs of distillation protocols. This knowledge directly implies an upper bound on the degree of non-locality of the output of the protocol.
{"title":"Non-locality distillation as cryptographic game","authors":"G. Brassard, Benno Salwey, S. Wolf","doi":"10.1109/ITW.2015.7133124","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133124","url":null,"abstract":"Besides being one of the most puzzling aspects of quantum information theory, non-locality has been recognised as a valuable resource for various cryptographic protocols. We study the phenomenon of distillation of non-locality, which is the ability to generate a stronger instance of non-locality from weaker ones. We construct an eavesdropping third party who gains knowledge about the outputs of distillation protocols. This knowledge directly implies an upper bound on the degree of non-locality of the output of the protocol.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128523387","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 : 2015-04-01DOI: 10.1109/ITW.2015.7133144
M. Yan, A. Sprintson
In the Cooperative Data Exchange (CDE) problem, a group of wireless clients need to exchange data over a shared broadcast channel, such that at the end of the transfer all clients have access to all packets held by other clients. In this paper, we focus on the robust version of the problem in which the clients must be able to complete the transfer even if one of the clients fails before the transfer is complete. The event of a client failure is referred to as an erasure. We show that, while the original CDE problem can be solved in polynomial time, the robust version of the problem is NP-hard, even in the special case when robustness to a single failure is required. Focusing on the practically important special case of a single failure, we establish an approximation algorithm for this problem that can find a solution within a constant factor of the optimum. Our simulation studies show that the algorithm is able to find solutions that are very close to the optimum.
{"title":"Approximation algorithms for erasure correcting Data Exchange","authors":"M. Yan, A. Sprintson","doi":"10.1109/ITW.2015.7133144","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133144","url":null,"abstract":"In the Cooperative Data Exchange (CDE) problem, a group of wireless clients need to exchange data over a shared broadcast channel, such that at the end of the transfer all clients have access to all packets held by other clients. In this paper, we focus on the robust version of the problem in which the clients must be able to complete the transfer even if one of the clients fails before the transfer is complete. The event of a client failure is referred to as an erasure. We show that, while the original CDE problem can be solved in polynomial time, the robust version of the problem is NP-hard, even in the special case when robustness to a single failure is required. Focusing on the practically important special case of a single failure, we establish an approximation algorithm for this problem that can find a solution within a constant factor of the optimum. Our simulation studies show that the algorithm is able to find solutions that are very close to the optimum.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"44 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120984686","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 : 2015-04-01DOI: 10.1109/ITW.2015.7133128
Pengfei Huang, Eitan Yaakobi, H. Uchikawa, P. Siegel
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do not explicitly take into consideration the field size q, i.e., the size of the code alphabet. In particular, for the binary case, only a few specific results are known by Goparaju and Calderbank. Recently, however, an upper bound on the dimension k of LRCs was presented by Cadambe and Mazumdar. The bound takes into account the length n, minimum distance d, locality r, and field size q, and it is applicable to both non-linear and linear codes. In this work, we first develop an improved version of the bound mentioned above for linear codes. We then focus on cyclic linear binary codes. By leveraging the cyclic structure, we notice that the locality of such a code is determined by the minimum distance of its dual code. Using this result, we investigate the locality of a variety of well known cyclic linear binary codes, e.g., Hamming codes and Simplex codes, and also prove their optimality with our improved bound for linear codes. We also discuss the locality of codes which are obtained by applying the operations of Extend, Shorten, Expurgate, Augment, and Lengthen to cyclic linear binary codes. Several families of such modified codes are considered and their optimality is addressed. Finally, we investigate the locality of Reed-Muller codes. Even though they are not cyclic, it is shown that some of the locality results for cyclic codes still apply.
{"title":"Cyclic linear binary locally repairable codes","authors":"Pengfei Huang, Eitan Yaakobi, H. Uchikawa, P. Siegel","doi":"10.1109/ITW.2015.7133128","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133128","url":null,"abstract":"Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do not explicitly take into consideration the field size q, i.e., the size of the code alphabet. In particular, for the binary case, only a few specific results are known by Goparaju and Calderbank. Recently, however, an upper bound on the dimension k of LRCs was presented by Cadambe and Mazumdar. The bound takes into account the length n, minimum distance d, locality r, and field size q, and it is applicable to both non-linear and linear codes. In this work, we first develop an improved version of the bound mentioned above for linear codes. We then focus on cyclic linear binary codes. By leveraging the cyclic structure, we notice that the locality of such a code is determined by the minimum distance of its dual code. Using this result, we investigate the locality of a variety of well known cyclic linear binary codes, e.g., Hamming codes and Simplex codes, and also prove their optimality with our improved bound for linear codes. We also discuss the locality of codes which are obtained by applying the operations of Extend, Shorten, Expurgate, Augment, and Lengthen to cyclic linear binary codes. Several families of such modified codes are considered and their optimality is addressed. Finally, we investigate the locality of Reed-Muller codes. Even though they are not cyclic, it is shown that some of the locality results for cyclic codes still apply.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122936799","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 : 2015-04-01DOI: 10.1109/ITW.2015.7133148
Songnam Hong, I. Marić, D. Hui, G. Caire
We introduce a multihop “virtual” full-duplex relay channel as a special case of a general multiple multicast relay network. For such network, quantize-map-and-forward (QMF) (or noisy network coding (NNC)) can achieve the cut-set upper bound within a constant gap where the gap grows linearly with the number of relay stages K. However, this gap may not be negligible for the systems with multihop transmissions (e.g., a power-limited wireless backhaul system operating at high frequencies). In this paper, we obtain an improved result to the capacity scaling where the gap grows logarithmically as log (K). This is achieved by using an optimal quantization at relays and by exploiting relays' messages (decoded in the previous time slot) as side-information at the destination. We further improve the performance of this network by presenting a mixed strategy where each relay can perform either decode-and-forward (DF) or QMF with possibly rate-splitting.
{"title":"Multihop virtual full-duplex relay channels","authors":"Songnam Hong, I. Marić, D. Hui, G. Caire","doi":"10.1109/ITW.2015.7133148","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133148","url":null,"abstract":"We introduce a multihop “virtual” full-duplex relay channel as a special case of a general multiple multicast relay network. For such network, quantize-map-and-forward (QMF) (or noisy network coding (NNC)) can achieve the cut-set upper bound within a constant gap where the gap grows linearly with the number of relay stages K. However, this gap may not be negligible for the systems with multihop transmissions (e.g., a power-limited wireless backhaul system operating at high frequencies). In this paper, we obtain an improved result to the capacity scaling where the gap grows logarithmically as log (K). This is achieved by using an optimal quantization at relays and by exploiting relays' messages (decoded in the previous time slot) as side-information at the destination. We further improve the performance of this network by presenting a mixed strategy where each relay can perform either decode-and-forward (DF) or QMF with possibly rate-splitting.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129200646","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 : 2015-03-26DOI: 10.1109/ITW.2015.7133167
G. Kramer, Mansoor I. Yousefi, F. Kschischang
An upper bound on the capacity of a cascade of nonlinear and noisy channels is presented. The cascade mimics the split-step Fourier method for computing waveform propagation governed by the stochastic generalized nonlinear Schrödinger equation. It is shown that the spectral efficiency of the cascade is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The results may be applied to optical fiber channels. However, the definition of bandwidth is subtle and leaves open interpretations of the bound. Some of these interpretations are discussed.
{"title":"Upper bound on the capacity of a cascade of nonlinear and noisy channels","authors":"G. Kramer, Mansoor I. Yousefi, F. Kschischang","doi":"10.1109/ITW.2015.7133167","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133167","url":null,"abstract":"An upper bound on the capacity of a cascade of nonlinear and noisy channels is presented. The cascade mimics the split-step Fourier method for computing waveform propagation governed by the stochastic generalized nonlinear Schrödinger equation. It is shown that the spectral efficiency of the cascade is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The results may be applied to optical fiber channels. However, the definition of bandwidth is subtle and leaves open interpretations of the bound. Some of these interpretations are discussed.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114228759","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 : 2015-03-18DOI: 10.1109/ITW.2015.7133153
Assaf Ben-Yishai, O. Shayevitz
We consider the problem of communication over a two-user Additive White Gaussian Noise Broadcast Channel (AWGN-BC) with an AWGN Multiple Access (MAC) active feedback. We describe a constructive reduction from this setup to the well-studied setup of linear-feedback coding over the AWGN-BC with noiseless feedback (and different parameters). This reduction facilitates the design of linear-feedback coding schemes in the (passive) noiseless feedback regime, which can then be easily and constructively transformed into coding schemes in the MAC feedback regime that attain the exact same rates. Our construction introduces an element of interaction into the coding protocol, and is based on modulo-lattice operations. As an example, we apply our method to the Ozarow-Leung scheme, and demonstrate how MAC feedback can be used to enlarge the capacity region of the AWGN-BC.
{"title":"The AWGN BC with MAC feedback: A reduction to noiseless feedback via interaction","authors":"Assaf Ben-Yishai, O. Shayevitz","doi":"10.1109/ITW.2015.7133153","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133153","url":null,"abstract":"We consider the problem of communication over a two-user Additive White Gaussian Noise Broadcast Channel (AWGN-BC) with an AWGN Multiple Access (MAC) active feedback. We describe a constructive reduction from this setup to the well-studied setup of linear-feedback coding over the AWGN-BC with noiseless feedback (and different parameters). This reduction facilitates the design of linear-feedback coding schemes in the (passive) noiseless feedback regime, which can then be easily and constructively transformed into coding schemes in the MAC feedback regime that attain the exact same rates. Our construction introduces an element of interaction into the coding protocol, and is based on modulo-lattice operations. As an example, we apply our method to the Ozarow-Leung scheme, and demonstrate how MAC feedback can be used to enlarge the capacity region of the AWGN-BC.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115030094","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 : 2015-03-09DOI: 10.1109/ITW.2015.7133169
Naftali Tishby, Noga Zaslavsky
Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output variables. Using this representation we can calculate the optimal information theoretic limits of the DNN and obtain finite sample generalization bounds. The advantage of getting closer to the theoretical limit is quantifiable both by the generalization bound and by the network's simplicity. We argue that both the optimal architecture, number of layers and features/connections at each layer, are related to the bifurcation points of the information bottleneck tradeoff, namely, relevant compression of the input layer with respect to the output layer. The hierarchical representations at the layered network naturally correspond to the structural phase transitions along the information curve. We believe that this new insight can lead to new optimality bounds and deep learning algorithms.
{"title":"Deep learning and the information bottleneck principle","authors":"Naftali Tishby, Noga Zaslavsky","doi":"10.1109/ITW.2015.7133169","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133169","url":null,"abstract":"Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output variables. Using this representation we can calculate the optimal information theoretic limits of the DNN and obtain finite sample generalization bounds. The advantage of getting closer to the theoretical limit is quantifiable both by the generalization bound and by the network's simplicity. We argue that both the optimal architecture, number of layers and features/connections at each layer, are related to the bifurcation points of the information bottleneck tradeoff, namely, relevant compression of the input layer with respect to the output layer. The hierarchical representations at the layered network naturally correspond to the structural phase transitions along the information curve. We believe that this new insight can lead to new optimality bounds and deep learning algorithms.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132472811","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 : 2015-02-24DOI: 10.1109/ITW.2015.7133123
A. Zeh, Eitan Yaakobi
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields with locality properties are developed. The first two approaches give binary cyclic codes with locality two. While the first construction has availability one, the second binary code is characterized by multiple available repair sets based on a binary Simplex code. The third approach extends the first one to q-ary cyclic codes including (binary) extension fields, where the locality property is determined by the properties of a shortened first-order Reed- Muller code. Non-cyclic optimal binary linear codes with locality greater than two are obtained by the fourth construction.
{"title":"Optimal linear and cyclic locally repairable codes over small fields","authors":"A. Zeh, Eitan Yaakobi","doi":"10.1109/ITW.2015.7133123","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133123","url":null,"abstract":"We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields with locality properties are developed. The first two approaches give binary cyclic codes with locality two. While the first construction has availability one, the second binary code is characterized by multiple available repair sets based on a binary Simplex code. The third approach extends the first one to q-ary cyclic codes including (binary) extension fields, where the locality property is determined by the properties of a shortened first-order Reed- Muller code. Non-cyclic optimal binary linear codes with locality greater than two are obtained by the fourth construction.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"99 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126101118","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 : 2015-02-23DOI: 10.1109/ITW.2015.7133079
I. Sason
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds for lossless source coding is provided, refining and improving a certain bound by Csiszár. A new inequality relating f-divergences is derived, and its use is exemplified. The last section of this conference paper is not included in the recent journal paper [16], as well as some new remarks that are linked to new references.
{"title":"Tight bounds for symmetric divergence measures and a new inequality relating f-divergences","authors":"I. Sason","doi":"10.1109/ITW.2015.7133079","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133079","url":null,"abstract":"Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds for lossless source coding is provided, refining and improving a certain bound by Csiszár. A new inequality relating f-divergences is derived, and its use is exemplified. The last section of this conference paper is not included in the recent journal paper [16], as well as some new remarks that are linked to new references.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127489750","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 : 2015-02-23DOI: 10.1109/ITW.2015.7133082
G. David Forney
The Conti-Boston factorization theorem (CBFT) for linear tail-biting trellis realizations is extended to group realizations with a new and simpler proof, based on a controller granule decomposition of the behavior and known controllability results for group realizations. Further controllability results are given; e.g., a trellis realization is controllable if and only if its top (controllability) granule is trivial.
{"title":"Unique factorization and controllability of tail-biting trellis realizations via controller granule decompositions","authors":"G. David Forney","doi":"10.1109/ITW.2015.7133082","DOIUrl":"https://doi.org/10.1109/ITW.2015.7133082","url":null,"abstract":"The Conti-Boston factorization theorem (CBFT) for linear tail-biting trellis realizations is extended to group realizations with a new and simpler proof, based on a controller granule decomposition of the behavior and known controllability results for group realizations. Further controllability results are given; e.g., a trellis realization is controllable if and only if its top (controllability) granule is trivial.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117078179","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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