{"title":"The Degraded Gaussian Many-Access Wiretap Channel","authors":"Rémi A. Chou, A. Yener","doi":"10.1109/ISIT.2019.8849675","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849675","url":null,"abstract":"The Gaussian multiple-access wiretap channel when the number of transmitters grows unbounded and at most linearly with the blocklength is studied. Its capacity region is characterized when the eavesdropper channel is degraded and when the transmitters’ activities are random. Unlike the conventional Gaussian multiple-access wiretap channel, the capacity region is independent of the power of the transmitters and depends only on the sum of the message lengths of the transmitters.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"200 1","pages":"672-676"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89036683","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}
{"title":"Relaying One Bit Across a Tandem of Binary-Symmetric Channels","authors":"Wasim Huleihel, Yury Polyanskiy, O. Shayevitz","doi":"10.1109/ISIT.2019.8849298","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849298","url":null,"abstract":"We consider the problem of transmitting reliably one bit of information across a tandem of binary symmetric channels interconnected by a relay/processor station. In our setting, the relay is instantaneous in the sense that its outputs are allowed to causally depend on previous received noisy bits. For this model, we investigate the optimal exponential decay rate of the average probability of error, when relaying one bit of information using n synchronous channel uses, by devising good relaying schemes.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"20 1","pages":"2928-2932"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75871174","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}
S. Kowshik, K. Andreev, A. Frolov, Yury Polyanskiy
{"title":"Energy efficient random access for the quasi-static fading MAC","authors":"S. Kowshik, K. Andreev, A. Frolov, Yury Polyanskiy","doi":"10.1109/ISIT.2019.8849288","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849288","url":null,"abstract":"We discuss the problem of designing channel access architectures for enabling fast, low-latency, grant-free and uncoordinated uplink for densely packed wireless nodes. Specifically, we extend the concept of random-access code introduced at ISIT’2017 by one of the authors to the practically more relevant case of the AWGN multiple-access channel (MAC) subject to Rayleigh fading, unknown to the decoder. We derive bounds on the fundamental limits of random-access coding and propose an alternating belief-propagation scheme as a candidate practical solution. The latter’s performance was found to be surprisingly close to the information-theoretic bounds. It is curious, thus, that while fading significantly increases the minimal required energy-per-bit Eb/N0 (from about 0-2 dB to about 8-11 dB), it appears that it is much easier to attain the optimal performance over the fading channel with a practical scheme by leveraging the inherent randomization introduced by the channel. Finally, we mention that while a number of candidate solutions (MUSA, SCMA, RSMA, etc.) are being discussed for the 5G, the information-theoretic analysis and benchmarking has not been attempted before (in part due to lack of common random-access model). Our work may be seen as a step towards unifying performance comparisons of these methods.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"67 1","pages":"2768-2772"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83585744","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}
{"title":"Broadcasting on Random Networks","authors":"A. Makur, Elchanan Mossel, Yury Polyanskiy","doi":"10.1109/ISIT.2019.8849393","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849393","url":null,"abstract":"We study a generalization of the problem of broadcasting on trees to the setting of directed acyclic graphs (DAGs). At time 0, a source vertex X transmits a uniform bit along binary symmetric channels (BSCs) to a set of vertices called layer 1. Each vertex except X has indegree d. At time k ≥ 1, vertices at layer k apply d-input Boolean processing functions to their received bits and send out the results to vertices at layer k + 1. We say that broadcasting is possible if we can reconstruct X with probability of error bounded away from $frac{1}{2}$ using the values of all vertices at an arbitrarily deep layer k. This question is closely related to models of reliable computation and storage, probabilistic cellular automata, and information flow in biological networks.In this work, we analyze randomly constructed DAGs and demonstrate that broadcasting is only possible if the BSC noise level is below a certain (degree and function dependent) critical threshold. Specifically, for every d ≥ 3, we identify the critical threshold for random DAGs with layers of size Ω(log(k)) and majority processing functions. For d = 2, we establish a similar result for the NAND processing function. Furthermore, for odd d ≥ 3, we prove that the identified thresholds cannot be improved by other processing functions if reconstruction is required from a single vertex. Finally, for any BSC noise level, in quasi-polynomial or randomized polylogarithmic time in the depth, we construct deterministic bounded degree DAGs with layers of size Θ(log(k)) that admit reconstruction using lossless expander graphs.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"73 1","pages":"1632-1636"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84281724","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}
{"title":"An Upper Bound on the Number of Mass Points in the Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel","authors":"S. Yagli, Alex Dytso, H. Poor, S. Shamai","doi":"10.1109/ISIT.2019.8849318","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849318","url":null,"abstract":"This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, the capacity-achieving input distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of shells of the optimal input distribution nor a bound on it was available.This paper provides an alternative proof of the finiteness of the number shells of the capacity-achieving input distribution and produces the first firm upper bound on the number of shells, paving an alternative way for approaching many such problems. In particular, for every dimension n, it is shown that the number of shells is given by O(A2) where A is the constraint on the input amplitude. Moreover, this paper also provides bounds on the number of points for the case of n = 1 with an additional power constraint.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"26 1","pages":"1907-1911"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87142041","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}
{"title":"Explicit constructions of MSR codes for the rack-aware storage model","authors":"Zitan Chen, A. Barg","doi":"10.1109/ISIT.2019.8849278","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849278","url":null,"abstract":"We consider erasure coding for a model of storage that assumes that nodes are organized into equally sized groups, called racks, such that repairing failed nodes is limited only by inter-rack communication, while transmission of data within a rack does not contribute to the repair bandwidth. We present explicit families of MDS array codes that support recovery of a single failed node from any number of helper racks using the minimum possible amount of inter-rack communication. One of our constructions also has the additional property of low access.Finally, we present a construction of scalar Reed-Solomon codes that support optimal repair for the rack-oriented storage model.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"218 1","pages":"226-230"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75618544","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}
Y. M. Chee, H. M. Kiah, A. Vinck, Van Khu Vu, Eitan Yaakobi
{"title":"Coding for Write ℓ-step-up Memories","authors":"Y. M. Chee, H. M. Kiah, A. Vinck, Van Khu Vu, Eitan Yaakobi","doi":"10.1109/ISIT.2019.8849835","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849835","url":null,"abstract":"In this work, we propose and study a new class of non-binary rewriting codes, called write ℓ-step-up memories (WℓM) codes. From an information-theoretic point of view, this coding scheme is a generalization of non-binary write-once memories (WOM) codes. From a practical point of view, this coding scheme can be used not only to increase the lifetime of flash memories but also mitigate their over-shooting problem. We first provide an exact formula for the capacity region and the maximum sum-rate of WℓM codes. Lastly, we present several explicit constructions of high-rate WℓM codes with efficient encoding/decoding algorithms.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"39 1","pages":"1597-1601"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74960395","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}
{"title":"Asymptotics of Entropy of the Dirichlet-Multinomial Distribution","authors":"K. Turowski, P. Jacquet, W. Szpankowski","doi":"10.1109/ISIT.2019.8849466","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849466","url":null,"abstract":"Dirichlet distribution and multinomial distribution play important role in information theory and statistics. They find applications in estimation, average minimax redundancy in source coding, Pólya urn model, and graph compression. Dirichlet-multinomial distribution is a multinomial distribution in which parameters are distributed according to the Dirichlet distribution. In this paper, we present some characteristics of the Dirichlet-multinomial distribution, including a precise asymptotic for the entropy. It should be point out that such a characterization turns out to be technically quite challenging requiring analytic tools including analytic continuation of hypergeometric series.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"25 1","pages":"1517-1521"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79329983","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}
{"title":"High-Dimensional Linear Regression and Phase Retrieval via PSLQ Integer Relation Algorithm","authors":"D. Gamarnik, Eren C. Kizildag","doi":"10.1109/ISIT.2019.8849681","DOIUrl":"https://doi.org/10.1109/ISIT.2019.8849681","url":null,"abstract":"We study high-dimensional linear regression problem without sparsity, and address the question of efficient recovery with small number of measurements. We propose an algorithm which efficiently recovers an unknown feature vector β∗ ∈ ℝp from its linear measurements Y = Xβ∗ in polynomially many steps, with high probability (as p → ∞), even with a single measurement, provided elements of β∗ are supported on a rationally independent set of at most polynomial in p size known to learner. We use a combination of PSLQ integer relation and LLL lattice basis reduction algorithms to achieve our goal. We then apply our ideas to develop an efficient, single-sample algorithm for the phase retrieval problem, where ${beta ^ * } in {mathbb{C}^p}$ is to be recovered from magnitude-only observations Y = |〈X, β∗〉|.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"206 1","pages":"1437-1441"},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77056228","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}