Shuo Shao, Jesús Gomicronmez-Vilardebomicron, Kai Zhang, C. Tian
{"title":"On the Fundamental Limit of Coded Caching Systems with a Single Demand Type","authors":"Shuo Shao, Jesús Gomicronmez-Vilardebomicron, Kai Zhang, C. Tian","doi":"10.1109/ITW44776.2019.8989383","DOIUrl":"https://doi.org/10.1109/ITW44776.2019.8989383","url":null,"abstract":"Caching is a technique to reduce the communication load in peak hours by prefetching contents during off-peak hours. Recently Maddah-Ali and Niesen introduced an information theoretic framework for coded caching, and showed that significant improvement can be obtained compared to uncoded caching. Considerable efforts have been devoted to identify the precise information theoretic fundamental limit of such systems, however the difficulty of this task has also become clear. One of the reasons for this difficulty is that the original coded caching setting allows multiple demand types during delivery, which in fact introduces tension in the coding strategy to accommodate all of them. In this paper, we seek to develop a better understanding of the fundamental limit of coded caching by investigating single demand type systems. We first show that in the canonical three-user three-file systems, such single demand type systems already provide important insights. Motivated by these findings, we focus on systems where the number of users and the number of files are the same, and the demand type is when all files are being requested. A novel coding scheme is proposed, which provides several optimal memory-transmission operating points. Outer bounds for this class of systems are also considered, and their relation with existing bounds is discussed.","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"283 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127554428","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":"Optimal Broadcast Rate of a Class of Two-Sender Unicast Index Coding Problems","authors":"Chinmayananda Arunachala, V. Aggarwal, B. Rajan","doi":"10.1109/ITW44776.2019.8989283","DOIUrl":"https://doi.org/10.1109/ITW44776.2019.8989283","url":null,"abstract":"The two-sender unicast index coding problem consists of two senders collectively having all the demanded messages of a set of receivers, where each receiver demands a unique message. The senders avail the knowledge of the side-information present at all the receivers to reduce the total number of broadcast transmissions. This problem is relevant in many practical communication problems like multi-source satellite communication, multi-user coded cooperative data exchange, and other related problems. In this paper, the two-sender unicast index coding problem is analyzed using three independent single-sender subproblems. Optimal broadcast rate (total number of transmitted bits per message bit as the message length tends to infinity) for all the unsolved instances of a special class of the two-sender unicast index coding problem is provided in terms of those of the three associated subproblems. The optimal broadcast rate established in this work serves as a lower bound for the optimal broadcast rate of any general associated two-sender unicast index coding problem. An achievable broadcast rate (total number of transmitted bits per message bit) with finite length messages for any finite length, is given for a subclass of the two-sender unicast index coding problem by providing a code-construction. This serves as a tighter upper bound when compared to the prior state of art.","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114726513","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":"ITW 2019 Program","authors":"","doi":"10.1109/itw44776.2019.8989312","DOIUrl":"https://doi.org/10.1109/itw44776.2019.8989312","url":null,"abstract":"","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125522877","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":"Design of Guruswami-Sudan List Decoding for Elliptic Codes","authors":"Yunqi Wan, Li Chen, Fangguo Zhang","doi":"10.1109/ITW44776.2019.8989286","DOIUrl":"https://doi.org/10.1109/ITW44776.2019.8989286","url":null,"abstract":"Advancing from Reed-Solomon (RS) codes, the length of algebraic-geometric (AG) codes can exceed the size of finite field, resulting in a greater error-correction capability. However, this is realized with a genus penalty. Usually, they are not maximum distance separable (MDS) codes. One-point elliptic codes are either MDS or almost MDS, yielding a good tradeoff between codeword length and distance property. This paper proposes the Guruswami-Sudan (GS) list decoding algorithm for elliptic codes. To define the interpolated polynomial $Q(x, y, z)$, an explicit construction for the zero basis of each affine point is introduced. Given an interpolation multiplicity m, the error-correction capability $tau_{m}$ and the maximum decoding output cardinality lm of the GS algorithm are characterized. An efficient interpolation algorithm is further presented for elliptic codes. Performance of elliptic codes is shown for the first time, demonstrating their advantage over RS codes.","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129679652","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":"Error Exponents of Typical Random Codes of Source-Channel Coding","authors":"Ran Averbuch, N. Merhav","doi":"10.1109/ITW44776.2019.8989340","DOIUrl":"https://doi.org/10.1109/ITW44776.2019.8989340","url":null,"abstract":"The error exponent of the typical random code (TRC) in a communication scenario of source-channel coding with side information at the decoder is the main objective of this work. We derive a lower bound, which is at least as large as the random binning-coding exponent due to Merhav (2016), and we show numerically that it may be strictly larger. We deduce the exponents of the TRCs in two special cases: Slepian-Wolf (SW) source coding and joint source-channel coding. Each of these models is further studied in order to provide deeper intuition concerning the behavior of the typical random code. We also propose an alternative expression for the error exponent of typical random binning in SW model, which is given by an optimization over four parameters only, instead of a computationally heavy optimization over probability distributions.","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126185047","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":"ITW 2019 Technical Program Committee","authors":"","doi":"10.1109/itw44776.2019.8989207","DOIUrl":"https://doi.org/10.1109/itw44776.2019.8989207","url":null,"abstract":"","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131422147","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":"Intrinsic Randomness Problem with Respect to a Subclass of f-divergence","authors":"R. Nomura","doi":"10.1109/itw44776.2019.8989245","DOIUrl":"https://doi.org/10.1109/itw44776.2019.8989245","url":null,"abstract":"This paper deals with the intrinsic randomness (IR) problem, which is one of typical random number generation problems. In the literature, the optimum achievable rates in the IR problem with respect to the variational distance as well as the Kullback-Leibler (KL) divergence have already been analyzed. On the other hand, in this study we consider the IR problem with respect to a subclass of f-divergences. The f-divergence is a general non-negative measure between two probabilistic distributions and includes several important measures such as the total variational distance, the $chi^{2}-$divergence, the KL divergence, and so on. Hence, it is meaningful to consider the IR problem with respect to the f-divergence. In this paper, we assume some conditions on the f-divergence for simplifying the analysis. That is, we focus on a subclass of f-divergences. In this problem setting, we first derive the general formula of the optimum achievable rate. Next, we show that it is easy to derive the optimum achievable rate with respect to the variational distance, the KL divergence, and the Hellinger distance from our general formula.","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114757612","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":"Non-Colluding Attacks Identification in Distributed Computing","authors":"Arnav Solanki, Martina Cardone, S. Mohajer","doi":"10.1109/ITW44776.2019.8989337","DOIUrl":"https://doi.org/10.1109/ITW44776.2019.8989337","url":null,"abstract":"This paper studies a distributed computing setting in which the computing task consists of multiplying a matrix by a vector. A number of worker machines are attacked, i.e., the result of their computation is maliciously perturbed by some adversaries. In particular, the focus is on the case where these adversaries are non-colluding and non-communicating and hence they cannot jointly perturb the results of all the attacked worker machines. First, a condition that ensures that the result of the computing task can be successfully recovered with high probability is derived as a function of the setting parameters. Then, a probabilistic mechanism inspired by group testing is proposed to identify the set of the attacked worker machines, and the corresponding probability of error is derived.","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133136847","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":"Dynamics of Damped Approximate Message Passing Algorithms","authors":"Kazushi Mimura, J. Takeuchi","doi":"10.1109/ITW44776.2019.8989237","DOIUrl":"https://doi.org/10.1109/ITW44776.2019.8989237","url":null,"abstract":"For linear system models, the approximate massage passing (AMP) is one of the effective iterative sparse recovery algorithms. However, depending on a measurement matrix ensemble, AMP may face convergence issues. Some algorithms are proposed so far to avoid the convergence issues, e.g., the orthogonal AMP (OAMP) and the mean removal. One of the simplest ways to avoid the convergence issues is to introduce a damping effect into AMP. In this paper, we derive a simple recursive equations that characterizes the damped OAMP, which is an OAMP in which the damping effect is introduced, and show that the result can be applied to the damped version of the original AMP.","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134118472","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":"The Metagenomic Binning Problem: Clustering Markov Sequences","authors":"Grant Greenberg, Ilan Shomorony","doi":"10.1109/ITW44776.2019.8988939","DOIUrl":"https://doi.org/10.1109/ITW44776.2019.8988939","url":null,"abstract":"The goal of metagenomics is to study the composition of microbial communities, typically using high-throughput shotgun sequencing. In the metagenomic binning problem, we observe random substrings (called contigs) from a mixture of genomes and want to cluster them according to their genome of origin. Based on the empirical observation that genomes of different bacterial species can be distinguished based on their tetranucleotide frequencies, we model this task as the problem of clustering N sequences generated by M distinct Markov processes, where $Mll N$. Utilizing the large-deviation principle for Markov processes, we establish the information-theoretic limit for perfect binning. Specifically, we show that the length of the contigs must scale with the inverse of the Chernoff Information between the two most similar species. Our result also implies that contigs should be binned using the conditional relative entropy as a measure of distance, as opposed to the Euclidean distance often used in practice.","PeriodicalId":214379,"journal":{"name":"2019 IEEE Information Theory Workshop (ITW)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128234640","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}